Weibull distribution in reliability data analysis in nuclear power plant

International Nuclear Information System (INIS)

Ma Yingfei; Zhang Zhijian; Zhang Min; Zheng Gangyang

2015-01-01

Reliability is an important issue affecting each stage of the life cycle ranging from birth to death of a product or a system. The reliability engineering includes the equipment failure data processing, quantitative assessment of system reliability and maintenance, etc. Reliability data refers to the variety of data that describe the reliability of system or component during its operation. These data may be in the form of numbers, graphics, symbols, texts and curves. Quantitative reliability assessment is the task of the reliability data analysis. It provides the information related to preventing, detect, and correct the defects of the reliability design. Reliability data analysis under proceed with the various stages of product life cycle and reliability activities. Reliability data of Systems Structures and Components (SSCs) in Nuclear Power Plants is the key factor of probabilistic safety assessment (PSA); reliability centered maintenance and life cycle management. The Weibull distribution is widely used in reliability engineering, failure analysis, industrial engineering to represent manufacturing and delivery times. It is commonly used to model time to fail, time to repair and material strength. In this paper, an improved Weibull distribution is introduced to analyze the reliability data of the SSCs in Nuclear Power Plants. An example is given in the paper to present the result of the new method. The Weibull distribution of mechanical equipment for reliability data fitting ability is very strong in nuclear power plant. It's a widely used mathematical model for reliability analysis. The current commonly used methods are two-parameter and three-parameter Weibull distribution. Through comparison and analysis, the three-parameter Weibull distribution fits the data better. It can reflect the reliability characteristics of the equipment and it is more realistic to the actual situation. (author)

Statistical Analysis Of Failure Strength Of Material Using Weibull Distribution

International Nuclear Information System (INIS)

Entin Hartini; Mike Susmikanti; Antonius Sitompul

2008-01-01

In evaluation of ceramic and glass materials strength a statistical approach is necessary Strength of ceramic and glass depend on its measure and size distribution of flaws in these material. The distribution of strength for ductile material is narrow and close to a Gaussian distribution while strength of brittle materials as ceramic and glass following Weibull distribution. The Weibull distribution is an indicator of the failure of material strength resulting from a distribution of flaw size. In this paper, cumulative probability of material strength to failure probability, cumulative probability of failure versus fracture stress and cumulative probability of reliability of material were calculated. Statistical criteria calculation supporting strength analysis of Silicon Nitride material were done utilizing MATLAB. (author)

(AJST) MULTIPLE DEFECT DISTRIBUTIONS ON WEIBULL ...

African Journals Online (AJOL)

such as ceramics, which cannot correctly be statistically described by single Weibull distribution models. (Equations (1) and (2)) [6]. .... bottom filling through a filter at an initial runner velocity of less than 0.5 ms−1 beyond the filter, producing turbulence free conditions. The as-cast test bars were subjected to identical T6 heat.

Probabilistic analysis of glass elements with three-parameter Weibull distribution

International Nuclear Information System (INIS)

Ramos, A.; Muniz-Calvente, M.; Fernandez, P.; Fernandez Cantel, A.; Lamela, M. J.

2015-01-01

Glass and ceramics present a brittle behaviour so a large scatter in the test results is obtained. This dispersion is mainly due to the inevitable presence of micro-cracks on its surface, edge defects or internal defects, which must be taken into account using an appropriate failure criteria non-deterministic but probabilistic. Among the existing probability distributions, the two or three parameter Weibull distribution is generally used in adjusting material resistance results, although the method of use thereof is not always correct. Firstly, in this work, the results of a large experimental programme using annealed glass specimens of different dimensions based on four-point bending and coaxial double ring tests was performed. Then, the finite element models made for each type of test, the adjustment of the parameters of the three-parameter Weibull distribution function (cdf) (λ: location, β: shape, d: scale) for a certain failure criterion and the calculation of the effective areas from the cumulative distribution function are presented. Summarizing, this work aims to generalize the use of the three-parameter Weibull function in structural glass elements with stress distributions not analytically described, allowing to apply the probabilistic model proposed in general loading distributions. (Author)

Bayesian estimation of Weibull distribution parameters

International Nuclear Information System (INIS)

Bacha, M.; Celeux, G.; Idee, E.; Lannoy, A.; Vasseur, D.

1994-11-01

In this paper, we expose SEM (Stochastic Expectation Maximization) and WLB-SIR (Weighted Likelihood Bootstrap - Sampling Importance Re-sampling) methods which are used to estimate Weibull distribution parameters when data are very censored. The second method is based on Bayesian inference and allow to take into account available prior informations on parameters. An application of this method, with real data provided by nuclear power plants operation feedback analysis has been realized. (authors). 8 refs., 2 figs., 2 tabs

Probabilistic analysis of glass elements with three-parameter Weibull distribution; Analisis probabilistico de elementos de vidrio recocido mediante una distribucion triparametrica Weibull

Energy Technology Data Exchange (ETDEWEB)

Ramos, A.; Muniz-Calvente, M.; Fernandez, P.; Fernandez Cantel, A.; Lamela, M. J.

2015-10-01

Glass and ceramics present a brittle behaviour so a large scatter in the test results is obtained. This dispersion is mainly due to the inevitable presence of micro-cracks on its surface, edge defects or internal defects, which must be taken into account using an appropriate failure criteria non-deterministic but probabilistic. Among the existing probability distributions, the two or three parameter Weibull distribution is generally used in adjusting material resistance results, although the method of use thereof is not always correct. Firstly, in this work, the results of a large experimental programme using annealed glass specimens of different dimensions based on four-point bending and coaxial double ring tests was performed. Then, the finite element models made for each type of test, the adjustment of the parameters of the three-parameter Weibull distribution function (cdf) (λ: location, β: shape, d: scale) for a certain failure criterion and the calculation of the effective areas from the cumulative distribution function are presented. Summarizing, this work aims to generalize the use of the three-parameter Weibull function in structural glass elements with stress distributions not analytically described, allowing to apply the probabilistic model proposed in general loading distributions. (Author)

Using Weibull Distribution Analysis to Evaluate ALARA Performance

International Nuclear Information System (INIS)

Frome, E.L.; Watkins, J.P.; Hagemeyer, D.A.

2009-01-01

As Low as Reasonably Achievable (ALARA) is the underlying principle for protecting nuclear workers from potential health outcomes related to occupational radiation exposure. Radiation protection performance is currently evaluated by measures such as collective dose and average measurable dose, which do not indicate ALARA performance. The purpose of this work is to show how statistical modeling of individual doses using the Weibull distribution can provide objective supplemental performance indicators for comparing ALARA implementation among sites and for insights into ALARA practices within a site. Maximum likelihood methods were employed to estimate the Weibull shape and scale parameters used for performance indicators. The shape parameter reflects the effectiveness of maximizing the number of workers receiving lower doses and is represented as the slope of the fitted line on a Weibull probability plot. Additional performance indicators derived from the model parameters include the 99th percentile and the exceedance fraction. When grouping sites by collective total effective dose equivalent (TEDE) and ranking by 99th percentile with confidence intervals, differences in performance among sites can be readily identified. Applying this methodology will enable more efficient and complete evaluation of the effectiveness of ALARA implementation.

Reliability Implications in Wood Systems of a Bivariate Gaussian-Weibull Distribution and the Associated Univariate Pseudo-truncated Weibull

Science.gov (United States)

Steve P. Verrill; James W. Evans; David E. Kretschmann; Cherilyn A. Hatfield

2014-01-01

Two important wood properties are the modulus of elasticity (MOE) and the modulus of rupture (MOR). In the past, the statistical distribution of the MOE has often been modeled as Gaussian, and that of the MOR as lognormal or as a two- or three-parameter Weibull distribution. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior...

Calculation of life distributions, in particular Weibull distributions, from operational observations

International Nuclear Information System (INIS)

Rauhut, J.

1982-01-01

Established methods are presented by which life distributions of machine elements can be determined on the basis of laboratory experiments and operational observations. Practical observations are given special attention as the results estimated on the basis of conventional have not been accurate enough. As an introduction, the stochastic life concept, the general method of determining life distributions, various sampling methods, and the Weibull distribution are explained. Further, possible life testing schedules and maximum-likelihood estimates are discussed for the complete sample case and for censered sampling without replacement in laboratory experiments. Finally, censered sampling with replacement in laboratory experiments is discussed; it is shown how suitable parameter estimates can be obtained for given life distributions by means of the maximum-likelihood method. (orig./RW) [de

Anomalous diffusion and q-Weibull velocity distributions in epithelial cell migration.

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Tatiane Souza Vilela Podestá

Full Text Available In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, the control of cell motion is a major demand in the creation of artificial tissues and organs. Here, cell migration assays on plastic 2D surfaces involving normal (MDCK and tumoral (B16F10 epithelial cell lines were performed varying the initial density of plated cells. Through time-lapse microscopy quantities such as speed distributions, velocity autocorrelations and spatial correlations, as well as the scaling of mean-squared displacements were determined. We find that these cells exhibit anomalous diffusion with q-Weibull speed distributions that evolves non-monotonically to a Maxwellian distribution as the initial density of plated cells increases. Although short-ranged spatial velocity correlations mark the formation of small cell clusters, the emergence of collective motion was not observed. Finally, simulational results from a correlated random walk and the Vicsek model of collective dynamics evidence that fluctuations in cell velocity orientations are sufficient to produce q-Weibull speed distributions seen in our migration assays.

Inference on the reliability of Weibull distribution with multiply Type-I censored data

International Nuclear Information System (INIS)

Jia, Xiang; Wang, Dong; Jiang, Ping; Guo, Bo

2016-01-01

In this paper, we focus on the reliability of Weibull distribution under multiply Type-I censoring, which is a general form of Type-I censoring. In multiply Type-I censoring in this study, all units in the life testing experiment are terminated at different times. Reliability estimation with the maximum likelihood estimate of Weibull parameters is conducted. With the delta method and Fisher information, we propose a confidence interval for reliability and compare it with the bias-corrected and accelerated bootstrap confidence interval. Furthermore, a scenario involving a few expert judgments of reliability is considered. A method is developed to generate extended estimations of reliability according to the original judgments and transform them to estimations of Weibull parameters. With Bayes theory and the Monte Carlo Markov Chain method, a posterior sample is obtained to compute the Bayes estimate and credible interval for reliability. Monte Carlo simulation demonstrates that the proposed confidence interval outperforms the bootstrap one. The Bayes estimate and credible interval for reliability are both satisfactory. Finally, a real example is analyzed to illustrate the application of the proposed methods. - Highlights: • We focus on reliability of Weibull distribution under multiply Type-I censoring. • The proposed confidence interval for the reliability is superior after comparison. • The Bayes estimates with a few expert judgements on reliability are satisfactory. • We specify the cases where the MLEs do not exist and present methods to remedy it. • The distribution of estimate of reliability should be used for accurate estimate.

On changing points of mean residual life and failure rate function for some generalized Weibull distributions

International Nuclear Information System (INIS)

Xie, M.; Goh, T.N.; Tang, Y.

2004-01-01

The failure rate function and mean residual life function are two important characteristics in reliability analysis. Although many papers have studied distributions with bathtub-shaped failure rate and their properties, few have focused on the underlying associations between the mean residual life and failure rate function of these distributions, especially with respect to their changing points. It is known that the change point for mean residual life can be much earlier than that of failure rate function. In fact, the failure rate function should be flat for a long period of time for a distribution to be useful in practice. When the difference between the change points is large, the flat portion tends to be longer. This paper investigates the change points and focuses on the difference of the changing points. The exponentiated Weibull, a modified Weibull, and an extended Weibull distribution, all with bathtub-shaped failure rate function will be used. Some other issues related to the flatness of the bathtub curve are discussed

Statistics for Ratios of Rayleigh, Rician, Nakagami-m, and Weibull Distributed Random Variables

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Dragana Č. Pavlović

2013-01-01

Full Text Available The distributions of ratios of random variables are of interest in many areas of the sciences. In this brief paper, we present the joint probability density function (PDF and PDF of maximum of ratios μ1=R1/r1 and μ2=R2/r2 for the cases where R1, R2, r1, and r2 are Rayleigh, Rician, Nakagami-m, and Weibull distributed random variables. Random variables R1 and R2, as well as random variables r1 and r2, are correlated. Ascertaining on the suitability of the Weibull distribution to describe fading in both indoor and outdoor environments, special attention is dedicated to the case of Weibull random variables. For this case, analytical expressions for the joint PDF, PDF of maximum, PDF of minimum, and product moments of arbitrary number of ratios μi=Ri/ri, i=1,…,L are obtained. Random variables in numerator, Ri, as well as random variables in denominator, ri, are exponentially correlated. To the best of the authors' knowledge, analytical expressions for the PDF of minimum and product moments of {μi}i=1L are novel in the open technical literature. The proposed mathematical analysis is complemented by various numerical results. An application of presented theoretical results is illustrated with respect to performance assessment of wireless systems.

The Transmuted Geometric-Weibull distribution: Properties, Characterizations and Regression Models

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Zohdy M Nofal

2017-06-01

Full Text Available We propose a new lifetime model called the transmuted geometric-Weibull distribution. Some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is discussed to estimate the model parameters by means of Monte Carlo simulation study. A new location-scale regression model is introduced based on the proposed distribution. The new distribution is applied to two real data sets to illustrate its flexibility. Empirical results indicate that proposed distribution can be alternative model to other lifetime models available in the literature for modeling real data in many areas.

Analysis of wind speed distributions: Wind distribution function derived from minimum cross entropy principles as better alternative to Weibull function

International Nuclear Information System (INIS)

Kantar, Yeliz Mert; Usta, Ilhan

2008-01-01

In this study, the minimum cross entropy (MinxEnt) principle is applied for the first time to the wind energy field. This principle allows the inclusion of previous information of a wind speed distribution and covers the maximum entropy (MaxEnt) principle, which is also discussed by Li and Li and Ramirez as special cases in their wind power study. The MinxEnt probability density function (pdf) derived from the MinxEnt principle are used to determine the diurnal, monthly, seasonal and annual wind speed distributions. A comparison between MinxEnt pdfs defined on the basis of the MinxEnt principle and the Weibull pdf on wind speed data, which are taken from different sources and measured in various regions, is conducted. The wind power densities of the considered regions obtained from Weibull and MinxEnt pdfs are also compared. The results indicate that the pdfs derived from the MinxEnt principle fit better to a variety of measured wind speed data than the conventionally applied empirical Weibull pdf. Therefore, it is shown that the MinxEnt principle can be used as an alternative method to estimate both wind distribution and wind power accurately

A robust approach based on Weibull distribution for clustering gene expression data

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Gong Binsheng

2011-05-01

Full Text Available Abstract Background Clustering is a widely used technique for analysis of gene expression data. Most clustering methods group genes based on the distances, while few methods group genes according to the similarities of the distributions of the gene expression levels. Furthermore, as the biological annotation resources accumulated, an increasing number of genes have been annotated into functional categories. As a result, evaluating the performance of clustering methods in terms of the functional consistency of the resulting clusters is of great interest. Results In this paper, we proposed the WDCM (Weibull Distribution-based Clustering Method, a robust approach for clustering gene expression data, in which the gene expressions of individual genes are considered as the random variables following unique Weibull distributions. Our WDCM is based on the concept that the genes with similar expression profiles have similar distribution parameters, and thus the genes are clustered via the Weibull distribution parameters. We used the WDCM to cluster three cancer gene expression data sets from the lung cancer, B-cell follicular lymphoma and bladder carcinoma and obtained well-clustered results. We compared the performance of WDCM with k-means and Self Organizing Map (SOM using functional annotation information given by the Gene Ontology (GO. The results showed that the functional annotation ratios of WDCM are higher than those of the other methods. We also utilized the external measure Adjusted Rand Index to validate the performance of the WDCM. The comparative results demonstrate that the WDCM provides the better clustering performance compared to k-means and SOM algorithms. The merit of the proposed WDCM is that it can be applied to cluster incomplete gene expression data without imputing the missing values. Moreover, the robustness of WDCM is also evaluated on the incomplete data sets. Conclusions The results demonstrate that our WDCM produces clusters

Weibull Distribution for Estimating the Parameters and Application of Hilbert Transform in case of a Low Wind Speed at Kolaghat

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P Bhattacharya

2016-09-01

Full Text Available The wind resource varies with of the day and the season of the year and even some extent from year to year. Wind energy has inherent variances and hence it has been expressed by distribution functions. In this paper, we present some methods for estimating Weibull parameters in case of a low wind speed characterization, namely, shape parameter (k, scale parameter (c and characterize the discrete wind data sample by the discrete Hilbert transform. We know that the Weibull distribution is an important distribution especially for reliability and maintainability analysis. The suitable values for both shape parameter and scale parameters of Weibull distribution are important for selecting locations of installing wind turbine generators. The scale parameter of Weibull distribution also important to determine whether a wind farm is good or not. Thereafter the use of discrete Hilbert transform (DHT for wind speed characterization provides a new era of using DHT besides its application in digital signal processing. Basically in this paper, discrete Hilbert transform has been applied to characterize the wind sample data measured on College of Engineering and Management, Kolaghat, East Midnapore, India in January 2011.

Statistical analysis of wind speed using two-parameter Weibull distribution in Alaçatı region

International Nuclear Information System (INIS)

Ozay, Can; Celiktas, Melih Soner

2016-01-01

Highlights: • Wind speed & direction data from September 2008 to March 2014 has been analyzed. • Mean wind speed for the whole data set has been found to be 8.11 m/s. • Highest wind speed is observed in July with a monthly mean value of 9.10 m/s. • Wind speed with the most energy has been calculated as 12.77 m/s. • Observed data has been fit to a Weibull distribution and k &c parameters have been calculated as 2.05 and 9.16. - Abstract: Weibull Statistical Distribution is a common method for analyzing wind speed measurements and determining wind energy potential. Weibull probability density function can be used to forecast wind speed, wind density and wind energy potential. In this study a two-parameter Weibull statistical distribution is used to analyze the wind characteristics of Alaçatı region, located in Çeşme, İzmir. The data used in the density function are acquired from a wind measurement station in Alaçatı. Measurements were gathered on three different heights respectively 70, 50 and 30 m between 10 min intervals for five and half years. As a result of this study; wind speed frequency distribution, wind direction trends, mean wind speed, and the shape and the scale (k&c) Weibull parameters have been calculated for the region. Mean wind speed for the entirety of the data set is found to be 8.11 m/s. k&c parameters are found as 2.05 and 9.16 in relative order. Wind direction analysis along with a wind rose graph for the region is also provided with the study. Analysis suggests that higher wind speeds which range from 6–12 m/s are prevalent between the sectors 340–360°. Lower wind speeds, from 3 to 6 m/s occur between sectors 10–29°. Results of this study contribute to the general knowledge about the regions wind energy potential and can be used as a source for investors and academics.

A spatial scan statistic for survival data based on Weibull distribution.

Science.gov (United States)

Bhatt, Vijaya; Tiwari, Neeraj

2014-05-20

The spatial scan statistic has been developed as a geographical cluster detection analysis tool for different types of data sets such as Bernoulli, Poisson, ordinal, normal and exponential. We propose a scan statistic for survival data based on Weibull distribution. It may also be used for other survival distributions, such as exponential, gamma, and log normal. The proposed method is applied on the survival data of tuberculosis patients for the years 2004-2005 in Nainital district of Uttarakhand, India. Simulation studies reveal that the proposed method performs well for different survival distribution functions. Copyright © 2013 John Wiley & Sons, Ltd.

A flexible Weibull extension

International Nuclear Information System (INIS)

Bebbington, Mark; Lai, C.-D.; Zitikis, Ricardas

2007-01-01

We propose a new two-parameter ageing distribution which is a generalization of the Weibull and study its properties. It has a simple failure rate (hazard rate) function. With appropriate choice of parameter values, it is able to model various ageing classes of life distributions including IFR, IFRA and modified bathtub (MBT). The ranges of the two parameters are clearly demarcated to separate these classes. It thus provides an alternative to many existing life distributions. Details of parameter estimation are provided through a Weibull-type probability plot and maximum likelihood. We also derive explicit formulas for the turning points of the failure rate function in terms of its parameters. This, combined with the parameter estimation procedures, will allow empirical estimation of the turning points for real data sets, which provides useful information for reliability policies

A log-Weibull spatial scan statistic for time to event data.

Science.gov (United States)

Usman, Iram; Rosychuk, Rhonda J

2018-06-13

Spatial scan statistics have been used for the identification of geographic clusters of elevated numbers of cases of a condition such as disease outbreaks. These statistics accompanied by the appropriate distribution can also identify geographic areas with either longer or shorter time to events. Other authors have proposed the spatial scan statistics based on the exponential and Weibull distributions. We propose the log-Weibull as an alternative distribution for the spatial scan statistic for time to events data and compare and contrast the log-Weibull and Weibull distributions through simulation studies. The effect of type I differential censoring and power have been investigated through simulated data. Methods are also illustrated on time to specialist visit data for discharged patients presenting to emergency departments for atrial fibrillation and flutter in Alberta during 2010-2011. We found northern regions of Alberta had longer times to specialist visit than other areas. We proposed the spatial scan statistic for the log-Weibull distribution as a new approach for detecting spatial clusters for time to event data. The simulation studies suggest that the test performs well for log-Weibull data.

arXiv Describing dynamical fluctuations and genuine correlations by Weibull regularity

CERN Document Server

Nayak, Ranjit K.; Sarkisyan-Grinbaum, Edward K.; Tasevsky, Marek

The Weibull parametrization of the multiplicity distribution is used to describe the multidimensional local fluctuations and genuine multiparticle correlations measured by OPAL in the large statistics $e^{+}e^{-} \\to Z^{0} \\to hadrons$ sample. The data are found to be well reproduced by the Weibull model up to higher orders. The Weibull predictions are compared to the predictions by the two other models, namely by the negative binomial and modified negative binomial distributions which mostly failed to fit the data. The Weibull regularity, which is found to reproduce the multiplicity distributions along with the genuine correlations, looks to be the optimal model to describe the multiparticle production process.

An EOQ Model with Two-Parameter Weibull Distribution Deterioration and Price-Dependent Demand

Science.gov (United States)

Mukhopadhyay, Sushanta; Mukherjee, R. N.; Chaudhuri, K. S.

2005-01-01

An inventory replenishment policy is developed for a deteriorating item and price-dependent demand. The rate of deterioration is taken to be time-proportional and the time to deterioration is assumed to follow a two-parameter Weibull distribution. A power law form of the price dependence of demand is considered. The model is solved analytically…

On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

International Nuclear Information System (INIS)

Xu, Meng; Droguett, Enrique López; Lins, Isis Didier; Chagas Moura, Márcio das

2017-01-01

The q-Weibull model is based on the Tsallis non-extensive entropy and is able to model various behaviors of the hazard rate function, including bathtub curves, by using a single set of parameters. Despite its flexibility, the q-Weibull has not been widely used in reliability applications partly because of the complicated parameters estimation. In this work, the parameters of the q-Weibull are estimated by the maximum likelihood (ML) method. Due to the intricate system of nonlinear equations, derivative-based optimization methods may fail to converge. Thus, the heuristic optimization method of artificial bee colony (ABC) is used instead. To deal with the slow convergence of ABC, it is proposed an adaptive hybrid ABC (AHABC) algorithm that dynamically combines Nelder-Mead simplex search method with ABC for the ML estimation of the q-Weibull parameters. Interval estimates for the q-Weibull parameters, including confidence intervals based on the ML asymptotic theory and on bootstrap methods, are also developed. The AHABC is validated via numerical experiments involving the q-Weibull ML for reliability applications and results show that it produces faster and more accurate convergence when compared to ABC and similar approaches. The estimation procedure is applied to real reliability failure data characterized by a bathtub-shaped hazard rate. - Highlights: • Development of an Adaptive Hybrid ABC (AHABC) algorithm for q-Weibull distribution. • AHABC combines local Nelder-Mead simplex method with ABC to enhance local search. • AHABC efficiently finds the optimal solution for the q-Weibull ML problem. • AHABC outperforms ABC and self-adaptive hybrid ABC in accuracy and convergence speed. • Useful model for reliability data with non-monotonic hazard rate.

Comparing performances of clements, box-cox, Johnson methods with weibull distributions for assessing process capability

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Ozlem Senvar

2016-08-01

Full Text Available Purpose: This study examines Clements’ Approach (CA, Box-Cox transformation (BCT, and Johnson transformation (JT methods for process capability assessments through Weibull-distributed data with different parameters to figure out the effects of the tail behaviours on process capability and compares their estimation performances in terms of accuracy and precision. Design/methodology/approach: Usage of process performance index (PPI Ppu is handled for process capability analysis (PCA because the comparison issues are performed through generating Weibull data without subgroups. Box plots, descriptive statistics, the root-mean-square deviation (RMSD, which is used as a measure of error, and a radar chart are utilized all together for evaluating the performances of the methods. In addition, the bias of the estimated values is important as the efficiency measured by the mean square error. In this regard, Relative Bias (RB and the Relative Root Mean Square Error (RRMSE are also considered. Findings: The results reveal that the performance of a method is dependent on its capability to fit the tail behavior of the Weibull distribution and on targeted values of the PPIs. It is observed that the effect of tail behavior is more significant when the process is more capable. Research limitations/implications: Some other methods such as Weighted Variance method, which also give good results, were also conducted. However, we later realized that it would be confusing in terms of comparison issues between the methods for consistent interpretations. Practical implications: Weibull distribution covers a wide class of non-normal processes due to its capability to yield a variety of distinct curves based on its parameters. Weibull distributions are known to have significantly different tail behaviors, which greatly affects the process capability. In quality and reliability applications, they are widely used for the analyses of failure data in order to understand how

Improvement for Amelioration Inventory Model with Weibull Distribution

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Han-Wen Tuan

2017-01-01

Full Text Available Most inventory models dealt with deteriorated items. On the contrary, just a few papers considered inventory systems under amelioration environment. We study an amelioration inventory model with Weibull distribution. However, there are some questionable results in the amelioration paper. We will first point out those questionable results in the previous paper that did not derive the optimal solution and then provide some improvements. We will provide a rigorous analytical work for different cases dependent on the size of the shape parameter. We present a detailed numerical example for different ranges of the sharp parameter to illustrate that our solution method attains the optimal solution. We developed a new amelioration model and then provided a detailed analyzed procedure to find the optimal solution. Our findings will help researchers develop their new inventory models.

A Study on The Mixture of Exponentiated-Weibull Distribution

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Adel Tawfik Elshahat

2016-12-01

Full Text Available Mixtures of measures or distributions occur frequently in the theory and applications of probability and statistics. In the simplest case it may, for example, be reasonable to assume that one is dealing with the mixture in given proportions of a finite number of normal populations with different means or variances. The mixture parameter may also be denumerable infinite, as in the theory of sums of a random number of random variables, or continuous, as in the compound Poisson distribution. The use of finite mixture distributions, to control for unobserved heterogeneity, has become increasingly popular among those estimating dynamic discrete choice models. One of the barriers to using mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive reparability of the log likelihood function. In this thesis, the maximum likelihood estimators have been obtained for the parameters of the mixture of exponentiated Weibull distribution when sample is available from censoring scheme. The maximum likelihood estimators of the parameters and the asymptotic variance covariance matrix have been also obtained. A numerical illustration for these new results is given.

Influence of the Determination Methods of K and C Parameters on the Ability of Weibull Distribution to Suitably Estimate Wind Potential and Electric Energy

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Ruben M. Mouangue

2014-05-01

Full Text Available The modeling of the wind speed distribution is of great importance for the assessment of wind energy potential and the performance of wind energy conversion system. In this paper, the choice of two determination methods of Weibull parameters shows theirs influences on the Weibull distribution performances. Because of important calm winds on the site of Ngaoundere airport, we characterize the wind potential using the approach of Weibull distribution with parameters which are determined by the modified maximum likelihood method. This approach is compared to the Weibull distribution with parameters which are determined by the maximum likelihood method and the hybrid distribution which is recommended for wind potential assessment of sites having nonzero probability of calm. Using data provided by the ASECNA Weather Service (Agency for the Safety of Air Navigation in Africa and Madagascar, we evaluate the goodness of fit of the various fitted distributions to the wind speed data using the Q – Q plots, the Pearson’s coefficient of correlation, the mean wind speed, the mean square error, the energy density and its relative error. It appears from the results that the accuracy of the Weibull distribution with parameters which are determined by the modified maximum likelihood method is higher than others. Then, this approach is used to estimate the monthly and annual energy productions of the site of the Ngaoundere airport. The most energy contribution is made in March with 255.7 MWh. It also appears from the results that a wind turbine generator installed on this particular site could not work for at least a half of the time because of higher frequency of calm. For this kind of sites, the modified maximum likelihood method proposed by Seguro and Lambert in 2000 is one of the best methods which can be used to determinate the Weibull parameters.

Weibull statistic analysis of bending strength in the cemented carbide coatings

International Nuclear Information System (INIS)

Yi Yong; Shen Baoluo; Qiu Shaoyu; Li Cong

2003-01-01

The theoretical basis using Weibull statistics to analyze the strength of coating has been established that the Weibull distribution will be the asymptotic distribution of strength for coating as the volume of coating increase, provided that the local strength of coating is statistic independent, and has been confirmed in the following test for the bending strength of two cemented carbide coatings. The result shows that Weibull statistics can be well used to analyze the strength of two coatings. (authors)

Comparing performances of clements, box-cox, Johnson methods with weibull distributions for assessing process capability

Energy Technology Data Exchange (ETDEWEB)

Senvar, O.; Sennaroglu, B.

2016-07-01

This study examines Clements’ Approach (CA), Box-Cox transformation (BCT), and Johnson transformation (JT) methods for process capability assessments through Weibull-distributed data with different parameters to figure out the effects of the tail behaviours on process capability and compares their estimation performances in terms of accuracy and precision. Design/methodology/approach: Usage of process performance index (PPI) Ppu is handled for process capability analysis (PCA) because the comparison issues are performed through generating Weibull data without subgroups. Box plots, descriptive statistics, the root-mean-square deviation (RMSD), which is used as a measure of error, and a radar chart are utilized all together for evaluating the performances of the methods. In addition, the bias of the estimated values is important as the efficiency measured by the mean square error. In this regard, Relative Bias (RB) and the Relative Root Mean Square Error (RRMSE) are also considered. Findings: The results reveal that the performance of a method is dependent on its capability to fit the tail behavior of the Weibull distribution and on targeted values of the PPIs. It is observed that the effect of tail behavior is more significant when the process is more capable. Research limitations/implications: Some other methods such as Weighted Variance method, which also give good results, were also conducted. However, we later realized that it would be confusing in terms of comparison issues between the methods for consistent interpretations... (Author)

Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study

International Nuclear Information System (INIS)

Musleh, Rola M.; Helu, Amal

2014-01-01

In this article we consider statistical inferences about the unknown parameters of the Inverse Weibull distribution based on progressively type-II censoring using classical and Bayesian procedures. For classical procedures we propose using the maximum likelihood; the least squares methods and the approximate maximum likelihood estimators. The Bayes estimators are obtained based on both the symmetric and asymmetric (Linex, General Entropy and Precautionary) loss functions. There are no explicit forms for the Bayes estimators, therefore, we propose Lindley's approximation method to compute the Bayes estimators. A comparison between these estimators is provided by using extensive simulation and three criteria, namely, Bias, mean squared error and Pitman nearness (PN) probability. It is concluded that the approximate Bayes estimators outperform the classical estimators most of the time. Real life data example is provided to illustrate our proposed estimators. - Highlights: • We consider progressively type-II censored data from the Inverse Weibull distribution (IW). • We derive MLEs, approximate MLEs, LS and Bayes estimate methods of scale and shape parameters of the IW. • Bayes estimator of shape parameter cannot be expressed in closed forms. • We suggest using Lindley's approximation. • We conclude that the Bayes estimates outperform the classical methods

Evaluating failure rate of fault-tolerant multistage interconnection networks using Weibull life distribution

International Nuclear Information System (INIS)

Bistouni, Fathollah; Jahanshahi, Mohsen

2015-01-01

Fault-tolerant multistage interconnection networks (MINs) play a vital role in the performance of multiprocessor systems where reliability evaluation becomes one of the main concerns in analyzing these networks properly. In many cases, the primary objective in system reliability analysis is to compute a failure distribution of the entire system according to that of its components. However, since the problem is known to be NP-hard, in none of the previous efforts, the precise evaluation of the system failure rate has been performed. Therefore, our goal is to investigate this parameter for different fault-tolerant MINs using Weibull life distribution that is one of the most commonly used distributions in reliability. In this paper, four important groups of fault-tolerant MINs will be examined to find the best fault-tolerance techniques in terms of failure rate; (1) Extra-stage MINs, (2) Parallel MINs, (3) Rearrangeable non-blocking MINs, and (4) Replicated MINs. This paper comprehensively analyzes all perspectives of the reliability (terminal, broadcast, and network reliability). Moreover, in this study, all reliability equations are calculated for different network sizes. - Highlights: • The failure rate of different MINs is analyzed by using Weibull life distribution. • This article tries to find the best fault-tolerance technique in the field of MINs. • Complex series-parallel RBDs are used to determine the reliability of the MINs. • All aspects of the reliability (i.e. terminal, broadcast, and network) are analyzed. • All reliability equations will be calculated for different size N×N.

Weibull and lognormal Taguchi analysis using multiple linear regression

International Nuclear Information System (INIS)

Piña-Monarrez, Manuel R.; Ortiz-Yañez, Jesús F.

2015-01-01

The paper provides to reliability practitioners with a method (1) to estimate the robust Weibull family when the Taguchi method (TM) is applied, (2) to estimate the normal operational Weibull family in an accelerated life testing (ALT) analysis to give confidence to the extrapolation and (3) to perform the ANOVA analysis to both the robust and the normal operational Weibull family. On the other hand, because the Weibull distribution neither has the normal additive property nor has a direct relationship with the normal parameters (µ, σ), in this paper, the issues of estimating a Weibull family by using a design of experiment (DOE) are first addressed by using an L_9 (3"4) orthogonal array (OA) in both the TM and in the Weibull proportional hazard model approach (WPHM). Then, by using the Weibull/Gumbel and the lognormal/normal relationships and multiple linear regression, the direct relationships between the Weibull and the lifetime parameters are derived and used to formulate the proposed method. Moreover, since the derived direct relationships always hold, the method is generalized to the lognormal and ALT analysis. Finally, the method’s efficiency is shown through its application to the used OA and to a set of ALT data. - Highlights: • It gives the statistical relations and steps to use the Taguchi Method (TM) to analyze Weibull data. • It gives the steps to determine the unknown Weibull family to both the robust TM setting and the normal ALT level. • It gives a method to determine the expected lifetimes and to perform its ANOVA analysis in TM and ALT analysis. • It gives a method to give confidence to the extrapolation in an ALT analysis by using the Weibull family of the normal level.

Weibull Model Allowing Nearly Instantaneous Failures

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C. D. Lai

2007-01-01

expressed as a mixture of the uniform distribution and the Weibull distribution. Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained. Some selected plots of these functions are also presented. An R script was written to fit the model parameters. An application of the modified model is illustrated.

Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys' Prior Information with Three Loss Functions

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Chris Bambey Guure

2012-01-01

Full Text Available The Weibull distribution has been observed as one of the most useful distribution, for modelling and analysing lifetime data in engineering, biology, and others. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameters estimation which is in contention with other estimation methods. In this paper, we examine the performance of maximum likelihood estimator and Bayesian estimator using extension of Jeffreys prior information with three loss functions, namely, the linear exponential loss, general entropy loss, and the square error loss function for estimating the two-parameter Weibull failure time distribution. These methods are compared using mean square error through simulation study with varying sample sizes. The results show that Bayesian estimator using extension of Jeffreys' prior under linear exponential loss function in most cases gives the smallest mean square error and absolute bias for both the scale parameter α and the shape parameter β for the given values of extension of Jeffreys' prior.

Bayesian Estimation of the Scale Parameter of Inverse Weibull Distribution under the Asymmetric Loss Functions

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Farhad Yahgmaei

2013-01-01

Full Text Available This paper proposes different methods of estimating the scale parameter in the inverse Weibull distribution (IWD. Specifically, the maximum likelihood estimator of the scale parameter in IWD is introduced. We then derived the Bayes estimators for the scale parameter in IWD by considering quasi, gamma, and uniform priors distributions under the square error, entropy, and precautionary loss functions. Finally, the different proposed estimators have been compared by the extensive simulation studies in corresponding the mean square errors and the evolution of risk functions.

Comparing Johnson’s SBB, Weibull and Logit-Logistic bivariate distributions for modeling tree diameters and heights using copulas

Energy Technology Data Exchange (ETDEWEB)

Cardil Forradellas, A.; Molina Terrén, D.M.; Oliveres, J.; Castellnou, M.

2016-07-01

Aim of study: In this study we compare the accuracy of three bivariate distributions: Johnson’s SBB, Weibull-2P and LL-2P functions for characterizing the joint distribution of tree diameters and heights. Area of study: North-West of Spain. Material and methods: Diameter and height measurements of 128 plots of pure and even-aged Tasmanian blue gum (Eucalyptus globulus Labill.) stands located in the North-west of Spain were considered in the present study. The SBB bivariate distribution was obtained from SB marginal distributions using a Normal Copula based on a four-parameter logistic transformation. The Plackett Copula was used to obtain the bivariate models from the Weibull and Logit-logistic univariate marginal distributions. The negative logarithm of the maximum likelihood function was used to compare the results and the Wilcoxon signed-rank test was used to compare the related samples of these logarithms calculated for each sample plot and each distribution. Main results: The best results were obtained by using the Plackett copula and the best marginal distribution was the Logit-logistic. Research highlights: The copulas used in this study have shown a good performance for modeling the joint distribution of tree diameters and heights. They could be easily extended for modelling multivariate distributions involving other tree variables, such as tree volume or biomass. (Author)

Statistical analysis of the Vickers micro hardness of precipitates in a Cu-10% wt. Ni-3% wt. Al alloy using the Weibull distribution function

International Nuclear Information System (INIS)

Diaz, Gerardo; Donoso, Eduardo; Varschavsky, Ari

2004-01-01

A statistical analysis was carried out of the distribution of Vickers micro hardness values of nickel and aluminum atom precipitates from a solid solution of Cu-Ni-Al. Non isothermal calorimetric curves confirmed the formation of two types of precipitates: Ni Al from 45 K to 600 K, and Ni 3 Al from 650 K to 800 K. The micro hardness measurements were done at room temperature in the previously quenched material and submitted to isothermal and iso chronic annealing treatments. A lower dispersion in the distribution of the Vickers micro hardness values in the Ni Al precipitate for the entire formation temperature was determined with a lesser average micro hardness than the Ni 3 Al precipitate. The Weibull modules were estimated from the respective Weibull diagrams. The lesser dispersion was proven by the elevated values of the Wobble modules. The maximum average micro hardness attained by the Ni Al phase was 148, with a Weibull module of 26 and an annealing temperature of 553 K maintained for 40 minutes. The Ni 3 Al reached a maximum average micro hardness of 248 with a Weibull module of 10 and a annealing temperature of 793 K during 40 minutes (CW)

Statistical distribution of the estimator of Weibull modulus

OpenAIRE

Barbero, Enrique; Fernández-Sáez, José; Navarro Ugena, Carlos

2001-01-01

3 pages, 3 figures. The Weibull statistic has been widely used to study the inherent scatter existing in the strength properties of many advanced materials, as well as in the fracture toughness of steels in the ductile-brittle transition region. The authors are indebted to the Fundación Ramón Areces (Área de Materiales, IX Concurso Nacional) for its financial support of this research. Publicado

Prediction of Strength for Inhomogeneous : Defective Glass Elements Based on the Sequential Partitioning of the Data and Weibull Statistical Distribution

NARCIS (Netherlands)

Shabetia, Alexander; Rodichev, Yurii; Veer, F.A.; Soroka, Elena; Louter, Christian; Bos, Freek; Belis, Jan; Veer, Fred; Nijsse, Rob

An analytical approach based on the on the sequential partitioning of the data and Weibull Statistical Distribution for inhomogeneous - defective materials is proposed. It allows assessing the guaranteed strength of glass structures for the low probability of fracture with a higher degree of

Redundancy allocation problem of a system with increasing failure rates of components based on Weibull distribution: A simulation-based optimization approach

International Nuclear Information System (INIS)

Guilani, Pedram Pourkarim; Azimi, Parham; Niaki, S.T.A.; Niaki, Seyed Armin Akhavan

2016-01-01

The redundancy allocation problem (RAP) is a useful method to enhance system reliability. In most works involving RAP, failure rates of the system components are assumed to follow either exponential or k-Erlang distributions. In real world problems however, many systems have components with increasing failure rates. This indicates that as time passes by, the failure rates of the system components increase in comparison to their initial failure rates. In this paper, the redundancy allocation problem of a series–parallel system with components having an increasing failure rate based on Weibull distribution is investigated. An optimization method via simulation is proposed for modeling and a genetic algorithm is developed to solve the problem. - Highlights: • The redundancy allocation problem of a series–parallel system is aimed. • Components possess an increasing failure rate based on Weibull distribution. • An optimization method via simulation is proposed for modeling. • A genetic algorithm is developed to solve the problem.

Generalized renewal process for repairable systems based on finite Weibull mixture

International Nuclear Information System (INIS)

Veber, B.; Nagode, M.; Fajdiga, M.

2008-01-01

Repairable systems can be brought to one of possible states following a repair. These states are: 'as good as new', 'as bad as old' and 'better than old but worse than new'. The probabilistic models traditionally used to estimate the expected number of failures account for the first two states, but they do not properly apply to the last one, which is more realistic in practice. In this paper, a probabilistic model that is applicable to all of the three after-repair states, called generalized renewal process (GRP), is applied. Simplistically, GRP addresses the repair assumption by introducing the concept of virtual age into the stochastic point processes to enable them to represent the full spectrum of repair assumptions. The shape of measured or design life distributions of systems can vary considerably, and therefore frequently cannot be approximated by simple distribution functions. The scope of the paper is to prove that a finite Weibull mixture, with positive component weights only, can be used as underlying distribution of the time to first failure (TTFF) of the GRP model, on condition that the unknown parameters can be estimated. To support the main idea, three examples are presented. In order to estimate the unknown parameters of the GRP model with m-fold Weibull mixture, the EM algorithm is applied. The GRP model with m mixture components distributions is compared to the standard GRP model based on two-parameter Weibull distribution by calculating the expected number of failures. It can be concluded that the suggested GRP model with Weibull mixture with an arbitrary but finite number of components is suitable for predicting failures based on the past performance of the system

Parameter Estimations and Optimal Design of Simple Step-Stress Model for Gamma Dual Weibull Distribution

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Hamdy Mohamed Salem

2018-03-01

Full Text Available This paper considers life-testing experiments and how it is effected by stress factors: namely temperature, electricity loads, cycling rate and pressure. A major type of accelerated life tests is a step-stress model that allows the experimenter to increase stress levels more than normal use during the experiment to see the failure items. The test items are assumed to follow Gamma Dual Weibull distribution. Different methods for estimating the parameters are discussed. These include Maximum Likelihood Estimations and Confidence Interval Estimations which is based on asymptotic normality generate narrow intervals to the unknown distribution parameters with high probability. MathCAD (2001 program is used to illustrate the optimal time procedure through numerical examples.

Bayesian Approach for Constant-Stress Accelerated Life Testing for Kumaraswamy Weibull Distribution with Censoring

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Abeer Abd-Alla EL-Helbawy

2016-09-01

Full Text Available The accelerated life tests provide quick information on the life time distributions by testing materials or products at higher than basic conditional levels of stress such as pressure, high temperature, vibration, voltage or load to induce failures. In this paper, the acceleration model assumed is log linear model. Constant stress tests are discussed based on Type I and Type II censoring. The Kumaraswmay Weibull distribution is used. The estimators of the parameters, reliability, hazard rate functions and p-th percentile at normal condition, low stress, and high stress are obtained. In addition, credible intervals for parameters of the models are constructed. Optimum test plan are designed. Some numerical studies are used to solve the complicated integrals such as Laplace and Markov Chain Monte Carlo methods.

Bayesian Approach for Constant-Stress Accelerated Life Testing for Kumaraswamy Weibull Distribution with Censoring

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Abeer Abd-Alla EL-Helbawy

2016-12-01

Full Text Available The accelerated life tests provide quick information on the life time distributions by testing materials or products at higher than basic conditional levels of stress such as pressure, high temperature, vibration, voltage or load to induce failures. In this paper, the acceleration model assumed is log linear model. Constant stress tests are discussed based on Type I and Type II censoring. The Kumaraswmay Weibull distribution is used. The estimators of the parameters, reliability, hazard rate functions and p-th percentile at normal condition, low stress, and high stress are obtained. In addition, credible intervals for parameters of the models are constructed. Optimum test plan are designed. Some numerical studies are used to solve the complicated integrals such as Laplace and Markov Chain Monte Carlo methods.

MEP family of wind speed distribution function and comparison with the empirical Weibull distribution. Paper no. IGEC-1-156

International Nuclear Information System (INIS)

Li, M.; Li, X.

2005-01-01

The probabilistic distribution of wind speed is one of the important wind characteristics for the assessment of wind energy potential and for the performance of wind energy conversion systems, as well as for the structural and environmental design and analysis. In this study, an exponential family of distribution functions has been developed for the description of the probabilistic distribution of wind speed, and comparison with the wind speed data taken from different sources and measured at different geographical locations in the world has been made. This family of distributions is developed by introducing a pre-exponential term to the theoretical distribution derived from the Maximum Entropy Principle (MEP). The statistical analysis parameter based on the wind power density is used as the suitability judgement for the distribution functions. It is shown that the MEP-type distributions not only agree better with a variety of the measured wind speed data than the conventionally used empirical Weibull distribution, but also can represent the wind power density much more accurately. Therefore, the MEP-type distributions are more suitable for the assessment of the wind energy potential and the performance of wind energy conversion systems. (author)

Determining the theoretical reliability function of thermal power system using simple and complex Weibull distribution

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Kalaba Dragan V.

2014-01-01

Full Text Available The main subject of this paper is the representation of the probabilistic technique for thermal power system reliability assessment. Exploitation research of the reliability of the fossil fuel power plant system has defined the function, or the probabilistic law, according to which the random variable behaves (occurrence of complete unplanned standstill. Based on these data, and by applying the reliability theory to this particular system, using simple and complex Weibull distribution, a hypothesis has been confirmed that the distribution of the observed random variable fully describes the behaviour of such a system in terms of reliability. Establishing a comprehensive insight in the field of probabilistic power system reliability assessment technique could serve as an input for further research and development in the area of power system planning and operation.

Failure-censored accelerated life test sampling plans for Weibull distribution under expected test time constraint

International Nuclear Information System (INIS)

Bai, D.S.; Chun, Y.R.; Kim, J.G.

1995-01-01

This paper considers the design of life-test sampling plans based on failure-censored accelerated life tests. The lifetime distribution of products is assumed to be Weibull with a scale parameter that is a log linear function of a (possibly transformed) stress. Two levels of stress higher than the use condition stress, high and low, are used. Sampling plans with equal expected test times at high and low test stresses which satisfy the producer's and consumer's risk requirements and minimize the asymptotic variance of the test statistic used to decide lot acceptability are obtained. The properties of the proposed life-test sampling plans are investigated

Weibull-Based Design Methodology for Rotating Structures in Aircraft Engines

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Erwin V. Zaretsky

2003-01-01

Full Text Available The NASA Energy-Efficient Engine (E3-Engine is used as the basis of a Weibull-based life and reliability analysis. Each component's life, and thus the engine's life, is defined by high-cycle fatigue or low-cycle fatigue. Knowing the cumulative life distribution of each of the components making up the engine as represented by a Weibull slope is a prerequisite to predicting the life and reliability of the entire engine. As the engine's Weibull slope increases, the predicted life decreases. The predicted engine lives L5 (95% probability of survival of approximately 17,000 and 32,000 hr do correlate with current engine-maintenance practices without and with refurbishment, respectively. The individual high-pressure turbine (HPT blade lives necessary to obtain a blade system life L0.1 (99.9% probability of survival of 9000 hr for Weibull slopes of 3, 6, and 9 are 47,391; 20,652; and 15,658 hr, respectively. For a design life of the HPT disks having probable points of failure equal to or greater than 36,000 hr at a probability of survival of 99.9%, the predicted disk system life L0.1 can vary from 9408 to 24,911 hr.

Weibull statistical analysis of Krouse type bending fatigue of nuclear materials

Energy Technology Data Exchange (ETDEWEB)

Haidyrah, Ahmed S., E-mail: ashdz2@mst.edu [Nuclear Engineering, Missouri University of Science & Technology, 301 W. 14th, Rolla, MO 65409 (United States); Nuclear Science Research Institute, King Abdulaziz City for Science and Technology (KACST), P.O. Box 6086, Riyadh 11442 (Saudi Arabia); Newkirk, Joseph W. [Materials Science & Engineering, Missouri University of Science & Technology, 1440 N. Bishop Ave, Rolla, MO 65409 (United States); Castaño, Carlos H. [Nuclear Engineering, Missouri University of Science & Technology, 301 W. 14th, Rolla, MO 65409 (United States)

2016-03-15

A bending fatigue mini-specimen (Krouse-type) was used to study the fatigue properties of nuclear materials. The objective of this paper is to study fatigue for Grade 91 ferritic-martensitic steel using a mini-specimen (Krouse-type) suitable for reactor irradiation studies. These mini-specimens are similar in design (but smaller) to those described in the ASTM B593 standard. The mini specimen was machined by waterjet and tested as-received. The bending fatigue machine was modified to test the mini-specimen with a specially designed adapter. The cycle bending fatigue behavior of Grade 91 was studied under constant deflection. The S–N curve was created and mean fatigue life was analyzed using mean fatigue life. In this study, the Weibull function was predicted probably for high stress to low stress at 563, 310 and 265 MPa. The commercial software Minitab 17 was used to calculate the distribution of fatigue life under different stress levels. We have used 2 and 3- parameters Weibull analysis to introduce the probability of failure. The plots indicated that the 3- parameter Weibull distribution fits the data well.

Weibull statistical analysis of Krouse type bending fatigue of nuclear materials

International Nuclear Information System (INIS)

Haidyrah, Ahmed S.; Newkirk, Joseph W.; Castaño, Carlos H.

2016-01-01

A bending fatigue mini-specimen (Krouse-type) was used to study the fatigue properties of nuclear materials. The objective of this paper is to study fatigue for Grade 91 ferritic-martensitic steel using a mini-specimen (Krouse-type) suitable for reactor irradiation studies. These mini-specimens are similar in design (but smaller) to those described in the ASTM B593 standard. The mini specimen was machined by waterjet and tested as-received. The bending fatigue machine was modified to test the mini-specimen with a specially designed adapter. The cycle bending fatigue behavior of Grade 91 was studied under constant deflection. The S–N curve was created and mean fatigue life was analyzed using mean fatigue life. In this study, the Weibull function was predicted probably for high stress to low stress at 563, 310 and 265 MPa. The commercial software Minitab 17 was used to calculate the distribution of fatigue life under different stress levels. We have used 2 and 3- parameters Weibull analysis to introduce the probability of failure. The plots indicated that the 3- parameter Weibull distribution fits the data well.

SEMI-COMPETING RISKS ON A TRIVARIATE WEIBULL SURVIVAL MODEL

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Jenq-Daw Lee

2008-07-01

Full Text Available A setting of a trivairate survival function using semi-competing risks concept is proposed, in which a terminal event can only occur after other events. The Stanford Heart Transplant data is reanalyzed using a trivariate Weibull distribution model with the proposed survival function.

Characterization of the wind behavior in Botucatu-SP region (Brazil) by Weibull distributing; Caracterizacao do comportamento eolico da regiao de Botucatu-SP atraves da distribuicao de Weibull

Energy Technology Data Exchange (ETDEWEB)

Gabriel Filho, Luis Roberto Almeida [Universidade Estadual Paulista (CE/UNESP), Tupa, SP (Brazil). Coordenacao de Estagio; Cremasco, Camila Pires [Faculdade de Tecnologia de Presidente Prudente, SP (Brazil); Seraphim, Odivaldo Jose [Universidade Estadual Paulista (FCA/UNESP), Botucatu, SP (Brazil). Fac. de Ciencias Agronomicas; Cagnon, Jose Angelo [Universidade Estadual Paulista (FEB/UNESP), Bauru, SP (Brazil). Faculdade de Engenharia

2008-07-01

The wind behavior of a region can be described by frequency distribution that provide information and characteristics needed for a possible deployment of wind energy harvesting in the region. These characteristics, such as the annual average speed, the variance and shunting line standard of the registered speeds and the density of aeolian power average hourly, can be gotten by the frequency of occurrence of determined speed, that in turn must be studied through analytical expressions. The more adjusted analytical function for aeolian distributions is the function of density of Weibull, that can be determined by numerical methods and linear regressions. Once you have determined this function, all wind characteristics mentioned above may be determined accurately. The objective of this work is to characterize the aeolian behavior in the region of Botucatu-SP and to determine the energy potential for implementation of aeolian turbines. For the development of the present research, was used an Monitorial Young Wind anemometer of Campbell company installed a 10 meters of height. The experiment was developed in the Nucleus of Alternative Energies and Renewed - NEAR of the Laboratory of Agricultural Energize of the Department of Agricultural Engineering of the UNESP, Agronomy Sciences Faculty, Lageado Experimental Farm, located in the city of Botucatu - SP. The geographic localization is defined by the coordinates 22 deg 51' South latitude (S) and 48 deg 26' Longitude West (W) and average altitude of 786 meters above sea level. The analysis was carried through using registers of speed of the wind during the period of September of 2004 the September of 2005. After determined the distribution of frequencies of the hourly average speed of the wind, it was determined function of associated Weibull, thus making possible the determination of the annual average speed of the wind (2,77 m/s), of the shunting line standard of the registered speeds (0,55 m/s), of the

A study of two estimation approaches for parameters of Weibull distribution based on WPP

International Nuclear Information System (INIS)

Zhang, L.F.; Xie, M.; Tang, L.C.

2007-01-01

Least-squares estimation (LSE) based on Weibull probability plot (WPP) is the most basic method for estimating the Weibull parameters. The common procedure of this method is using the least-squares regression of Y on X, i.e. minimizing the sum of squares of the vertical residuals, to fit a straight line to the data points on WPP and then calculate the LS estimators. This method is known to be biased. In the existing literature the least-squares regression of X on Y, i.e. minimizing the sum of squares of the horizontal residuals, has been used by the Weibull researchers. This motivated us to carry out this comparison between the estimators of the two LS regression methods using intensive Monte Carlo simulations. Both complete and censored data are examined. Surprisingly, the result shows that LS Y on X performs better for small, complete samples, while the LS X on Y performs better in other cases in view of bias of the estimators. The two methods are also compared in terms of other model statistics. In general, when the shape parameter is less than one, LS Y on X provides a better model; otherwise, LS X on Y tends to be better

A drawback and an improvement of the classical Weibull probability plot

International Nuclear Information System (INIS)

Jiang, R.

2014-01-01

The classical Weibull Probability Paper (WPP) plot has been widely used to identify a model for fitting a given dataset. It is based on a match between the WPP plots of the model and data in shape. This paper carries out an analysis for the Weibull transformations that create the WPP plot and shows that the shape of the WPP plot of the data randomly generated from a distribution model can be significantly different from the shape of the WPP plot of the model due to the high non-linearity of the Weibull transformations. As such, choosing model based on the shape of the WPP plot of data can be unreliable. A cdf-based weighted least squares method is proposed to improve the parameter estimation accuracy; and an improved WPP plot is suggested to avoid the drawback of the classical WPP plot. The appropriateness and usefulness of the proposed estimation method and probability plot are illustrated by simulation and real-world examples

Optimal pricing and lot-sizing decisions under Weibull distribution deterioration and trade credit policy

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Manna S.K.

2008-01-01

Full Text Available In this paper, we consider the problem of simultaneous determination of retail price and lot-size (RPLS under the assumption that the supplier offers a fixed credit period to the retailer. It is assumed that the item in stock deteriorates over time at a rate that follows a two-parameter Weibull distribution and that the price-dependent demand is represented by a constant-price-elasticity function of retail price. The RPLS decision model is developed and solved analytically. Results are illustrated with the help of a base example. Computational results show that the supplier earns more profits when the credit period is greater than the replenishment cycle length. Sensitivity analysis of the solution to changes in the value of input parameters of the base example is also discussed.

An Approach to Determine the Weibull Parameters and Wind Power Analysis of Saint Martin’s Island, Bangladesh

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Islam Khandaker Dahirul

2016-01-01

Full Text Available This paper explores wind speed distribution using Weibull probability distribution and Rayleigh distribution methods that are proven to provide accurate and efficient estimation of energy output in terms of wind energy conversion systems. Two parameters of Weibull (shape and scale parameters k and c respectively and scale parameter of Rayleigh distribution have been determined based on hourly time-series wind speed data recorded from October 2014 to October 2015 at Saint Martin’s island, Bangladesh. This research has been carried out to examine three numerical methods namely Graphical Method (GM, Empirical Method (EM, Energy Pattern Factor method (EPF to estimate Weibull parameters. Also, Rayleigh distribution method has been analyzed throughout the study. The results in the research revealed that the Graphical method followed by Empirical method and Energy Pattern Factor method were the most accurate and efficient way for determining the value of k and c to approximate wind speed distribution in terms of estimating power error. Rayleigh distribution gives the most power error in the research. Potential for wind energy development in Saint Martin’s island, Bangladesh as found from the data analysis has been explained in this paper.

The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data

International Nuclear Information System (INIS)

Bebbington, Mark; Lai, Chin-Diew; Wellington, Morgan; Zitikis, Ričardas

2012-01-01

Although failure data are usually treated as being continuous, they may have been collected in a discrete manner, or in fact be discrete in nature. Reliability models with bathtub-shaped hazard rate are fundamental to the concepts of burn-in and maintenance, but how well do they incorporate discrete data? We explore discrete versions of the additive Weibull distribution, which has the twin virtues of mathematical tractability and the ability to produce bathtub-shaped hazard rate functions. We derive conditions on the parameters for the hazard rate function to be increasing, decreasing, or bathtub shaped. While discrete versions may have the same shaped hazard rate for the same parameter values, we find that when fitted to data the fitted hazard rate shapes can vary between versions. Our results are illustrated using several real-life data sets, and the implications of using continuous models for discrete data discussed.

Statistical Diagnosis of the Best Weibull Methods for Wind Power Assessment for Agricultural Applications

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Abul Kalam Azad

2014-05-01

Full Text Available The best Weibull distribution methods for the assessment of wind energy potential at different altitudes in desired locations are statistically diagnosed in this study. Seven different methods, namely graphical method (GM, method of moments (MOM, standard deviation method (STDM, maximum likelihood method (MLM, power density method (PDM, modified maximum likelihood method (MMLM and equivalent energy method (EEM were used to estimate the Weibull parameters and six statistical tools, namely relative percentage of error, root mean square error (RMSE, mean percentage of error, mean absolute percentage of error, chi-square error and analysis of variance were used to precisely rank the methods. The statistical fittings of the measured and calculated wind speed data are assessed for justifying the performance of the methods. The capacity factor and total energy generated by a small model wind turbine is calculated by numerical integration using Trapezoidal sums and Simpson’s rules. The results show that MOM and MLM are the most efficient methods for determining the value of k and c to fit Weibull distribution curves.

A Monte Carlo study of Weibull reliability analysis for space shuttle main engine components

Science.gov (United States)

Abernethy, K.

1986-01-01

The incorporation of a number of additional capabilities into an existing Weibull analysis computer program and the results of Monte Carlo computer simulation study to evaluate the usefulness of the Weibull methods using samples with a very small number of failures and extensive censoring are discussed. Since the censoring mechanism inherent in the Space Shuttle Main Engine (SSME) data is hard to analyze, it was decided to use a random censoring model, generating censoring times from a uniform probability distribution. Some of the statistical techniques and computer programs that are used in the SSME Weibull analysis are described. The methods documented in were supplemented by adding computer calculations of approximate (using iteractive methods) confidence intervals for several parameters of interest. These calculations are based on a likelihood ratio statistic which is asymptotically a chisquared statistic with one degree of freedom. The assumptions built into the computer simulations are described. The simulation program and the techniques used in it are described there also. Simulation results are tabulated for various combinations of Weibull shape parameters and the numbers of failures in the samples.

On Weibull's Spectrum of Nonrelativistic Energetic Particles at IP Shocks: Observations and Theoretical Interpretation

Energy Technology Data Exchange (ETDEWEB)

Pallocchia, G.; Laurenza, M.; Consolini, G. [INAF—Istituto di Astrofisica e Planetologia Spaziali, Via Fosso del Cavaliere 100, I-00133 Roma (Italy)

2017-03-10

Some interplanetary shocks are associated with short-term and sharp particle flux enhancements near the shock front. Such intensity enhancements, known as shock-spike events (SSEs), represent a class of relatively energetic phenomena as they may extend to energies of some tens of MeV or even beyond. Here we present an SSE case study in order to shed light on the nature of the particle acceleration involved in this kind of event. Our observations refer to an SSE registered on 2011 October 3 at 22:23 UT, by STEREO B instrumentation when, at a heliocentric distance of 1.08 au, the spacecraft was swept by a perpendicular shock moving away from the Sun. The main finding from the data analysis is that a Weibull distribution represents a good fitting function to the measured particle spectrum over the energy range from 0.1 to 30 MeV. To interpret such an observational result, we provide a theoretical derivation of the Weibull spectrum in the framework of the acceleration by “killed” stochastic processes exhibiting power-law growth in time of the velocity expectation, such as the classical Fermi process. We find an overall coherence between the experimental values of the Weibull spectrum parameters and their physical meaning within the above scenario. Hence, our approach based on the Weibull distribution proves to be useful for understanding SSEs. With regard to the present event, we also provide an alternative explanation of the Weibull spectrum in terms of shock-surfing acceleration.

pT spectra in pp and AA collisions at RHIC and LHC energies using the Tsallis-Weibull approach

Science.gov (United States)

Dash, Sadhana; Mahapatra, D. P.

2018-04-01

The Tsallis q -statistics have been incorporated in the Weibull model of particle production, in the form of q-Weibull distribution, to describe the transverse momentum (pT) distribution of charged hadrons at mid-rapidity, measured at RHIC and LHC energies. The q-Weibull distribution is found to describe the observed pT distributions over all ranges of measured pT. Below 2.2 GeV/c, while going from peripheral to central collisions, the parameter q is found to decrease systematically towards unity, indicating an evolution from a non-equilibrated system in peripheral collisions, towards a more thermalized system in central collisions. However, the trend is reversed in the all inclusive pT regime. This can be attributed to an increase in relative contribution of hard pQCD processes in central collisions. The λ-parameter is found to be associated with the mean pT or the collective expansion velocity of the produced hadrons, which shows an expected increase with centrality of collisions. The k parameter is observed to increase with the onset of hard QCD scatterings, initial fluctuations, and other processes leading to non-equilibrium conditions.

A comparison of Weibull and βIc analyses of transition range data

International Nuclear Information System (INIS)

McCabe, D.E.

1991-01-01

Specimen size effects on K Jc data scatter in the transition range of fracture toughness have been explained by external (weakest link) statistics. In this investigation, compact specimens of A 533 grade B steel were tested in sizes ranging from 1/2TC(T) to 4TC(T) with sufficient replication to obtain good three-parameter Weibull characterization of data distributions. The optimum fitting parameters for an assumed Weibull slope of 4 were calculated. External statistics analysis was applied to the 1/2TC(T) data to predict median K Jc values for 1TC(T), 2TC(T), and 4TC(T) specimens. The distributions from experimentally developed 1TC(T), 2TC(T), and 4TC(T) data tended to confirm the predictions. However, the extremal prediction model does not work well at lower-shelf toughness. At -150 degree C the extremal model predicts a specimen size effect where in reality there is no size effect

Weibull modeling of particle cracking in metal matrix composites

International Nuclear Information System (INIS)

Lewis, C.A.; Withers, P.J.

1995-01-01

An investigation into the occurrence of reinforcement cracking within a particulate ZrO 2 /2618 Al alloy metal matrix composite under tensile plastic straining has been carried out, special attention being paid to the dependence of fracture on particle size and shape. The probability of particle cracking has been modeled using a Weibull approach, giving good agreement with the experimental data. Values for the Weibull modulus and the stress required to crack the particles were found to be within the range expected for the cracking of ceramic particles. Additional information regarding the fracture behavior of the particles was provided by in-situ neutron diffraction monitoring of the internal strains, measurement of the variation in the composite Young's modulus with straining and by direct observation of the cracked particles. The values of the particle stress required for the initiation of particle cracking deduced from these supplementary experiments were found to be in good agreement with each other and with the results from the Weibull analysis. Further, it is shown that while both the current experiments, as well as the previous work of others, can be well described by the Weibull approach, the exact values of the Weibull parameters do deduced are very sensitive to the approximations and the assumptions made in constructing the model

Assessing different parameters estimation methods of Weibull distribution to compute wind power density

International Nuclear Information System (INIS)

Mohammadi, Kasra; Alavi, Omid; Mostafaeipour, Ali; Goudarzi, Navid; Jalilvand, Mahdi

2016-01-01

Highlights: • Effectiveness of six numerical methods is evaluated to determine wind power density. • More appropriate method for computing the daily wind power density is estimated. • Four windy stations located in the south part of Alberta, Canada namely is investigated. • The more appropriate parameters estimation method was not identical among all examined stations. - Abstract: In this study, the effectiveness of six numerical methods is evaluated to determine the shape (k) and scale (c) parameters of Weibull distribution function for the purpose of calculating the wind power density. The selected methods are graphical method (GP), empirical method of Justus (EMJ), empirical method of Lysen (EML), energy pattern factor method (EPF), maximum likelihood method (ML) and modified maximum likelihood method (MML). The purpose of this study is to identify the more appropriate method for computing the wind power density in four stations distributed in Alberta province of Canada namely Edmonton City Center Awos, Grande Prairie A, Lethbridge A and Waterton Park Gate. To provide a complete analysis, the evaluations are performed on both daily and monthly scales. The results indicate that the precision of computed wind power density values change when different parameters estimation methods are used to determine the k and c parameters. Four methods of EMJ, EML, EPF and ML present very favorable efficiency while the GP method shows weak ability for all stations. However, it is found that the more effective method is not similar among stations owing to the difference in the wind characteristics.

Dependence of Weibull distribution parameters on the CNR threshold i wind lidar data

DEFF Research Database (Denmark)

Gryning, Sven-Erik; Batchvarova, Ekaterina; Floors, Rogier Ralph

2015-01-01

in the boundary layer. Observations from tall towers in combination with observations from a lidar of wind speed up to 600 m are used to study the long-term variability of the wind profile over sub-urban, rural, coastal and marine areas. The variability is expressed in terms of the shape parameter in the Weibull...... over land, both terms are about equally important in the coastal area where the height of the reversal height is low and in the marine conditions, the second term dominates....

Power Loss Analysis for Wind Power Grid Integration Based on Weibull Distribution

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Ahmed Al Ameri

2017-04-01

Full Text Available The growth of electrical demand increases the need of renewable energy sources, such as wind energy, to meet that need. Electrical power losses are an important factor when wind farm location and size are selected. The capitalized cost of constant power losses during the life of a wind farm will continue to high levels. During the operation period, a method to determine if the losses meet the requirements of the design is significantly needed. This article presents a Simulink simulation of wind farm integration into the grid; the aim is to achieve a better understanding of wind variation impact on grid losses. The real power losses are set as a function of the annual variation, considering a Weibull distribution. An analytical method has been used to select the size and placement of a wind farm, taking into account active power loss reduction. It proposes a fast linear model estimation to find the optimal capacity of a wind farm based on DC power flow and graph theory. The results show that the analytical approach is capable of predicting the optimal size and location of wind turbines. Furthermore, it revealed that the annual variation of wind speed could have a strong effect on real power loss calculations. In addition to helping to improve utility efficiency, the proposed method can develop specific designs to speeding up integration of wind farms into grids.

PERFORMANCE ANALYSIS OF METHODS FOR ESTIMATING WEIBULL PARAMETERS FOR WIND SPEED DISTRIBUTION IN THE DISTRICT OF MAROUA

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D. Kidmo Kaoga

2015-07-01

Full Text Available In this study, five numerical Weibull distribution methods, namely, the maximum likelihood method, the modified maximum likelihood method (MLM, the energy pattern factor method (EPF, the graphical method (GM, and the empirical method (EM were explored using hourly synoptic data collected from 1985 to 2013 in the district of Maroua in Cameroon. The performance analysis revealed that the MLM was the most accurate model followed by the EPF and the GM. Furthermore, the comparison between the wind speed standard deviation predicted by the proposed models and the measured data showed that the MLM has a smaller relative error of -3.33% on average compared to -11.67% on average for the EPF and -8.86% on average for the GM. As a result, the MLM was precisely recommended to estimate the scale and shape parameters for an accurate and efficient wind energy potential evaluation.

PERFORMANCE ANALYSIS OF METHODS FOR ESTIMATING WEIBULL PARAMETERS FOR WIND SPEED DISTRIBUTION IN THE DISTRICT OF MAROUA

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D. Kidmo Kaoga

2014-12-01

Full Text Available In this study, five numerical Weibull distribution methods, namely, the maximum likelihood method, the modified maximum likelihood method (MLM, the energy pattern factor method (EPF, the graphical method (GM, and the empirical method (EM were explored using hourly synoptic data collected from 1985 to 2013 in the district of Maroua in Cameroon. The performance analysis revealed that the MLM was the most accurate model followed by the EPF and the GM. Furthermore, the comparison between the wind speed standard deviation predicted by the proposed models and the measured data showed that the MLM has a smaller relative error of -3.33% on average compared to -11.67% on average for the EPF and -8.86% on average for the GM. As a result, the MLM was precisely recommended to estimate the scale and shape parameters for an accurate and efficient wind energy potential evaluation.

Estimation for a Weibull accelerated life testing model

International Nuclear Information System (INIS)

Glaser, R.E.

1984-01-01

It is sometimes reasonable to assume that the lifetime distribution of an item belongs to a certain parametric family, and that actual parameter values depend upon the testing environment of the item. In the two-parameter Weibull family setting, suppose both the shape and scale parameters are expressible as functions of the testing environment. For various models of functional dependency on environment, maximum likelihood methods are used to estimate characteristics of interest at specified environmental levels. The methodology presented handles exact, censored, and grouped data. A detailed accelerated life testing analysis of stress-rupture data for Kevlar/epoxy composites is given. 10 references, 1 figure, 2 tables

Kinetic Analysis of Isothermal Decomposition Process of Sodium Bicarbonate Using the Weibull Probability Function—Estimation of Density Distribution Functions of the Apparent Activation Energies

Science.gov (United States)

Janković, Bojan

2009-10-01

The decomposition process of sodium bicarbonate (NaHCO3) has been studied by thermogravimetry in isothermal conditions at four different operating temperatures (380 K, 400 K, 420 K, and 440 K). It was found that the experimental integral and differential conversion curves at the different operating temperatures can be successfully described by the isothermal Weibull distribution function with a unique value of the shape parameter ( β = 1.07). It was also established that the Weibull distribution parameters ( β and η) show independent behavior on the operating temperature. Using the integral and differential (Friedman) isoconversional methods, in the conversion (α) range of 0.20 ≤ α ≤ 0.80, the apparent activation energy ( E a ) value was approximately constant ( E a, int = 95.2 kJmol-1 and E a, diff = 96.6 kJmol-1, respectively). The values of E a calculated by both isoconversional methods are in good agreement with the value of E a evaluated from the Arrhenius equation (94.3 kJmol-1), which was expressed through the scale distribution parameter ( η). The Málek isothermal procedure was used for estimation of the kinetic model for the investigated decomposition process. It was found that the two-parameter Šesták-Berggren (SB) autocatalytic model best describes the NaHCO3 decomposition process with the conversion function f(α) = α0.18(1-α)1.19. It was also concluded that the calculated density distribution functions of the apparent activation energies ( ddfE a ’s) are not dependent on the operating temperature, which exhibit the highly symmetrical behavior (shape factor = 1.00). The obtained isothermal decomposition results were compared with corresponding results of the nonisothermal decomposition process of NaHCO3.

A Weibull statistics-based lignocellulose saccharification model and a built-in parameter accurately predict lignocellulose hydrolysis performance.

Science.gov (United States)

Wang, Mingyu; Han, Lijuan; Liu, Shasha; Zhao, Xuebing; Yang, Jinghua; Loh, Soh Kheang; Sun, Xiaomin; Zhang, Chenxi; Fang, Xu

2015-09-01

Renewable energy from lignocellulosic biomass has been deemed an alternative to depleting fossil fuels. In order to improve this technology, we aim to develop robust mathematical models for the enzymatic lignocellulose degradation process. By analyzing 96 groups of previously published and newly obtained lignocellulose saccharification results and fitting them to Weibull distribution, we discovered Weibull statistics can accurately predict lignocellulose saccharification data, regardless of the type of substrates, enzymes and saccharification conditions. A mathematical model for enzymatic lignocellulose degradation was subsequently constructed based on Weibull statistics. Further analysis of the mathematical structure of the model and experimental saccharification data showed the significance of the two parameters in this model. In particular, the λ value, defined the characteristic time, represents the overall performance of the saccharification system. This suggestion was further supported by statistical analysis of experimental saccharification data and analysis of the glucose production levels when λ and n values change. In conclusion, the constructed Weibull statistics-based model can accurately predict lignocellulose hydrolysis behavior and we can use the λ parameter to assess the overall performance of enzymatic lignocellulose degradation. Advantages and potential applications of the model and the λ value in saccharification performance assessment were discussed. Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Competing risk models in reliability systems, a Weibull distribution model with Bayesian analysis approach

International Nuclear Information System (INIS)

Iskandar, Ismed; Gondokaryono, Yudi Satria

2016-01-01

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range

Bayesian Analysis of the Survival Function and Failure Rate of Weibull Distribution with Censored Data

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Chris Bambey Guure

2012-01-01

Full Text Available The survival function of the Weibull distribution determines the probability that a unit or an individual will survive beyond a certain specified time while the failure rate is the rate at which a randomly selected individual known to be alive at time will die at time (. The classical approach for estimating the survival function and the failure rate is the maximum likelihood method. In this study, we strive to determine the best method, by comparing the classical maximum likelihood against the Bayesian estimators using an informative prior and a proposed data-dependent prior known as generalised noninformative prior. The Bayesian estimation is considered under three loss functions. Due to the complexity in dealing with the integrals using the Bayesian estimator, Lindley’s approximation procedure is employed to reduce the ratio of the integrals. For the purpose of comparison, the mean squared error (MSE and the absolute bias are obtained. This study is conducted via simulation by utilising different sample sizes. We observed from the study that the generalised prior we assumed performed better than the others under linear exponential loss function with respect to MSE and under general entropy loss function with respect to absolute bias.

Based on Weibull Information Fusion Analysis Semiconductors Quality the Key Technology of Manufacturing Execution Systems Reliability

Science.gov (United States)

Huang, Zhi-Hui; Tang, Ying-Chun; Dai, Kai

2016-05-01

Semiconductor materials and Product qualified rate are directly related to the manufacturing costs and survival of the enterprise. Application a dynamic reliability growth analysis method studies manufacturing execution system reliability growth to improve product quality. Refer to classical Duane model assumptions and tracking growth forecasts the TGP programming model, through the failure data, established the Weibull distribution model. Combining with the median rank of average rank method, through linear regression and least squares estimation method, match respectively weibull information fusion reliability growth curve. This assumption model overcome Duane model a weakness which is MTBF point estimation accuracy is not high, through the analysis of the failure data show that the method is an instance of the test and evaluation modeling process are basically identical. Median rank in the statistics is used to determine the method of random variable distribution function, which is a good way to solve the problem of complex systems such as the limited sample size. Therefore this method has great engineering application value.

Determination of Reliability Index and Weibull Modulus as a Measure of Hypereutectic Silumins Survival

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J. Szymszal

2007-07-01

Full Text Available The first part of the study describes the methods used to determine Weibull modulus and the related reliability index of hypereutectic silumins containing about 17% Si, assigned for manufacture of high-duty castings to be used in automotive applications and aviation. The second part of the study discusses the importance of chemical composition, including the additions of 3% Cu, 1,5% Ni and 1,5% Mg, while in the third part attention was focussed on the effect of process history, including mould type (sand or metal as well as the inoculation process and heat treatment (solutioning and ageing applied to the cast AlSi17Cu3Mg1,5Ni1,5 alloy, on the run of Weibull distribution function and reliability index calculated for the tensile strength Rm of the investigated alloys.

An EOQ model for weibull distribution deterioration with time-dependent cubic demand and backlogging

Science.gov (United States)

Santhi, G.; Karthikeyan, K.

2017-11-01

In this article we introduce an economic order quantity model with weibull deterioration and time dependent cubic demand rate where holding costs as a linear function of time. Shortages are allowed in the inventory system are partially and fully backlogging. The objective of this model is to minimize the total inventory cost by using the optimal order quantity and the cycle length. The proposed model is illustrated by numerical examples and the sensitivity analysis is performed to study the effect of changes in parameters on the optimum solutions.

A comparison of estimation methods for fitting Weibull, Johnson's SB and beta functions to Pinus pinaster, Pinus radiata and Pinus sylvestris stands in northwest Spain

Energy Technology Data Exchange (ETDEWEB)

Gorgoseo, J. J.; Rojo, A.; Camara-Obregon, A.; Dieguez-Aranda, U.

2012-07-01

The purpose of this study was to compare the accuracy of the Weibull, Johnson's SB and beta distributions, fitted with some of the most usual methods and with different fixed values for the location parameters, for describing diameter distributions in even-aged stands of Pinus pinaster, Pinus radiata and Pinus sylvestris in northwest Spain. A total of 155 permanent plots in Pinus sylvestris stands throughout Galicia, 183 plots in Pinus pinaster stands throughout Galicia and Asturias and 325 plots in Pinus radiata stands in both regions were measured to describe the diameter distributions. Parameters of the Weibull function were estimated by Moments and Maximum Likelihood approaches, those of Johnson's SB function by Conditional Maximum Likelihood and by Knoebel and Burkhart's method, and those of the beta function with the method based on the moments of the distribution. The beta and the Johnson's SB functions were slightly superior to Weibull function for Pinus pinaster stands; the Johnson's SB and beta functions were more accurate in the best fits for Pinus radiata stands, and the best results of the Weibull and the Johnson's SB functions were slightly superior to beta function for Pinus sylvestris stands. However, the three functions are suitable for this stands with an appropriate value of the location parameter and estimation of parameters method. (Author) 44 refs.

Weibull analysis of fracture test data on bovine cortical bone: influence of orientation.

Science.gov (United States)

Khandaker, Morshed; Ekwaro-Osire, Stephen

2013-01-01

The fracture toughness, K IC, of a cortical bone has been experimentally determined by several researchers. The variation of K IC values occurs from the variation of specimen orientation, shape, and size during the experiment. The fracture toughness of a cortical bone is governed by the severest flaw and, hence, may be analyzed using Weibull statistics. To the best of the authors' knowledge, however, no studies of this aspect have been published. The motivation of the study is the evaluation of Weibull parameters at the circumferential-longitudinal (CL) and longitudinal-circumferential (LC) directions. We hypothesized that Weibull parameters vary depending on the bone microstructure. In the present work, a two-parameter Weibull statistical model was applied to calculate the plane-strain fracture toughness of bovine femoral cortical bone obtained using specimens extracted from CL and LC directions of the bone. It was found that the Weibull modulus of fracture toughness was larger for CL specimens compared to LC specimens, but the opposite trend was seen for the characteristic fracture toughness. The reason for these trends is the microstructural and extrinsic toughening mechanism differences between CL and LC directions bone. The Weibull parameters found in this study can be applied to develop a damage-mechanics model for bone.

The distribution choice for the threshold of solid state relay

International Nuclear Information System (INIS)

Sun Beiyun; Zhou Hui; Cheng Xiangyue; Mao Congguang

2009-01-01

Either normal distribution or Weibull distribution can be accepted as sample distribution of the threshold of solid state relay. By goodness-of-fit method, bootstrap method and Bayesian method, the Weibull distribution is chosen later. (authors)

Testing homogeneity in Weibull-regression models.

Science.gov (United States)

Bolfarine, Heleno; Valença, Dione M

2005-10-01

In survival studies with families or geographical units it may be of interest testing whether such groups are homogeneous for given explanatory variables. In this paper we consider score type tests for group homogeneity based on a mixing model in which the group effect is modelled as a random variable. As opposed to hazard-based frailty models, this model presents survival times that conditioned on the random effect, has an accelerated failure time representation. The test statistics requires only estimation of the conventional regression model without the random effect and does not require specifying the distribution of the random effect. The tests are derived for a Weibull regression model and in the uncensored situation, a closed form is obtained for the test statistic. A simulation study is used for comparing the power of the tests. The proposed tests are applied to real data sets with censored data.

Small Sample Properties of Asymptotically Efficient Estimators of the Parameters of a Bivariate Gaussian–Weibull Distribution

Science.gov (United States)

Steve P. Verrill; James W. Evans; David E. Kretschmann; Cherilyn A. Hatfield

2012-01-01

Two important wood properties are stiffness (modulus of elasticity or MOE) and bending strength (modulus of rupture or MOR). In the past, MOE has often been modeled as a Gaussian and MOR as a lognormal or a two or three parameter Weibull. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of...

Statistical distributions as applied to environmental surveillance data

International Nuclear Information System (INIS)

Speer, D.R.; Waite, D.A.

1976-01-01

Application of normal, lognormal, and Weibull distributions to radiological environmental surveillance data was investigated for approximately 300 nuclide-medium-year-location combinations. The fit of data to distributions was compared through probability plotting (special graph paper provides a visual check) and W test calculations. Results show that 25% of the data fit the normal distribution, 50% fit the lognormal, and 90% fit the Weibull.Demonstration of how to plot each distribution shows that normal and lognormal distributions are comparatively easy to use while Weibull distribution is complicated and difficult to use. Although current practice is to use normal distribution statistics, normal fit the least number of data groups considered in this study

The distribution of first-passage times and durations in FOREX and future markets

Science.gov (United States)

Sazuka, Naoya; Inoue, Jun-ichi; Scalas, Enrico

2009-07-01

Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag-Leffler survival function and the Weibull distribution. For the Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter tmax, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag-Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag-Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting

A comparative study of mixed exponential and Weibull distributions in a stochastic model replicating a tropical rainfall process

Science.gov (United States)

Abas, Norzaida; Daud, Zalina M.; Yusof, Fadhilah

2014-11-01

A stochastic rainfall model is presented for the generation of hourly rainfall data in an urban area in Malaysia. In view of the high temporal and spatial variability of rainfall within the tropical rain belt, the Spatial-Temporal Neyman-Scott Rectangular Pulse model was used. The model, which is governed by the Neyman-Scott process, employs a reasonable number of parameters to represent the physical attributes of rainfall. A common approach is to attach each attribute to a mathematical distribution. With respect to rain cell intensity, this study proposes the use of a mixed exponential distribution. The performance of the proposed model was compared to a model that employs the Weibull distribution. Hourly and daily rainfall data from four stations in the Damansara River basin in Malaysia were used as input to the models, and simulations of hourly series were performed for an independent site within the basin. The performance of the models was assessed based on how closely the statistical characteristics of the simulated series resembled the statistics of the observed series. The findings obtained based on graphical representation revealed that the statistical characteristics of the simulated series for both models compared reasonably well with the observed series. However, a further assessment using the AIC, BIC and RMSE showed that the proposed model yields better results. The results of this study indicate that for tropical climates, the proposed model, using a mixed exponential distribution, is the best choice for generation of synthetic data for ungauged sites or for sites with insufficient data within the limit of the fitted region.

Determining the parameters of Weibull function to estimate the wind power potential in conditions of limited source meteorological data

Science.gov (United States)

Fetisova, Yu. A.; Ermolenko, B. V.; Ermolenko, G. V.; Kiseleva, S. V.

2017-04-01

We studied the information basis for the assessment of wind power potential on the territory of Russia. We described the methodology to determine the parameters of the Weibull function, which reflects the density of distribution of probabilities of wind flow speeds at a defined basic height above the surface of the earth using the available data on the average speed at this height and its repetition by gradations. The application of the least square method for determining these parameters, unlike the use of graphical methods, allows performing a statistical assessment of the results of approximation of empirical histograms by the Weibull formula. On the basis of the computer-aided analysis of the statistical data, it was shown that, at a fixed point where the wind speed changes at different heights, the range of parameter variation of the Weibull distribution curve is relatively small, the sensitivity of the function to parameter changes is quite low, and the influence of changes on the shape of speed distribution curves is negligible. Taking this into consideration, we proposed and mathematically verified the methodology of determining the speed parameters of the Weibull function at other heights using the parameter computations for this function at a basic height, which is known or defined by the average speed of wind flow, or the roughness coefficient of the geological substrate. We gave examples of practical application of the suggested methodology in the development of the Atlas of Renewable Energy Resources in Russia in conditions of deficiency of source meteorological data. The proposed methodology, to some extent, may solve the problem related to the lack of information on the vertical profile of repeatability of the wind flow speeds in the presence of a wide assortment of wind turbines with different ranges of wind-wheel axis heights and various performance characteristics in the global market; as a result, this methodology can become a powerful tool for

Maximum likelihood estimation of the parameters of a bivariate Gaussian-Weibull distribution from machine stress-rated data

Science.gov (United States)

Steve P. Verrill; David E. Kretschmann; James W. Evans

2016-01-01

Two important wood properties are stiffness (modulus of elasticity, MOE) and bending strength (modulus of rupture, MOR). In the past, MOE has often been modeled as a Gaussian and MOR as a lognormal or a two- or threeparameter Weibull. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of wood...

Calculation of the ceramics Weibull parameters

Czech Academy of Sciences Publication Activity Database

Fuis, Vladimír; Návrat, Tomáš

2011-01-01

Roč. 58, - (2011), s. 642-647 ISSN 2010-376X. [International Conference on Bioinformatics and Biomedicine 2011. Bali, 26.10.2011-28.10.2011] Institutional research plan: CEZ:AV0Z20760514 Keywords : biomaterial parameters * Weibull statistics * ceramics Subject RIV: BO - Biophysics http://www.waset.org/journals/waset/v58/v58-132.pdf

Distribution of crushing strength of tablets

DEFF Research Database (Denmark)

Sonnergaard, Jørn

2002-01-01

The distribution of a given set of data is important since most parametric statistical tests are based on the assumption that the studied data are normal distributed. In analysis of fracture mechanics the Weibull distribution is widely used and the derived Weibull modulus is interpreted as a mate...... data from nine model tablet formulations and four commercial tablets are shown to follow the normal distribution. The importance of proper cleaning of the crushing strength apparatus is demonstrated....

A Weibull Approach for Enabling Safety-Oriented Decision-Making for Electronic Railway Signaling Systems

Directory of Open Access Journals (Sweden)

Emanuele Pascale

2018-04-01

Full Text Available This paper presents the advantages of using Weibull distributions, within the context of railway signaling systems, for enabling safety-oriented decision-making. Failure rates are used to statistically model the basic event of fault-tree analysis, and their value sizes the maximum allowable latency of failures to fulfill the safety target for which the system has been designed. Relying on field-return failure data, Weibull parameters have been calculated for an existing electronic signaling system and a comparison with existing predictive reliability data, based on exponential distribution, is provided. Results are discussed in order to drive considerations on the respect of quantitative targets and on the impact that a wrong hypothesis might have on the choice of a given architecture. Despite the huge amount of information gathered through the after-sales logbook used to build reliability distribution, several key elements for reliable estimation of failure rate values are still missing. This might affect the uncertainty of reliability parameters and the effort required to collect all the information. We then present how to intervene when operational failure rates present higher values compared to the theoretical approach: increasing the redundancies of the system or performing preventive maintenance tasks. Possible consequences of unjustified adoption of constant failure rate are presented. Some recommendations are also shared in order to build reliability-oriented logbooks and avoid data censoring phenomena by enhancing the functions of the electronic boards composing the system.

The effect of mis-specification on mean and selection between the Weibull and lognormal models

Science.gov (United States)

Jia, Xiang; Nadarajah, Saralees; Guo, Bo

2018-02-01

The lognormal and Weibull models are commonly used to analyse data. Although selection procedures have been extensively studied, it is possible that the lognormal model could be selected when the true model is Weibull or vice versa. As the mean is important in applications, we focus on the effect of mis-specification on mean. The effect on lognormal mean is first considered if the lognormal sample is wrongly fitted by a Weibull model. The maximum likelihood estimate (MLE) and quasi-MLE (QMLE) of lognormal mean are obtained based on lognormal and Weibull models. Then, the impact is evaluated by computing ratio of biases and ratio of mean squared errors (MSEs) between MLE and QMLE. For completeness, the theoretical results are demonstrated by simulation studies. Next, the effect of the reverse mis-specification on Weibull mean is discussed. It is found that the ratio of biases and the ratio of MSEs are independent of the location and scale parameters of the lognormal and Weibull models. The influence could be ignored if some special conditions hold. Finally, a model selection method is proposed by comparing ratios concerning biases and MSEs. We also present a published data to illustrate the study in this paper.

On the Performance Analysis of Digital Communications over Weibull-Gamma Channels

KAUST Repository

Ansari, Imran Shafique; Alouini, Mohamed-Slim

2015-01-01

In this work, the performance analysis of digital communications over a composite Weibull-Gamma (WG) multipath-fading and shadowing channel is presented wherein WG distribution is appropriate for modeling fading environments when multipath is superimposed on shadowing. More specifically, in this work, exact closed-form expressions are derived for the probability density function, the cumulative distribution function, the moment generating function, and the moments of a composite WG channel. Capitalizing on these results, new exact closed-form expressions are offered for the outage probability, the higher- order amount of fading, the average error rate for binary and M-ary modulation schemes, and the ergodic capacity under various types of transmission policies, mostly in terms of Meijer's G functions. These new analytical results were also verified via computer-based Monte-Carlo simulation results. © 2015 IEEE.

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

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Isis Didier Lins

2018-03-01

Full Text Available The Generalized Renewal Process (GRP is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsallis’ non-extensive entropy, namely the q-Exponential and the q-Weibull distributions. The q-Exponential and Weibull distributions can model decreasing, constant or increasing failure intensity functions. However, the power law behavior of the q-Exponential probability density function for specific parameter values is an advantage over the Weibull distribution when adjusting data containing extreme values. The q-Weibull probability distribution, in turn, can also fit data with bathtub-shaped or unimodal failure intensities in addition to the behaviors already mentioned. Therefore, the q-Exponential-GRP is an alternative for the Weibull-GRP model and the q-Weibull-GRP generalizes both. The method of maximum likelihood is used for their parameters’ estimation by means of a particle swarm optimization algorithm, and Monte Carlo simulations are performed for the sake of validation. The proposed models and algorithms are applied to examples involving reliability-related data of complex systems and the obtained results suggest GRP plus q-distributions are promising techniques for the analyses of repairable systems.

An exponential distribution

International Nuclear Information System (INIS)

Anon

2009-01-01

In this presentation author deals with the probabilistic evaluation of product life on the example of the exponential distribution. The exponential distribution is special one-parametric case of the weibull distribution.

A general Bayes weibull inference model for accelerated life testing

International Nuclear Information System (INIS)

Dorp, J. Rene van; Mazzuchi, Thomas A.

2005-01-01

This article presents the development of a general Bayes inference model for accelerated life testing. The failure times at a constant stress level are assumed to belong to a Weibull distribution, but the specification of strict adherence to a parametric time-transformation function is not required. Rather, prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels and the common shape parameter. Using the approach, Bayes point estimates as well as probability statements for use-stress (and accelerated) life parameters may be inferred from a host of testing scenarios. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known MCMC (Markov Chain Monte Carlo) methods to derive posterior approximations. The approach is illustrated with an example

Accurate bearing remaining useful life prediction based on Weibull distribution and artificial neural network

Science.gov (United States)

Ben Ali, Jaouher; Chebel-Morello, Brigitte; Saidi, Lotfi; Malinowski, Simon; Fnaiech, Farhat

2015-05-01

Accurate remaining useful life (RUL) prediction of critical assets is an important challenge in condition based maintenance to improve reliability and decrease machine's breakdown and maintenance's cost. Bearing is one of the most important components in industries which need to be monitored and the user should predict its RUL. The challenge of this study is to propose an original feature able to evaluate the health state of bearings and to estimate their RUL by Prognostics and Health Management (PHM) techniques. In this paper, the proposed method is based on the data-driven prognostic approach. The combination of Simplified Fuzzy Adaptive Resonance Theory Map (SFAM) neural network and Weibull distribution (WD) is explored. WD is used just in the training phase to fit measurement and to avoid areas of fluctuation in the time domain. SFAM training process is based on fitted measurements at present and previous inspection time points as input. However, the SFAM testing process is based on real measurements at present and previous inspections. Thanks to the fuzzy learning process, SFAM has an important ability and a good performance to learn nonlinear time series. As output, seven classes are defined; healthy bearing and six states for bearing degradation. In order to find the optimal RUL prediction, a smoothing phase is proposed in this paper. Experimental results show that the proposed method can reliably predict the RUL of rolling element bearings (REBs) based on vibration signals. The proposed prediction approach can be applied to prognostic other various mechanical assets.

Mixture distributions of wind speed in the UAE

Science.gov (United States)

Shin, J.; Ouarda, T.; Lee, T. S.

2013-12-01

Wind speed probability distribution is commonly used to estimate potential wind energy. The 2-parameter Weibull distribution has been most widely used to characterize the distribution of wind speed. However, it is unable to properly model wind speed regimes when wind speed distribution presents bimodal and kurtotic shapes. Several studies have concluded that the Weibull distribution should not be used for frequency analysis of wind speed without investigation of wind speed distribution. Due to these mixture distributional characteristics of wind speed data, the application of mixture distributions should be further investigated in the frequency analysis of wind speed. A number of studies have investigated the potential wind energy in different parts of the Arabian Peninsula. Mixture distributional characteristics of wind speed were detected from some of these studies. Nevertheless, mixture distributions have not been employed for wind speed modeling in the Arabian Peninsula. In order to improve our understanding of wind energy potential in Arabian Peninsula, mixture distributions should be tested for the frequency analysis of wind speed. The aim of the current study is to assess the suitability of mixture distributions for the frequency analysis of wind speed in the UAE. Hourly mean wind speed data at 10-m height from 7 stations were used in the current study. The Weibull and Kappa distributions were employed as representatives of the conventional non-mixture distributions. 10 mixture distributions are used and constructed by mixing four probability distributions such as Normal, Gamma, Weibull and Extreme value type-one (EV-1) distributions. Three parameter estimation methods such as Expectation Maximization algorithm, Least Squares method and Meta-Heuristic Maximum Likelihood (MHML) method were employed to estimate the parameters of the mixture distributions. In order to compare the goodness-of-fit of tested distributions and parameter estimation methods for

On the Performance Analysis of Digital Communications over Weibull-Gamma Channels

KAUST Repository

Ansari, Imran Shafique

2015-05-01

In this work, the performance analysis of digital communications over a composite Weibull-Gamma (WG) multipath-fading and shadowing channel is presented wherein WG distribution is appropriate for modeling fading environments when multipath is superimposed on shadowing. More specifically, in this work, exact closed-form expressions are derived for the probability density function, the cumulative distribution function, the moment generating function, and the moments of a composite WG channel. Capitalizing on these results, new exact closed-form expressions are offered for the outage probability, the higher- order amount of fading, the average error rate for binary and M-ary modulation schemes, and the ergodic capacity under various types of transmission policies, mostly in terms of Meijer\\'s G functions. These new analytical results were also verified via computer-based Monte-Carlo simulation results. © 2015 IEEE.

A deterministic inventory model for deteriorating items with selling price dependent demand and three-parameter Weibull distributed deterioration

Directory of Open Access Journals (Sweden)

Asoke Kumar Bhunia

2014-06-01

Full Text Available In this paper, an attempt is made to develop two inventory models for deteriorating items with variable demand dependent on the selling price and frequency of advertisement of items. In the first model, shortages are not allowed whereas in the second, these are allowed and partially backlogged with a variable rate dependent on the duration of waiting time up to the arrival of next lot. In both models, the deterioration rate follows three-parameter Weibull distribution and the transportation cost is considered explicitly for replenishing the order quantity. This cost is dependent on the lot-size as well as the distance from the source to the destination. The corresponding models have been formulated and solved. Two numerical examples have been considered to illustrate the results and the significant features of the results are discussed. Finally, based on these examples, the effects of different parameters on the initial stock level, shortage level (in case of second model only, cycle length along with the optimal profit have been studied by sensitivity analyses taking one parameter at a time keeping the other parameters as same.

Probabilistic Analysis for Comparing Fatigue Data Based on Johnson-Weibull Parameters

Science.gov (United States)

Vlcek, Brian L.; Hendricks, Robert C.; Zaretsky, Erwin V.

2013-01-01

Leonard Johnson published a methodology for establishing the confidence that two populations of data are different. Johnson's methodology is dependent on limited combinations of test parameters (Weibull slope, mean life ratio, and degrees of freedom) and a set of complex mathematical equations. In this report, a simplified algebraic equation for confidence numbers is derived based on the original work of Johnson. The confidence numbers calculated with this equation are compared to those obtained graphically by Johnson. Using the ratios of mean life, the resultant values of confidence numbers at the 99 percent level deviate less than 1 percent from those of Johnson. At a 90 percent confidence level, the calculated values differ between +2 and 4 percent. The simplified equation is used to rank the experimental lives of three aluminum alloys (AL 2024, AL 6061, and AL 7075), each tested at three stress levels in rotating beam fatigue, analyzed using the Johnson- Weibull method, and compared to the ASTM Standard (E739 91) method of comparison. The ASTM Standard did not statistically distinguish between AL 6061 and AL 7075. However, it is possible to rank the fatigue lives of different materials with a reasonable degree of statistical certainty based on combined confidence numbers using the Johnson- Weibull analysis. AL 2024 was found to have the longest fatigue life, followed by AL 7075, and then AL 6061. The ASTM Standard and the Johnson-Weibull analysis result in the same stress-life exponent p for each of the three aluminum alloys at the median, or L(sub 50), lives

Adhesively bonded joints composed of pultruded adherends: Considerations at the upper tail of the material strength statistical distribution

International Nuclear Information System (INIS)

Vallee, T.; Keller, Th.; Fourestey, G.; Fournier, B.; Correia, J.R.

2009-01-01

The Weibull distribution, used to describe the scaling of strength of materials, has been verified on a wide range of materials and geometries: however, the quality of the fitting tended to be less good towards the upper tail. Based on a previously developed probabilistic strength prediction method for adhesively bonded joints composed of pultruded glass fiber-reinforced polymer (GFRP) adherends, where it was verified that a two-parameter Weibull probabilistic distribution was not able to model accurately the upper tail of a material strength distribution, different improved probabilistic distributions were compared to enhance the quality of strength predictions. The following probabilistic distributions were examined: a two-parameter Weibull (as a reference), m-fold Weibull, a Grafted Distribution, a Birnbaum-Saunders Distribution and a Generalized Lambda Distribution. The Generalized Lambda Distribution turned out to be the best analytical approximation for the strength data, providing a good fit to the experimental data, and leading to more accurate joint strength predictions than the original two-parameter Weibull distribution. It was found that a proper modeling of the upper tail leads to a noticeable increase of the quality of the predictions. (authors)

Adhesively bonded joints composed of pultruded adherends: Considerations at the upper tail of the material strength statistical distribution

Energy Technology Data Exchange (ETDEWEB)

Vallee, T.; Keller, Th. [Ecole Polytech Fed Lausanne, CCLab, CH-1015 Lausanne, (Switzerland); Fourestey, G. [Ecole Polytech Fed Lausanne, IACS, Chair Modeling and Sci Comp, CH-1015 Lausanne, (Switzerland); Fournier, B. [CEA SACLAY ENSMP, DEN, DANS, DMN, SRMA, LC2M, F-91191 Gif Sur Yvette, (France); Correia, J.R. [Univ Tecn Lisbon, Inst Super Tecn, Civil Engn and Architecture Dept, P-1049001 Lisbon, (Portugal)

2009-07-01

The Weibull distribution, used to describe the scaling of strength of materials, has been verified on a wide range of materials and geometries: however, the quality of the fitting tended to be less good towards the upper tail. Based on a previously developed probabilistic strength prediction method for adhesively bonded joints composed of pultruded glass fiber-reinforced polymer (GFRP) adherends, where it was verified that a two-parameter Weibull probabilistic distribution was not able to model accurately the upper tail of a material strength distribution, different improved probabilistic distributions were compared to enhance the quality of strength predictions. The following probabilistic distributions were examined: a two-parameter Weibull (as a reference), m-fold Weibull, a Grafted Distribution, a Birnbaum-Saunders Distribution and a Generalized Lambda Distribution. The Generalized Lambda Distribution turned out to be the best analytical approximation for the strength data, providing a good fit to the experimental data, and leading to more accurate joint strength predictions than the original two-parameter Weibull distribution. It was found that a proper modeling of the upper tail leads to a noticeable increase of the quality of the predictions. (authors)

Time-dependent fiber bundles with local load sharing. II. General Weibull fibers.

Science.gov (United States)

Phoenix, S Leigh; Newman, William I

2009-12-01

Fiber bundle models (FBMs) are useful tools in understanding failure processes in a variety of material systems. While the fibers and load sharing assumptions are easily described, FBM analysis is typically difficult. Monte Carlo methods are also hampered by the severe computational demands of large bundle sizes, which overwhelm just as behavior relevant to real materials starts to emerge. For large size scales, interest continues in idealized FBMs that assume either equal load sharing (ELS) or local load sharing (LLS) among fibers, rules that reflect features of real load redistribution in elastic lattices. The present work focuses on a one-dimensional bundle of N fibers under LLS where life consumption in a fiber follows a power law in its load, with exponent rho , and integrated over time. This life consumption function is further embodied in a functional form resulting in a Weibull distribution for lifetime under constant fiber stress and with Weibull exponent, beta. Thus the failure rate of a fiber depends on its past load history, except for beta=1 . We develop asymptotic results validated by Monte Carlo simulation using a computational algorithm developed in our previous work [Phys. Rev. E 63, 021507 (2001)] that greatly increases the size, N , of treatable bundles (e.g., 10(6) fibers in 10(3) realizations). In particular, our algorithm is O(N ln N) in contrast with former algorithms which were O(N2) making this investigation possible. Regimes are found for (beta,rho) pairs that yield contrasting behavior for large N. For rho>1 and large N, brittle weakest volume behavior emerges in terms of characteristic elements (groupings of fibers) derived from critical cluster formation, and the lifetime eventually goes to zero as N-->infinity , unlike ELS, which yields a finite limiting mean. For 1/21 but with 0Weibull exponent for fiber strength.

Evaluation of the Weibull and log normal distribution functions as survival models of Escherichia coli under isothermal and non isothermal conditions.

Science.gov (United States)

Aragao, Glaucia M F; Corradini, Maria G; Normand, Mark D; Peleg, Micha

2007-11-01

Published survival curves of Escherichia coli in two growth media, with and without the presence of salt, at various temperatures and in a Greek eggplant salad having various levels of essential oil, all had a characteristic downward concavity when plotted on semi logarithmic coordinates. Some also exhibited what appeared as a 'shoulder' of considerable length. Regardless of whether a shoulder was noticed, the survival pattern could be considered as a manifestation of an underlying unimodal distribution of the cells' death times. Mathematically, the data could be described equally well by the Weibull and log normal distribution functions, which had similar modes, means, standard deviations and coefficients of skewness. When plotted in their probability density function (PDF) form, the curves also appeared very similar visually. This enabled us to quantify and compare the effect of temperature or essential oil concentration on the organism's survival in terms of these temporal distributions' characteristics. Increased lethality was generally expressed in a shorter mean and mode, a smaller standard deviation and increased overall symmetry as judged by the distributions' degree of skewness. The 'shoulder', as expected, simply indicated that the distribution's standard deviation was much smaller than its mode. Rate models based on the two distribution functions could be used to predict non isothermal survival patterns. They were derived on the assumption that the momentary inactivation rate is the isothermal rate at the momentary temperature at a time that corresponds to the momentary survival ratio. In this application, however, the Weibullian model with a fixed power was not only simpler and more convenient mathematically than the one based on the log normal distribution, but it also provided more accurate estimates of the dynamic inactivation patterns.

An inventory model for generalized weibull deteriorating items with price dependent demand and permissible delay in payments under inflation

Directory of Open Access Journals (Sweden)

S.P.Singh

2015-09-01

Full Text Available This paper derives an inventory model is developed for items that deteriorates at a generalized Weibull distributed rate when demand for the items is dependent on the selling price. Shortages are not allowed and price inflation is taken into consideration over finite planning horizon. A brief analysis of the cost involved is carried out by theoretical analysis.

Maximum Likelihood Estimates of Parameters in Various Types of Distribution Fitted to Important Data Cases.

OpenAIRE

HIROSE,Hideo

1998-01-01

TYPES OF THE DISTRIBUTION:13;Normal distribution (2-parameter)13;Uniform distribution (2-parameter)13;Exponential distribution ( 2-parameter)13;Weibull distribution (2-parameter)13;Gumbel Distribution (2-parameter)13;Weibull/Frechet Distribution (3-parameter)13;Generalized extreme-value distribution (3-parameter)13;Gamma distribution (3-parameter)13;Extended Gamma distribution (3-parameter)13;Log-normal distribution (3-parameter)13;Extended Log-normal distribution (3-parameter)13;Generalized ...

Spatial and temporal patterns of global onshore wind speed distribution

International Nuclear Information System (INIS)

Zhou, Yuyu; Smith, Steven J

2013-01-01

Wind power, a renewable energy source, can play an important role in electrical energy generation. Information regarding wind energy potential is important both for energy related modeling and for decision-making in the policy community. While wind speed datasets with high spatial and temporal resolution are often ultimately used for detailed planning, simpler assumptions are often used in analysis work. An accurate representation of the wind speed frequency distribution is needed in order to properly characterize wind energy potential. Using a power density method, this study estimated global variation in wind parameters as fitted to a Weibull density function using NCEP/climate forecast system reanalysis (CFSR) data over land areas. The Weibull distribution performs well in fitting the time series wind speed data at most locations according to R 2 , root mean square error, and power density error. The wind speed frequency distribution, as represented by the Weibull k parameter, exhibits a large amount of spatial variation, a regionally varying amount of seasonal variation, and relatively low decadal variation. We also analyzed the potential error in wind power estimation when a commonly assumed Rayleigh distribution (Weibull k = 2) is used. We find that the assumption of the same Weibull parameter across large regions can result in non-negligible errors. While large-scale wind speed data are often presented in the form of mean wind speeds, these results highlight the need to also provide information on the wind speed frequency distribution. (letter)

A Weibull-based compositional approach for hierarchical dynamic fault trees

International Nuclear Information System (INIS)

Chiacchio, F.; Cacioppo, M.; D'Urso, D.; Manno, G.; Trapani, N.; Compagno, L.

2013-01-01

The solution of a dynamic fault tree (DFT) for the reliability assessment can be achieved using a wide variety of techniques. These techniques have a strong theoretical foundation as both the analytical and the simulation methods have been extensively developed. Nevertheless, they all present the same limits that appear with the increasing of the size of the fault trees (i.e., state space explosion, time-consuming simulations), compromising the resolution. We have tested the feasibility of a composition algorithm based on a Weibull distribution, addressed to the resolution of a general class of dynamic fault trees characterized by non-repairable basic events and generally distributed failure times. The proposed composition algorithm is used to generalize the traditional hierarchical technique that, as previous literature have extensively confirmed, is able to reduce the computational effort of a large DFT through the modularization of independent parts of the tree. The results of this study are achieved both through simulation and analytical techniques, thus confirming the capability to solve a quite general class of dynamic fault trees and overcome the limits of traditional techniques.

Distributions of Autocorrelated First-Order Kinetic Outcomes: Illness Severity.

Directory of Open Access Journals (Sweden)

James D Englehardt

Full Text Available Many complex systems produce outcomes having recurring, power law-like distributions over wide ranges. However, the form necessarily breaks down at extremes, whereas the Weibull distribution has been demonstrated over the full observed range. Here the Weibull distribution is derived as the asymptotic distribution of generalized first-order kinetic processes, with convergence driven by autocorrelation, and entropy maximization subject to finite positive mean, of the incremental compounding rates. Process increments represent multiplicative causes. In particular, illness severities are modeled as such, occurring in proportion to products of, e.g., chronic toxicant fractions passed by organs along a pathway, or rates of interacting oncogenic mutations. The Weibull form is also argued theoretically and by simulation to be robust to the onset of saturation kinetics. The Weibull exponential parameter is shown to indicate the number and widths of the first-order compounding increments, the extent of rate autocorrelation, and the degree to which process increments are distributed exponential. In contrast with the Gaussian result in linear independent systems, the form is driven not by independence and multiplicity of process increments, but by increment autocorrelation and entropy. In some physical systems the form may be attracting, due to multiplicative evolution of outcome magnitudes towards extreme values potentially much larger and smaller than control mechanisms can contain. The Weibull distribution is demonstrated in preference to the lognormal and Pareto I for illness severities versus (a toxicokinetic models, (b biologically-based network models, (c scholastic and psychological test score data for children with prenatal mercury exposure, and (d time-to-tumor data of the ED01 study.

Bayesian and Classical Estimation of Stress-Strength Reliability for Inverse Weibull Lifetime Models

Directory of Open Access Journals (Sweden)

Qixuan Bi

2017-06-01

Full Text Available In this paper, we consider the problem of estimating stress-strength reliability for inverse Weibull lifetime models having the same shape parameters but different scale parameters. We obtain the maximum likelihood estimator and its asymptotic distribution. Since the classical estimator doesn’t hold explicit forms, we propose an approximate maximum likelihood estimator. The asymptotic confidence interval and two bootstrap intervals are obtained. Using the Gibbs sampling technique, Bayesian estimator and the corresponding credible interval are obtained. The Metropolis-Hastings algorithm is used to generate random variates. Monte Carlo simulations are conducted to compare the proposed methods. Analysis of a real dataset is performed.

Recurrent frequency-size distribution of characteristic events

Directory of Open Access Journals (Sweden)

S. G. Abaimov

2009-04-01

Full Text Available Statistical frequency-size (frequency-magnitude properties of earthquake occurrence play an important role in seismic hazard assessments. The behavior of earthquakes is represented by two different statistics: interoccurrent behavior in a region and recurrent behavior at a given point on a fault (or at a given fault. The interoccurrent frequency-size behavior has been investigated by many authors and generally obeys the power-law Gutenberg-Richter distribution to a good approximation. It is expected that the recurrent frequency-size behavior should obey different statistics. However, this problem has received little attention because historic earthquake sequences do not contain enough events to reconstruct the necessary statistics. To overcome this lack of data, this paper investigates the recurrent frequency-size behavior for several problems. First, the sequences of creep events on a creeping section of the San Andreas fault are investigated. The applicability of the Brownian passage-time, lognormal, and Weibull distributions to the recurrent frequency-size statistics of slip events is tested and the Weibull distribution is found to be the best-fit distribution. To verify this result the behaviors of numerical slider-block and sand-pile models are investigated and the Weibull distribution is confirmed as the applicable distribution for these models as well. Exponents β of the best-fit Weibull distributions for the observed creep event sequences and for the slider-block model are found to have similar values ranging from 1.6 to 2.2 with the corresponding aperiodicities C_V of the applied distribution ranging from 0.47 to 0.64. We also note similarities between recurrent time-interval statistics and recurrent frequency-size statistics.

Comparação entre as distribuições normal e de Weibull para análise da resistência à compressão do concreto (doi:10.5216/reec.v9i3.28814

Directory of Open Access Journals (Sweden)

Paulo Eduardo Teodoro

2014-11-01

Full Text Available RESUMO: O projeto de estruturas de concreto possui uma modelagem matemática de natureza bastante subjetiva. Portanto, objetivou-se com esta pesquisa verificar se as distribuições Normal e de Weibull podem ser aplicadas aos dados resistências à compressão do concreto pronto, agrupados comercialmente. O estudo foi realizado durante o ano de 2011 na cidade de Campo Grande/MS. A resistência à compressão foi avaliada em ensaios de 189 amostras aos 28 dias a partir de diferentes construções de concreto armado realizados na cidade. Os ensaios ocorreram conforme prescrito pela NBR 5739 (ABNT, 2007. Para quantificar o grau em que a distribuição Normal e de Weibull se ajustaram os dados experimentais foram utilizados três testes de adequação: qui-quadrado, Anderson-Darling e Kolmogorov-Smirnov. Com base no presente estudo, a distribuição Weibull pode ser aplicada aos dados de resistência à compressão para concreto. Isto sugere que, apesar de os complexos processos envolvidos na falha de compressão para um material compósito quase frágil como o concreto, um modelo de força estatística é eficaz. Além disso, ao comparar os testes de ajuste, há grande diferença prática entre as distribuições Normal e de Weibull. Esta informação é uma importante adição experimental para a literatura científica no que diz respeito à ruptura de materiais “semi-frágeis”. ABSTRACT: The design of concrete structures and their mathematical modeling is rather subjective in its nature. Therefore, it is the purpose of this study to see whether the Weibull or Normal distributions can be applied to the compressive strengths of commercially batched ready-mixed concrete. The study was conducted during the year 2011 in the city of Campo Grande / MS. The compressive strength was evaluated in 189 test samples at 28 days from different concrete constructions conducted in the city. The trials took place as prescribed by NBR 5739 (ABNT, 2007. To

Theoretical derivation of wind power probability distribution function and applications

International Nuclear Information System (INIS)

Altunkaynak, Abdüsselam; Erdik, Tarkan; Dabanlı, İsmail; Şen, Zekai

2012-01-01

Highlights: ► Derivation of wind power stochastic characteristics are standard deviation and the dimensionless skewness. ► The perturbation is expressions for the wind power statistics from Weibull probability distribution function (PDF). ► Comparisons with the corresponding characteristics of wind speed PDF abides by the Weibull PDF. ► The wind power abides with the Weibull-PDF. -- Abstract: The instantaneous wind power contained in the air current is directly proportional with the cube of the wind speed. In practice, there is a record of wind speeds in the form of a time series. It is, therefore, necessary to develop a formulation that takes into consideration the statistical parameters of such a time series. The purpose of this paper is to derive the general wind power formulation in terms of the statistical parameters by using the perturbation theory, which leads to a general formulation of the wind power expectation and other statistical parameter expressions such as the standard deviation and the coefficient of variation. The formulation is very general and can be applied specifically for any wind speed probability distribution function. Its application to two-parameter Weibull probability distribution of wind speeds is presented in full detail. It is concluded that provided wind speed is distributed according to a Weibull distribution, the wind power could be derived based on wind speed data. It is possible to determine wind power at any desired risk level, however, in practical studies most often 5% or 10% risk levels are preferred and the necessary simple procedure is presented for this purpose in this paper.

On the Distribution of Earthquake Interevent Times and the Impact of Spatial Scale

Science.gov (United States)

Hristopulos, Dionissios

2013-04-01

The distribution of earthquake interevent times is a subject that has attracted much attention in the statistical physics literature [1-3]. A recent paper proposes that the distribution of earthquake interevent times follows from the the interplay of the crustal strength distribution and the loading function (stress versus time) of the Earth's crust locally [4]. It was also shown that the Weibull distribution describes earthquake interevent times provided that the crustal strength also follows the Weibull distribution and that the loading function follows a power-law during the loading cycle. I will discuss the implications of this work and will present supporting evidence based on the analysis of data from seismic catalogs. I will also discuss the theoretical evidence in support of the Weibull distribution based on models of statistical physics [5]. Since other-than-Weibull interevent times distributions are not excluded in [4], I will illustrate the use of the Kolmogorov-Smirnov test in order to determine which probability distributions are not rejected by the data. Finally, we propose a modification of the Weibull distribution if the size of the system under investigation (i.e., the area over which the earthquake activity occurs) is finite with respect to a critical link size. keywords: hypothesis testing, modified Weibull, hazard rate, finite size References [1] Corral, A., 2004. Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes, Phys. Rev. Lett., 9210) art. no. 108501. [2] Saichev, A., Sornette, D. 2007. Theory of earthquake recurrence times, J. Geophys. Res., Ser. B 112, B04313/1-26. [3] Touati, S., Naylor, M., Main, I.G., 2009. Origin and nonuniversality of the earthquake interevent time distribution Phys. Rev. Lett., 102 (16), art. no. 168501. [4] Hristopulos, D.T., 2003. Spartan Gibbs random field models for geostatistical applications, SIAM Jour. Sci. Comput., 24, 2125-2162. [5] I. Eliazar and J. Klafter, 2006

Quality-Related Monitoring and Grading of Granulated Products by Weibull-Distribution Modeling of Visual Images with Semi-Supervised Learning.

Science.gov (United States)

Liu, Jinping; Tang, Zhaohui; Xu, Pengfei; Liu, Wenzhong; Zhang, Jin; Zhu, Jianyong

2016-06-29

The topic of online product quality inspection (OPQI) with smart visual sensors is attracting increasing interest in both the academic and industrial communities on account of the natural connection between the visual appearance of products with their underlying qualities. Visual images captured from granulated products (GPs), e.g., cereal products, fabric textiles, are comprised of a large number of independent particles or stochastically stacking locally homogeneous fragments, whose analysis and understanding remains challenging. A method of image statistical modeling-based OPQI for GP quality grading and monitoring by a Weibull distribution(WD) model with a semi-supervised learning classifier is presented. WD-model parameters (WD-MPs) of GP images' spatial structures, obtained with omnidirectional Gaussian derivative filtering (OGDF), which were demonstrated theoretically to obey a specific WD model of integral form, were extracted as the visual features. Then, a co-training-style semi-supervised classifier algorithm, named COSC-Boosting, was exploited for semi-supervised GP quality grading, by integrating two independent classifiers with complementary nature in the face of scarce labeled samples. Effectiveness of the proposed OPQI method was verified and compared in the field of automated rice quality grading with commonly-used methods and showed superior performance, which lays a foundation for the quality control of GP on assembly lines.

Influence of the Testing Gage Length on the Strength, Young's Modulus and Weibull Modulus of Carbon Fibres and Glass Fibres

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Luiz Claudio Pardini

2002-10-01

Full Text Available Carbon fibres and glass fibres are reinforcements for advanced composites and the fiber strength is the most influential factor on the strength of the composites. They are essentially brittle and fail with very little reduction in cross section. Composites made with these fibres are characterized by a high strength/density ratio and their properties are intrisically related to their microstructure, i.e., amount and orientation of the fibres, surface treatment, among other factors. Processing parameters have an important role in the fibre mechanical behaviour (strength and modulus. Cracks, voids and impurities in the case of glass fibres and fibrillar misalignments in the case of carbon fibres are created during processing. Such inhomogeneities give rise to an appreciable scatter in properties. The most used statistical tool that deals with this characteristic variability in properties is the Weibull distribution. The present work investigates the influence of the testing gage length on the strength, Young's modulus and Weibull modulus of carbon fibres and glass fibres. The Young's modulus is calculated by two methods: (i ASTM D 3379M, and (ii interaction between testing equipment/specimen The first method resulted in a Young modulus of 183 GPa for carbon fibre, and 76 GPa for glass fibre. The second method gave a Young modulus of 250 GPa for carbon fibre and 50 GPa for glass fibre. These differences revelead differences on how the interaction specimen/testing machine can interfere in the Young modulus calculations. Weibull modulus can be a tool to evaluate the fibre's homogeneity in terms of properties and it is a good quality control parameter during processing. In the range of specimen gage length tested the Weibull modulus for carbon fibre is ~ 3.30 and for glass fibres is ~ 5.65, which indicates that for the batch of fibres tested, the glass fibre is more uniform in properties.

Probabilistic physics-of-failure models for component reliabilities using Monte Carlo simulation and Weibull analysis: a parametric study

International Nuclear Information System (INIS)

Hall, P.L.; Strutt, J.E.

2003-01-01

In reliability engineering, component failures are generally classified in one of three ways: (1) early life failures; (2) failures having random onset times; and (3) late life or 'wear out' failures. When the time-distribution of failures of a population of components is analysed in terms of a Weibull distribution, these failure types may be associated with shape parameters β having values 1 respectively. Early life failures are frequently attributed to poor design (e.g. poor materials selection) or problems associated with manufacturing or assembly processes. We describe a methodology for the implementation of physics-of-failure models of component lifetimes in the presence of parameter and model uncertainties. This treats uncertain parameters as random variables described by some appropriate statistical distribution, which may be sampled using Monte Carlo methods. The number of simulations required depends upon the desired accuracy of the predicted lifetime. Provided that the number of sampled variables is relatively small, an accuracy of 1-2% can be obtained using typically 1000 simulations. The resulting collection of times-to-failure are then sorted into ascending order and fitted to a Weibull distribution to obtain a shape factor β and a characteristic life-time η. Examples are given of the results obtained using three different models: (1) the Eyring-Peck (EP) model for corrosion of printed circuit boards; (2) a power-law corrosion growth (PCG) model which represents the progressive deterioration of oil and gas pipelines; and (3) a random shock-loading model of mechanical failure. It is shown that for any specific model the values of the Weibull shape parameters obtained may be strongly dependent on the degree of uncertainty of the underlying input parameters. Both the EP and PCG models can yield a wide range of values of β, from β>1, characteristic of wear-out behaviour, to β<1, characteristic of early-life failure, depending on the degree of

Stress-strength reliability for general bivariate distributions

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Alaa H. Abdel-Hamid

2016-10-01

Full Text Available An expression for the stress-strength reliability R=P(X1distribution. Such distribution includes bivariate compound Weibull, bivariate compound Gompertz, bivariate compound Pareto, among others. In the parametric case, the maximum likelihood estimates of the parameters and reliability function R are obtained. In the non-parametric case, point and interval estimates of R are developed using Govindarajulu's asymptotic distribution-free method when X1 and X2 are dependent. An example is given when the population distribution is bivariate compound Weibull. Simulation is performed, based on different sample sizes to study the performance of estimates.

Scaling in the distribution of intertrade durations of Chinese stocks

Science.gov (United States)

Jiang, Zhi-Qiang; Chen, Wei; Zhou, Wei-Xing

2008-10-01

The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. A scaling pattern is observed in the distributions of intertrade durations, where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve. The scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions. The ensemble distributions for all stocks are modeled by the Weibull and the Tsallis q-exponential distributions. Maximum likelihood estimation shows that the Weibull distribution outperforms the q-exponential for not-too-large intertrade durations which account for more than 98.5% of the data. Alternatively, nonlinear least-squares estimation selects the q-exponential as a better model, in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities. The distribution of intertrade durations is Weibull followed by a power-law tail with an asymptotic tail exponent close to 3.

Expectation Maximization Algorithm for Box-Cox Transformation Cure Rate Model and Assessment of Model Misspecification Under Weibull Lifetimes.

Science.gov (United States)

Pal, Suvra; Balakrishnan, Narayanaswamy

2018-05-01

In this paper, we develop likelihood inference based on the expectation maximization algorithm for the Box-Cox transformation cure rate model assuming the lifetimes to follow a Weibull distribution. A simulation study is carried out to demonstrate the performance of the proposed estimation method. Through Monte Carlo simulations, we also study the effect of model misspecification on the estimate of cure rate. Finally, we analyze a well-known data on melanoma with the model and the inferential method developed here.

Comparison of Weibull and Probit Analysis in Toxicity Testing of ...

African Journals Online (AJOL)

HP

Keywords: Hunteria umbellata, Weibull model, Acute toxicity, Median lethal dose (LD50). Received: 7 November ... (PBPK) models [14,15], and (v) biologically-. Based Models: Moolgavkar-Venzon-Kundson. (MVK) model [16] and Ellwein and Cohen model [17]. ... Nigeria, Ibadan, where a sample with number. FHI107618 ...

Comparision of the different probability distributions for earthquake hazard assessment in the North Anatolian Fault Zone

Energy Technology Data Exchange (ETDEWEB)

Yilmaz, Şeyda, E-mail: seydayilmaz@ktu.edu.tr; Bayrak, Erdem, E-mail: erdmbyrk@gmail.com [Karadeniz Technical University, Trabzon (Turkey); Bayrak, Yusuf, E-mail: bayrak@ktu.edu.tr [Ağrı İbrahim Çeçen University, Ağrı (Turkey)

2016-04-18

In this study we examined and compared the three different probabilistic distribution methods for determining the best suitable model in probabilistic assessment of earthquake hazards. We analyzed a reliable homogeneous earthquake catalogue between a time period 1900-2015 for magnitude M ≥ 6.0 and estimated the probabilistic seismic hazard in the North Anatolian Fault zone (39°-41° N 30°-40° E) using three distribution methods namely Weibull distribution, Frechet distribution and three-parameter Weibull distribution. The distribution parameters suitability was evaluated Kolmogorov-Smirnov (K-S) goodness-of-fit test. We also compared the estimated cumulative probability and the conditional probabilities of occurrence of earthquakes for different elapsed time using these three distribution methods. We used Easyfit and Matlab software to calculate these distribution parameters and plotted the conditional probability curves. We concluded that the Weibull distribution method was the most suitable than other distribution methods in this region.

Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications

KAUST Repository

Oubei, Hassan M.; Zedini, Emna; Elafandy, Rami T.; Kammoun, Abla; Ng, Tien Khee; Alouini, Mohamed-Slim; Ooi, Boon S.

2017-01-01

Recent advances in underwater wireless optical communications necessitate a better understanding of the underwater channel. We propose the Weibull model to characterize the fading of salinity induced turbulent underwater wireless optical channels

Test Population Selection from Weibull-Based, Monte Carlo Simulations of Fatigue Life

Science.gov (United States)

Vlcek, Brian L.; Zaretsky, Erwin V.; Hendricks, Robert C.

2012-01-01

Fatigue life is probabilistic and not deterministic. Experimentally establishing the fatigue life of materials, components, and systems is both time consuming and costly. As a result, conclusions regarding fatigue life are often inferred from a statistically insufficient number of physical tests. A proposed methodology for comparing life results as a function of variability due to Weibull parameters, variability between successive trials, and variability due to size of the experimental population is presented. Using Monte Carlo simulation of randomly selected lives from a large Weibull distribution, the variation in the L10 fatigue life of aluminum alloy AL6061 rotating rod fatigue tests was determined as a function of population size. These results were compared to the L10 fatigue lives of small (10 each) populations from AL2024, AL7075 and AL6061. For aluminum alloy AL6061, a simple algebraic relationship was established for the upper and lower L10 fatigue life limits as a function of the number of specimens failed. For most engineering applications where less than 30 percent variability can be tolerated in the maximum and minimum values, at least 30 to 35 test samples are necessary. The variability of test results based on small sample sizes can be greater than actual differences, if any, that exists between materials and can result in erroneous conclusions. The fatigue life of AL2024 is statistically longer than AL6061 and AL7075. However, there is no statistical difference between the fatigue lives of AL6061 and AL7075 even though AL7075 had a fatigue life 30 percent greater than AL6061.

comparison of estimation methods for fitting weibull distribution

African Journals Online (AJOL)

Tersor

Tree diameter characterisation using probability distribution functions is essential for determining the structure of forest stands. This has been an intrinsic part of forest management planning, decision-making and research in recent times. The distribution of species and tree size in a forest area gives the structure of the stand.

Prediction and reconstruction of future and missing unobservable modified Weibull lifetime based on generalized order statistics

Directory of Open Access Journals (Sweden)

Amany E. Aly

2016-04-01

Full Text Available When a system consisting of independent components of the same type, some appropriate actions may be done as soon as a portion of them have failed. It is, therefore, important to be able to predict later failure times from earlier ones. One of the well-known failure distributions commonly used to model component life, is the modified Weibull distribution (MWD. In this paper, two pivotal quantities are proposed to construct prediction intervals for future unobservable lifetimes based on generalized order statistics (gos from MWD. Moreover, a pivotal quantity is developed to reconstruct missing observations at the beginning of experiment. Furthermore, Monte Carlo simulation studies are conducted and numerical computations are carried out to investigate the efficiency of presented results. Finally, two illustrative examples for real data sets are analyzed.

The effect of wall thickness distribution on mechanical reliability and strength in unidirectional porous ceramics

Science.gov (United States)

Seuba, Jordi; Deville, Sylvain; Guizard, Christian; Stevenson, Adam J.

2016-01-01

Macroporous ceramics exhibit an intrinsic strength variability caused by the random distribution of defects in their structure. However, the precise role of microstructural features, other than pore volume, on reliability is still unknown. Here, we analyze the applicability of the Weibull analysis to unidirectional macroporous yttria-stabilized-zirconia (YSZ) prepared by ice-templating. First, we performed crush tests on samples with controlled microstructural features with the loading direction parallel to the porosity. The compressive strength data were fitted using two different fitting techniques, ordinary least squares and Bayesian Markov Chain Monte Carlo, to evaluate whether Weibull statistics are an adequate descriptor of the strength distribution. The statistical descriptors indicated that the strength data are well described by the Weibull statistical approach, for both fitting methods used. Furthermore, we assess the effect of different microstructural features (volume, size, densification of the walls, and morphology) on Weibull modulus and strength. We found that the key microstructural parameter controlling reliability is wall thickness. In contrast, pore volume is the main parameter controlling the strength. The highest Weibull modulus (?) and mean strength (198.2 MPa) were obtained for the samples with the smallest and narrowest wall thickness distribution (3.1 ?m) and lower pore volume (54.5%).

THE COMPARATIVE ANALYSIS OF TWO DIFFERENT STATISTICAL DISTRIBUTIONS USED TO ESTIMATE THE WIND ENERGY POTENTIAL

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Mehmet KURBAN

2007-01-01

Full Text Available In this paper, the wind energy potential of the region is analyzed with Weibull and Reyleigh statistical distribution functions by using the wind speed data measured per 15 seconds in July, August, September, and October of 2005 at 10 m height of 30-m observation pole in the wind observation station constructed in the coverage of the scientific research project titled "The Construction of Hybrid (Wind-Solar Power Plant Model by Determining the Wind and Solar Potential in the Iki Eylul Campus of A.U." supported by Anadolu University. The Maximum likelihood method is used for finding the parameters of these distributions. The conclusion of the analysis for the months taken represents that the Weibull distribution models the wind speeds better than the Rayleigh distribution. Furthermore, the error rate in the monthly values of power density computed by using the Weibull distribution is smaller than the values by Rayleigh distribution.

O modelo q-weibull em confiabilidade, árvores de falha dinâmicas e implementação de manutenção

OpenAIRE

Assis, Edilson Machado de

2013-01-01

A distribuição q-Weibull foi aplicada em análise de con abilidade. Trata-se de uma generalização com quatro parâmetros de uma distribuição amplamente utilizada em con- abilidade, a distribuição Weibull, que possui três parâmetros. A distribuição Weibull é baseada na função exponencial do negativo de uma potência. A distribuição q-Weibull utiliza uma generalização da função exponencial, chamada q-exponencial, que apresenta o comportamento assintótico a uma lei de potência e recupe...

The Level of Calculation Errors in the Case of Using the Weibull Distribution for Estimating the Eolian Potential According to the Real Potential Based on Effective Measurements of the Weather Characteristics

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Ioan Ion

2011-09-01

Full Text Available The management of an investment program in wind power generators must consider the proper evaluation of the possibilities offered by the location where the park will be disposed and will operate: the available existing electric networks, access roads, the shape of relief, climate, extreme weather phenomena, the average wind speed, etc. Among the items listed above, the most important is wind potential of the area, quantified, measured mainly by multi-annual average wind speed. Evaluation, without special measurements, can be done based on general information such as measurements obtained from meteorological stations, using Weibull distribution for wind speed. When using the weather characteristics measurement results, the evaluation is closer to real multi- annual potential.

Modelling Wind for Wind Farm Layout Optimization Using Joint Distribution of Wind Speed and Wind Direction

OpenAIRE

Ju Feng; Wen Zhong Shen

2015-01-01

Reliable wind modelling is of crucial importance for wind farm development. The common practice of using sector-wise Weibull distributions has been found inappropriate for wind farm layout optimization. In this study, we propose a simple and easily implementable method to construct joint distributions of wind speed and wind direction, which is based on the parameters of sector-wise Weibull distributions and interpolations between direction sectors. It is applied to the wind measurement data a...

Comparison of Weibull strength parameters from flexure and spin tests of brittle materials

Science.gov (United States)

Holland, Frederic A., Jr.; Zaretsky, Erwin V.

1991-01-01

Fracture data from five series of four point bend tests of beam and spin tests of flat annular disks were reanalyzed. Silicon nitride and graphite were the test materials. The experimental fracture strengths of the disks were compared with the predicted strengths based on both volume flaw and surface flaw analyses of four point bend data. Volume flaw analysis resulted in a better correlation between disks and beams in three of the five test series than did surface flaw analysis. The Weibull (moduli) and characteristic gage strengths for the disks and beams were also compared. Differences in the experimental Weibull slopes were not statistically significant. It was shown that results from the beam tests can predict the fracture strength of rotating disks.

Impact of Blending on Strength Distribution of Ambient Cured Metakaolin and Palm Oil Fuel Ash Based Geopolymer Mortar

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Taliat Ola Yusuf

2014-01-01

Full Text Available This paper investigates the influence of blending of metakaolin with silica rich palm oil fuel ash (POFA on the strength distribution of geopolymer mortar. The broadness of strength distribution of quasi-brittle to brittle materials depends strongly on the existence of flaws such as voids, microcracks, and impurities in the material. Blending of materials containing alumina and silica with the objective of improving the performance of geopolymer makes comprehensive characterization necessary. The Weibull distribution is used to study the strength distribution and the reliability of geopolymer mortar specimens prepared from 100% metakaolin, 50% and 70% palm and cured under ambient condition. Mortar prisms and cubes were used to test the materials in flexure and compression, respectively, at 28 days and the results were analyzed using Weibull distribution. In flexure, Weibull modulus increased with POFA replacement, indicating reduced broadness of strength distribution from an increased homogeneity of the material. Modulus, however, decreased with increase in replacement of POFA in the specimens tested under compression. It is concluded that Weibull distribution is suitable for analyses of the blended geopolymer system. While porous microstructure is mainly responsible for flexural failure, heterogeneity of reaction relics is responsible for the compression failure.

Reliability demonstration test for load-sharing systems with exponential and Weibull components.

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Jianyu Xu

Full Text Available Conducting a Reliability Demonstration Test (RDT is a crucial step in production. Products are tested under certain schemes to demonstrate whether their reliability indices reach pre-specified thresholds. Test schemes for RDT have been studied in different situations, e.g., lifetime testing, degradation testing and accelerated testing. Systems designed with several structures are also investigated in many RDT plans. Despite the availability of a range of test plans for different systems, RDT planning for load-sharing systems hasn't yet received the attention it deserves. In this paper, we propose a demonstration method for two specific types of load-sharing systems with components subject to two distributions: exponential and Weibull. Based on the assumptions and interpretations made in several previous works on such load-sharing systems, we set the mean time to failure (MTTF of the total system as the demonstration target. We represent the MTTF as a summation of mean time between successive component failures. Next, we introduce generalized test statistics for both the underlying distributions. Finally, RDT plans for the two types of systems are established on the basis of these test statistics.

Modified Weibull theory and stress-concentration factors of polycrystalline graphite

International Nuclear Information System (INIS)

Ho, F.H.

1980-12-01

Stress concentration factors (SCF) due to geometric discontinuities in graphite specimens are observed to be much less than the theoretical SCF in an elastic material. In fact, the experimental SCF is always less than two and sometimes even less than one. A four parameter Weibull theory which recognizes the grain size effect is found to give an adequate explanation of the above observed discrepancies

Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications

KAUST Repository

Oubei, Hassan M.

2017-12-13

Recent advances in underwater wireless optical communications necessitate a better understanding of the underwater channel. We propose the Weibull model to characterize the fading of salinity induced turbulent underwater wireless optical channels. The model shows an excellent agreement with the measured data under all channel conditions.

Foam-forming properties of Ilex paraguariensis (mate saponin: foamability and foam lifetime analysis by Weibull equation

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Janine Treter

2010-01-01

Full Text Available Saponins are natural soaplike foam-forming compounds widely used in foods, cosmetic and pharmaceutical preparations. In this work foamability and foam lifetime of foams obtained from Ilex paraguariensis unripe fruits were analyzed. Polysorbate 80 and sodium dodecyl sulfate were used as reference surfactants. Aiming a better data understanding a linearized 4-parameters Weibull function was proposed. The mate hydroethanolic extract (ME and a mate saponin enriched fraction (MSF afforded foamability and foam lifetime comparable to the synthetic surfactants. The linearization of the Weibull equation allowed the statistical comparison of foam decay curves, improving former mathematical approaches.

Likelihood inference for COM-Poisson cure rate model with interval-censored data and Weibull lifetimes.

Science.gov (United States)

Pal, Suvra; Balakrishnan, N

2017-10-01

In this paper, we consider a competing cause scenario and assume the number of competing causes to follow a Conway-Maxwell Poisson distribution which can capture both over and under dispersion that is usually encountered in discrete data. Assuming the population of interest having a component cure and the form of the data to be interval censored, as opposed to the usually considered right-censored data, the main contribution is in developing the steps of the expectation maximization algorithm for the determination of the maximum likelihood estimates of the model parameters of the flexible Conway-Maxwell Poisson cure rate model with Weibull lifetimes. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination within the Conway-Maxwell Poisson distribution is addressed using the likelihood ratio test and information-based criteria to select a suitable competing cause distribution that provides the best fit to the data. A simulation study is also carried out to demonstrate the loss in efficiency when selecting an improper competing cause distribution which justifies the use of a flexible family of distributions for the number of competing causes. Finally, the proposed methodology and the flexibility of the Conway-Maxwell Poisson distribution are illustrated with two known data sets from the literature: smoking cessation data and breast cosmesis data.

Development of a Weibull model of cleavage fracture toughness for shallow flaws in reactor pressure vessel material

Energy Technology Data Exchange (ETDEWEB)

Bass, B.R.; Williams, P.T.; McAfee, W.J.; Pugh, C.E. [Oak Ridge National Lab., Heavy-Section Steel Technology Program, Oak Ridge, TN (United States)

2001-07-01

A primary objective of the United States Nuclear Regulatory Commission (USNRC) -sponsored Heavy-Section Steel Technology (HSST) Program is to develop and validate technology applicable to quantitative assessments of fracture prevention margins in nuclear reactor pressure vessels (RPVs) containing flaws and subjected to service-induced material toughness degradation. This paper describes an experimental/analytical program for the development of a Weibull statistical model of cleavage fracture toughness for applications to shallow surface-breaking and embedded flaws in RPV materials subjected to multi-axial loading conditions. The experimental part includes both material characterization testing and larger fracture toughness experiments conducted using a special-purpose cruciform beam specimen developed by Oak Ridge National Laboratory for applying biaxial loads to shallow cracks. Test materials (pressure vessel steels) included plate product forms (conforming to ASTM A533 Grade B Class 1 specifications) and shell segments procured from a pressurized-water reactor vessel intended for a nuclear power plant. Results from tests performed on cruciform specimens demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower-transition temperature region. A local approach methodology based on a three-parameter Weibull model was developed to correlate these experimentally-observed biaxial effects on fracture toughness. The Weibull model, combined with a new hydrostatic stress criterion in place of the more commonly used maximum principal stress in the kernel of the Weibull stress integral definition, is shown to provide a scaling mechanism between uniaxial and biaxial loading states for 2-dimensional flaws located in the A533-B plate material. The Weibull stress density was introduced as a matrice for identifying regions along a semi-elliptical flaw front that have a higher probability of cleavage initiation. Cumulative

Development of a Weibull model of cleavage fracture toughness for shallow flaws in reactor pressure vessel material

International Nuclear Information System (INIS)

Bass, B.R.; Williams, P.T.; McAfee, W.J.; Pugh, C.E.

2001-01-01

A primary objective of the United States Nuclear Regulatory Commission (USNRC) -sponsored Heavy-Section Steel Technology (HSST) Program is to develop and validate technology applicable to quantitative assessments of fracture prevention margins in nuclear reactor pressure vessels (RPVs) containing flaws and subjected to service-induced material toughness degradation. This paper describes an experimental/analytical program for the development of a Weibull statistical model of cleavage fracture toughness for applications to shallow surface-breaking and embedded flaws in RPV materials subjected to multi-axial loading conditions. The experimental part includes both material characterization testing and larger fracture toughness experiments conducted using a special-purpose cruciform beam specimen developed by Oak Ridge National Laboratory for applying biaxial loads to shallow cracks. Test materials (pressure vessel steels) included plate product forms (conforming to ASTM A533 Grade B Class 1 specifications) and shell segments procured from a pressurized-water reactor vessel intended for a nuclear power plant. Results from tests performed on cruciform specimens demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower-transition temperature region. A local approach methodology based on a three-parameter Weibull model was developed to correlate these experimentally-observed biaxial effects on fracture toughness. The Weibull model, combined with a new hydrostatic stress criterion in place of the more commonly used maximum principal stress in the kernel of the Weibull stress integral definition, is shown to provide a scaling mechanism between uniaxial and biaxial loading states for 2-dimensional flaws located in the A533-B plate material. The Weibull stress density was introduced as a matrice for identifying regions along a semi-elliptical flaw front that have a higher probability of cleavage initiation. Cumulative

A study of optimization problem for amplify-and-forward relaying over weibull fading channels

KAUST Repository

Ikki, Salama Said; Aissa, Sonia

2010-01-01

This paper addresses the power allocation and relay positioning problems in amplify-and-forward cooperative networks operating in Weibull fading environments. We study adaptive power allocation (PA) with fixed relay location, optimal relay location

Assessing a Tornado Climatology from Global Tornado Intensity Distributions

OpenAIRE

Feuerstein, B.; Dotzek, N.; Grieser, J.

2005-01-01

Recent work demonstrated that the shape of tornado intensity distributions from various regions worldwide is well described by Weibull functions. This statistical modeling revealed a strong correlation between the fit parameters c for shape and b for scale regardless of the data source. In the present work it is shown that the quality of the Weibull fits is optimized if only tornado reports of F1 and higher intensity are used and that the c–b correlation does indeed reflect a universal featur...

Two sample Bayesian prediction intervals for order statistics based on the inverse exponential-type distributions using right censored sample

Directory of Open Access Journals (Sweden)

M.M. Mohie El-Din

2011-10-01

Full Text Available In this paper, two sample Bayesian prediction intervals for order statistics (OS are obtained. This prediction is based on a certain class of the inverse exponential-type distributions using a right censored sample. A general class of prior density functions is used and the predictive cumulative function is obtained in the two samples case. The class of the inverse exponential-type distributions includes several important distributions such the inverse Weibull distribution, the inverse Burr distribution, the loglogistic distribution, the inverse Pareto distribution and the inverse paralogistic distribution. Special cases of the inverse Weibull model such as the inverse exponential model and the inverse Rayleigh model are considered.

Probability distribution of machining center failures

International Nuclear Information System (INIS)

Jia Yazhou; Wang Molin; Jia Zhixin

1995-01-01

Through field tracing research for 24 Chinese cutter-changeable CNC machine tools (machining centers) over a period of one year, a database of operation and maintenance for machining centers was built, the failure data was fitted to the Weibull distribution and the exponential distribution, the effectiveness was tested, and the failure distribution pattern of machining centers was found. Finally, the reliability characterizations for machining centers are proposed

Weibull Parameters Estimation Based on Physics of Failure Model

DEFF Research Database (Denmark)

Kostandyan, Erik; Sørensen, John Dalsgaard

2012-01-01

Reliability estimation procedures are discussed for the example of fatigue development in solder joints using a physics of failure model. The accumulated damage is estimated based on a physics of failure model, the Rainflow counting algorithm and the Miner’s rule. A threshold model is used...... for degradation modeling and failure criteria determination. The time dependent accumulated damage is assumed linearly proportional to the time dependent degradation level. It is observed that the deterministic accumulated damage at the level of unity closely estimates the characteristic fatigue life of Weibull...

A reappraisal of drug release laws using Monte Carlo simulations: the prevalence of the Weibull function.

Science.gov (United States)

Kosmidis, Kosmas; Argyrakis, Panos; Macheras, Panos

2003-07-01

To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

An appraisal of wind speed distribution prediction by soft computing methodologies: A comparative study

International Nuclear Information System (INIS)

Petković, Dalibor; Shamshirband, Shahaboddin; Anuar, Nor Badrul; Saboohi, Hadi; Abdul Wahab, Ainuddin Wahid; Protić, Milan; Zalnezhad, Erfan; Mirhashemi, Seyed Mohammad Amin

2014-01-01

Highlights: • Probabilistic distribution functions of wind speed. • Two parameter Weibull probability distribution. • To build an effective prediction model of distribution of wind speed. • Support vector regression application as probability function for wind speed. - Abstract: The probabilistic distribution of wind speed is among the more significant wind characteristics in examining wind energy potential and the performance of wind energy conversion systems. When the wind speed probability distribution is known, the wind energy distribution can be easily obtained. Therefore, the probability distribution of wind speed is a very important piece of information required in assessing wind energy potential. For this reason, a large number of studies have been established concerning the use of a variety of probability density functions to describe wind speed frequency distributions. Although the two-parameter Weibull distribution comprises a widely used and accepted method, solving the function is very challenging. In this study, the polynomial and radial basis functions (RBF) are applied as the kernel function of support vector regression (SVR) to estimate two parameters of the Weibull distribution function according to previously established analytical methods. Rather than minimizing the observed training error, SVR p oly and SVR r bf attempt to minimize the generalization error bound, so as to achieve generalized performance. According to the experimental results, enhanced predictive accuracy and capability of generalization can be achieved using the SVR approach compared to other soft computing methodologies

Lifetime modelling with a Weibull law: comparison of three Bayesian Methods

International Nuclear Information System (INIS)

Billy, F.; Remy, E.; Bousquet, N.; Celeux, G.

2006-01-01

For a nuclear power plant, being able to estimate the lifetime of important components is strategic. But data is usually insufficient to do so. Thus, it is relevant to use expertise, together with data, in order to assess the value of lifetime on the grounds of both sources. The Bayesian frame and the choice of a Weibull law to model the random time for replacement are relevant. They have been chosen for this article. Two indicators are computed : the mean lifetime of any component and the mean residual lifetime of a given component, after it has been controlled. Three different Bayesian methods are compared on three sets of data. The article shows that the three methods lead to coherent results and that uncertainties are strongly reduced. The method developed around PMC has two main advantages: it models a conditional dependence of the two parameters of the Weibull law, which enables more coherent results on the prior; it has a parameter that weights the strength of the expertise. This last point is very important to do lifetime assessments, because then, expertise is not used to increase too small samples as much as to do a real extrapolation, far beyond what data itself say. (authors)

The effect of core material, veneering porcelain, and fabrication technique on the biaxial flexural strength and weibull analysis of selected dental ceramics.

Science.gov (United States)

Lin, Wei-Shao; Ercoli, Carlo; Feng, Changyong; Morton, Dean

2012-07-01

The objective of this study was to compare the effect of veneering porcelain (monolithic or bilayer specimens) and core fabrication technique (heat-pressed or CAD/CAM) on the biaxial flexural strength and Weibull modulus of leucite-reinforced and lithium-disilicate glass ceramics. In addition, the effect of veneering technique (heat-pressed or powder/liquid layering) for zirconia ceramics on the biaxial flexural strength and Weibull modulus was studied. Five ceramic core materials (IPS Empress Esthetic, IPS Empress CAD, IPS e.max Press, IPS e.max CAD, IPS e.max ZirCAD) and three corresponding veneering porcelains (IPS Empress Esthetic Veneer, IPS e.max Ceram, IPS e.max ZirPress) were selected for this study. Each core material group contained three subgroups based on the core material thickness and the presence of corresponding veneering porcelain as follows: 1.5 mm core material only (subgroup 1.5C), 0.8 mm core material only (subgroup 0.8C), and 1.5 mm core/veneer group: 0.8 mm core with 0.7 mm corresponding veneering porcelain with a powder/liquid layering technique (subgroup 0.8C-0.7VL). The ZirCAD group had one additional 1.5 mm core/veneer subgroup with 0.7 mm heat-pressed veneering porcelain (subgroup 0.8C-0.7VP). The biaxial flexural strengths were compared for each subgroup (n = 10) according to ISO standard 6872:2008 with ANOVA and Tukey's post hoc multiple comparison test (p≤ 0.05). The reliability of strength was analyzed with the Weibull distribution. For all core materials, the 1.5 mm core/veneer subgroups (0.8C-0.7VL, 0.8C-0.7VP) had significantly lower mean biaxial flexural strengths (p Empress and e.max groups, regardless of core thickness and fabrication techniques. Comparing fabrication techniques, Empress Esthetic/CAD, e.max Press/CAD had similar biaxial flexural strength (p= 0.28 for Empress pair; p= 0.87 for e.max pair); however, e.max CAD/Press groups had significantly higher flexural strength (p Empress Esthetic/CAD groups. Monolithic core

Weibull aging models for the single protective channel unavailability analysis by the device of stages

International Nuclear Information System (INIS)

Nunes, M.E.C.; Noriega, H.C.; Melo, P.F.F.

1997-01-01

Among the features to take into account in the unavailability analysis of protective channels, there is one that plays a dominant role - that of considering the equipment aging. In this sense, the exponential failure model is not adequate, since some transition rates are no more constant. As a consequence, Markovian models cannot be used anymore. As an alternative, one may use the device of stages that allows for transforming a Non Markovian model into an equivalent Markovian one by insertion of a fictitious states set, called stages. For a given time-dependent transition rate, its failure density is analysed as to the best combination of exponential distributions and then the moments of the original distribution and those of the combination are matched to estimate the necessary parameters. In this paper, the aging of the protective channel is supposed to follow Weibull distributions. Typical means and variances for the times to failure are considered and combinations of stages are checked. Initial conditions features are discussed in connection with states that are fictitious and to check the validity of the developed models. Alternative solutions by the discretization of the failure rates are generated. The results obtained agree quite well. (author). 7 refs., 6 figs

Determining the distribution of fitness effects using a generalized Beta-Burr distribution.

Science.gov (United States)

Joyce, Paul; Abdo, Zaid

2017-07-12

In Beisel et al. (2007), a likelihood framework, based on extreme value theory (EVT), was developed for determining the distribution of fitness effects for adaptive mutations. In this paper we extend this framework beyond the extreme distributions and develop a likelihood framework for testing whether or not extreme value theory applies. By making two simple adjustments to the Generalized Pareto Distribution (GPD) we introduce a new simple five parameter probability density function that incorporates nearly every common (continuous) probability model ever used. This means that all of the common models are nested. This has important implications in model selection beyond determining the distribution of fitness effects. However, we demonstrate the use of this distribution utilizing likelihood ratio testing to evaluate alternative distributions to the Gumbel and Weibull domains of attraction of fitness effects. We use a bootstrap strategy, utilizing importance sampling, to determine where in the parameter space will the test be most powerful in detecting deviations from these domains and at what sample size, with focus on small sample sizes (n<20). Our results indicate that the likelihood ratio test is most powerful in detecting deviation from the Gumbel domain when the shape parameters of the model are small while the test is more powerful in detecting deviations from the Weibull domain when these parameters are large. As expected, an increase in sample size improves the power of the test. This improvement is observed to occur quickly with sample size n≥10 in tests related to the Gumbel domain and n≥15 in the case of the Weibull domain. This manuscript is in tribute to the contributions of Dr. Paul Joyce to the areas of Population Genetics, Probability Theory and Mathematical Statistics. A Tribute section is provided at the end that includes Paul's original writing in the first iterations of this manuscript. The Introduction and Alternatives to the GPD sections

Statistical distributions as applied to environmental surveillance data

International Nuclear Information System (INIS)

Speer, D.R.; Waite, D.A.

1975-09-01

Application of normal, log normal, and Weibull distributions to environmental surveillance data was investigated for approximately 300 nuclide-medium-year-location combinations. Corresponding W test calculations were made to determine the probability of a particular data set falling within the distribution of interest. Conclusions are drawn as to the fit of any data group to the various distributions. The significance of fitting statistical distributions to the data is discussed

Homogeneity and scale testing of generalized gamma distribution

International Nuclear Information System (INIS)

Stehlik, Milan

2008-01-01

The aim of this paper is to derive the exact distributions of the likelihood ratio tests of homogeneity and scale hypothesis when the observations are generalized gamma distributed. The special cases of exponential, Rayleigh, Weibull or gamma distributed observations are discussed exclusively. The photoemulsion experiment analysis and scale test with missing time-to-failure observations are present to illustrate the applications of methods discussed

Calculation of Wind Speeds for Return Period Using Weibull Parameter: A Case Study of Hanbit NPP Area

Energy Technology Data Exchange (ETDEWEB)

Lee, Jongk Uk; Lee, Kwan Hee; Kim, Sung Il; Yook, Dae Sik; Ahn, Sang Myeon [KINS, Daejeon (Korea, Republic of)

2016-05-15

Evaluation of the meteorological characteristics at the nuclear power plant and in the surrounding area should be performed in determining the site suitability for safe operation of the nuclear power plant. Under unexpected emergency condition, knowledge of meteorological information on the site area is important to provide the basis for estimating environmental impacts resulting from radioactive materials released in gaseous effluents during the accident condition. In the meteorological information, wind speed and direction are the important meteorological factors for examination of the safety analysis in the nuclear power plant area. Wind characteristics was analyzed on Hanbit NPP area. It was found that the Weibull parameters k and c vary 2.56 to 4.77 and 4.53 to 6.79 for directional wind speed distribution, respectively. Maximum wind frequency was NE and minimum was NNW.

A mixture of exponentials distribution for a simple and precise assessment of the volcanic hazard

Directory of Open Access Journals (Sweden)

A. T. Mendoza-Rosas

2009-03-01

Full Text Available The assessment of volcanic hazard is the first step for disaster mitigation. The distribution of repose periods between eruptions provides important information about the probability of new eruptions occurring within given time intervals. The quality of the probability estimate, i.e., of the hazard assessment, depends on the capacity of the chosen statistical model to describe the actual distribution of the repose times. In this work, we use a mixture of exponentials distribution, namely the sum of exponential distributions characterized by the different eruption occurrence rates that may be recognized inspecting the cumulative number of eruptions with time in specific VEI (Volcanic Explosivity Index categories. The most striking property of an exponential mixture density is that the shape of the density function is flexible in a way similar to the frequently used Weibull distribution, matching long-tailed distributions and allowing clustering and time dependence of the eruption sequence, with distribution parameters that can be readily obtained from the observed occurrence rates. Thus, the mixture of exponentials turns out to be more precise and much easier to apply than the Weibull distribution. We recommended the use of a mixture of exponentials distribution when regimes with well-defined eruption rates can be identified in the cumulative series of events. As an example, we apply the mixture of exponential distributions to the repose-time sequences between explosive eruptions of the Colima and Popocatépetl volcanoes, México, and compare the results obtained with the Weibull and other distributions.

Probability Distribution Function of the Upper Equatorial Pacific Current Speeds

National Research Council Canada - National Science Library

Chu, Peter C

2005-01-01

...), constructed from hourly ADCP data (1990-2007) at six stations for the Tropical Atmosphere Ocean project satisfies the two-parameter Weibull distribution reasonably well with different characteristics between El Nino and La Nina events...

Idealized models of the joint probability distribution of wind speeds

Science.gov (United States)

Monahan, Adam H.

2018-05-01

The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.

Use of finite mixture distribution models in the analysis of wind energy in the Canarian Archipelago

International Nuclear Information System (INIS)

Carta, Jose Antonio; Ramirez, Penelope

2007-01-01

The statistical characteristics of hourly mean wind speed data recorded at 16 weather stations located in the Canarian Archipelago are analyzed in this paper. As a result of this analysis we see that the typical two parameter Weibull wind speed distribution (W-pdf) does not accurately represent all wind regimes observed in that region. However, a Singly Truncated from below Normal Weibull mixture distribution (TNW-pdf) and a two component mixture Weibull distribution (WW-pdf) developed here do provide very good fits for both unimodal and bimodal wind speed frequency distributions observed in that region and offer less relative errors in determining the annual mean wind power density. The parameters of the distributions are estimated using the least squares method, which is resolved in this paper using the Levenberg-Marquardt algorithm. The suitability of the distributions is judged from the probability plot correlation coefficient plot R 2 , adjusted for degrees of freedom. Based on the results obtained, we conclude that the two mixture distributions proposed here provide very flexible models for wind speed studies and can be applied in a widespread manner to represent the wind regimes in the Canarian archipelago and in other regions with similar characteristics. The TNW-pdf takes into account the frequency of null winds, whereas the WW-pdf and W-pdf do not. It can, therefore, better represent wind regimes with high percentages of null wind speeds. However, calculation of the TNW-pdf is markedly slower

Utilization of Weibull equation to obtain soil-water diffusivity in horizontal infiltration

International Nuclear Information System (INIS)

Guerrini, I.A.

1982-06-01

Water movement was studied in horizontal infiltration experiments using laboratory columns of air-dry and homogeneous soil to obtain a simple and suitable equation for soil-water diffusivity. Many water content profiles for each one of the ten soil columns utilized were obtained through gamma-ray attenuation technique using a 137 Cs source. During the measurement of a particular water content profile, the soil column was held in the same position in order to measure changes in time and so to reduce the errors in water content determination. The Weibull equation utilized was excellent in fitting water content profiles experimental data. The use of an analytical function for ν, the Boltzmann variable, according to Weibull model, allowed to obtain a simple equation for soil water diffusivity. Comparisons among the equation here obtained for diffusivity and others solutions found in literature were made, and the unsuitability of a simple exponential variation of diffusivity with water content for the full range of the latter was shown. The necessity of admitting the time dependency for diffusivity was confirmed and also the possibility fixing that dependency on a well known value extended to generalized soil water infiltration studies was found. Finally, it was shown that the soil water diffusivity function given by the equation here proposed can be obtained just by the analysis of the wetting front advance as a function of time. (Author) [pt

SMALL-SCALE AND GLOBAL DYNAMOS AND THE AREA AND FLUX DISTRIBUTIONS OF ACTIVE REGIONS, SUNSPOT GROUPS, AND SUNSPOTS: A MULTI-DATABASE STUDY

Energy Technology Data Exchange (ETDEWEB)

Muñoz-Jaramillo, Andrés; Windmueller, John C.; Amouzou, Ernest C.; Longcope, Dana W. [Department of Physics, Montana State University, Bozeman, MT 59717 (United States); Senkpeil, Ryan R. [Department of Physics, Purdue University, West Lafayette, IN 47907 (United States); Tlatov, Andrey G. [Kislovodsk Mountain Astronomical Station of the Pulkovo Observatory, Kislovodsk 357700 (Russian Federation); Nagovitsyn, Yury A. [Pulkovo Astronomical Observatory, Russian Academy of Sciences, St. Petersburg 196140 (Russian Federation); Pevtsov, Alexei A. [National Solar Observatory, Sunspot, NM 88349 (United States); Chapman, Gary A.; Cookson, Angela M. [San Fernando Observatory, Department of Physics and Astronomy, California State University Northridge, Northridge, CA 91330 (United States); Yeates, Anthony R. [Department of Mathematical Sciences, Durham University, South Road, Durham DH1 3LE (United Kingdom); Watson, Fraser T. [National Solar Observatory, Tucson, AZ 85719 (United States); Balmaceda, Laura A. [Institute for Astronomical, Terrestrial and Space Sciences (ICATE-CONICET), San Juan (Argentina); DeLuca, Edward E. [Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 (United States); Martens, Petrus C. H., E-mail: munoz@solar.physics.montana.edu [Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30303 (United States)

2015-02-10

In this work, we take advantage of 11 different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by linear combination of Weibull and log-normal distributions—where a pure Weibull (log-normal) characterizes the distribution of structures with fluxes below (above) 10{sup 21}Mx (10{sup 22}Mx). Additionally, we demonstrate that the Weibull distribution shows the expected linear behavior of a power-law distribution (when extended to smaller fluxes), making our results compatible with the results of Parnell et al. We propose that this is evidence of two separate mechanisms giving rise to visible structures on the photosphere: one directly connected to the global component of the dynamo (and the generation of bipolar active regions), and the other with the small-scale component of the dynamo (and the fragmentation of magnetic structures due to their interaction with turbulent convection)

Distribution and Mobility of Wealth of Nations

NARCIS (Netherlands)

R. Paap (Richard); H.K. van Dijk (Herman)

2009-01-01

textabstractWe estimate the empirical bimodal cross-section distribution of real Gross Domestic Product per capita of 120 countries over the period 1960–1989 by a mixture of a Weibull and a truncated normal density. The components of the mixture represent a group of poor and a group of rich

Inference for exponentiated general class of distributions based on record values

Directory of Open Access Journals (Sweden)

Samah N. Sindi

2017-09-01

Full Text Available The main objective of this paper is to suggest and study a new exponentiated general class (EGC of distributions. Maximum likelihood, Bayesian and empirical Bayesian estimators of the parameter of the EGC of distributions based on lower record values are obtained. Furthermore, Bayesian prediction of future records is considered. Based on lower record values, the exponentiated Weibull distribution, its special cases of distributions and exponentiated Gompertz distribution are applied to the EGC of distributions.  

The stochastic distribution of available coefficient of friction on quarry tiles for human locomotion.

Science.gov (United States)

Chang, Wen-Ruey; Matz, Simon; Chang, Chien-Chi

2012-01-01

The available coefficient of friction (ACOF) for human locomotion is the maximum coefficient of friction that can be supported without a slip at the shoe and floor interface. A statistical model was introduced to estimate the probability of slip by comparing the ACOF with the required coefficient of friction, assuming that both coefficients have stochastic distributions. This paper presents an investigation of the stochastic distributions of the ACOF of quarry tiles under dry, water and glycerol conditions. One hundred friction measurements were performed on a walkway under the surface conditions of dry, water and 45% glycerol concentration. The Kolmogorov-Smirnov goodness-of-fit test was used to determine if the distribution of the ACOF was a good fit with the normal, log-normal and Weibull distributions. The results indicated that the ACOF appears to fit the normal and log-normal distributions better than the Weibull distribution for the water and glycerol conditions. However, no match was found between the distribution of ACOF under the dry condition and any of the three continuous distributions evaluated. Based on limited data, a normal distribution might be more appropriate due to its simplicity, practicality and familiarity among the three distributions evaluated.

Fitting Statistical Distributions Functions on Ozone Concentration Data at Coastal Areas

International Nuclear Information System (INIS)

Muhammad Yazid Nasir; Nurul Adyani Ghazali; Muhammad Izwan Zariq Mokhtar; Norhazlina Suhaimi

2016-01-01

Ozone is known as one of the pollutant that contributes to the air pollution problem. Therefore, it is important to carry out the study on ozone. The objective of this study is to find the best statistical distribution for ozone concentration. There are three distributions namely Inverse Gaussian, Weibull and Lognormal were chosen to fit one year hourly average ozone concentration data in 2010 at Port Dickson and Port Klang. Maximum likelihood estimation (MLE) method was used to estimate the parameters to develop the probability density function (PDF) graph and cumulative density function (CDF) graph. Three performance indicators (PI) that are normalized absolute error (NAE), prediction accuracy (PA), and coefficient of determination (R 2 ) were used to determine the goodness-of-fit criteria of the distribution. Result shows that Weibull distribution is the best distribution with the smallest error measure value (NAE) at Port Klang and Port Dickson is 0.08 and 0.31, respectively. The best score for highest adequacy measure (PA: 0.99) with the value of R 2 is 0.98 (Port Klang) and 0.99 (Port Dickson). These results provide useful information to local authorities for prediction purpose. (author)

Fitting diameter distribution models to data from forest inventories with concentric plot design

Directory of Open Access Journals (Sweden)

Nikos Nanos

2017-10-01

Research highlights:We designed a new method to fit the Weibull distribution to forest inventory data from concentric plots that achieves high accuracy and precision in parameter estimates regardless of the within-plot spatial tree pattern.

Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data

International Nuclear Information System (INIS)

Zhang, L.F.; Xie, M.; Tang, L.C.

2006-01-01

Estimation of the Weibull shape parameter is important in reliability engineering. However, commonly used methods such as the maximum likelihood estimation (MLE) and the least squares estimation (LSE) are known to be biased. Bias correction methods for MLE have been studied in the literature. This paper investigates the methods for bias correction when model parameters are estimated with LSE based on probability plot. Weibull probability plot is very simple and commonly used by practitioners and hence such a study is useful. The bias of the LS shape parameter estimator for multiple censored data is also examined. It is found that the bias can be modeled as the function of the sample size and the censoring level, and is mainly dependent on the latter. A simple bias function is introduced and bias correcting formulas are proposed for both complete and censored data. Simulation results are also presented. The bias correction methods proposed are very easy to use and they can typically reduce the bias of the LSE of the shape parameter to less than half percent

Robust D-optimal designs under correlated error, applicable invariantly for some lifetime distributions

International Nuclear Information System (INIS)

Das, Rabindra Nath; Kim, Jinseog; Park, Jeong-Soo

2015-01-01

In quality engineering, the most commonly used lifetime distributions are log-normal, exponential, gamma and Weibull. Experimental designs are useful for predicting the optimal operating conditions of the process in lifetime improvement experiments. In the present article, invariant robust first-order D-optimal designs are derived for correlated lifetime responses having the above four distributions. Robust designs are developed for some correlated error structures. It is shown that robust first-order D-optimal designs for these lifetime distributions are always robust rotatable but the converse is not true. Moreover, it is observed that these designs depend on the respective error covariance structure but are invariant to the above four lifetime distributions. This article generalizes the results of Das and Lin [7] for the above four lifetime distributions with general (intra-class, inter-class, compound symmetry, and tri-diagonal) correlated error structures. - Highlights: • This paper presents invariant robust first-order D-optimal designs under correlated lifetime responses. • The results of Das and Lin [7] are extended for the four lifetime (log-normal, exponential, gamma and Weibull) distributions. • This paper also generalizes the results of Das and Lin [7] to more general correlated error structures

The Weibull probabilities analysis on the single kenaf fiber

Science.gov (United States)

Ibrahim, I.; Sarip, S.; Bani, N. A.; Ibrahim, M. H.; Hassan, M. Z.

2018-05-01

Kenaf fiber has a great potential to be replaced with the synthetic composite due to their advantages such as environmentally friendly and outstanding performance. However, the main issue of this natural fiber that to be used in structural composite is inconsistency of their mechanical properties. Here, the influence of the gage length on the mechanical properties of single kenaf fiber was evaluated. This fiber was tested using the Universal testing machine at a loading rate of 1mm per min following ASTM D3822 standard. In this study, the different length of treated fiber including 20, 30 and 40mm were being tested. Following, Weibull probabilities analysis was used to characterize the tensile strength and Young modulus of kenaf fiber. The predicted average tensile strength from this approach is in good agreement with experimental results for the obtained parameter.

Evaluación poscosecha y estimación de vida útil de guayaba fresca utilizando el modelo de Weibull Postharvest evaluation and estimate of shelf-life of fresh guava using the Weibull model

Directory of Open Access Journals (Sweden)

Carlos García Mogollón

2010-07-01

Full Text Available La guayaba (Psidium guajava L. es una fruta tropical susceptible de sufrir alteraciones indeseables que afectan su vida útil debido a condiciones inadecuadas de almacenamiento y acondicionamiento. En este trabajo se estimó la vida útil de guayaba en fresco utilizando el modelo probabilístico de Weibull y se valuó la calidad de los frutos durante almacenamiento en diferentes condiciones de temperatura y empaque. La evaluación poscosecha se hizo por 15 días con guayabas variedad regional roja. Se utilizó un dise&#ntilde;o completamente al azar con arreglo factorial consistente en tres factores: tiempo de almacenamiento con seis niveles (0, 3, 6, 9, 12 y 15 días, temperatura de almacenamiento con dos niveles: ambiente (37 °C y humedad relativa (HR entre 85 y 90% y refrigeración (9±2 °C y HR de 85 - 90%; dos tipo de empaques: bandeja de poliestireno con film plástico de PVC y 'foil' de aluminio. Durante la evaluación sensorial en el periodo de almacenamiento se usó una escala estructurada de tres puntos grado de satisfacción. El modelo de Weibull demostró ser adecuado para predecir la vida útil de la guayaba fresca basados en los criterios de ajustes, límites de confianza de aceptación y fallo. Durante el periodo de almacenamiento se observó que el factor tiempo, la temperatura y el tipo de empaque tienen un efecto estadístico significativo (P Guava is a tropical fruit susceptible to undesirable alterations that affect the shelf-life due to inadequate conditions of storage and packing. In this work the shelf-life of guava in fresh using the probabilistic model of Weibull was considered and the quality of the fruits was estimated during storage to different conditions of temperature and packing. The postharvest evaluation was made during 15 days with guavas variety `Red Regional´. The completely randomized design and factorial design with 3 factors: storage time with 6 levels (0, 3, 6, 9, 12, 15 days, storage temperature with

Fast Reliability Assessing Method for Distribution Network with Distributed Renewable Energy Generation

Science.gov (United States)

Chen, Fan; Huang, Shaoxiong; Ding, Jinjin; Ding, Jinjin; Gao, Bo; Xie, Yuguang; Wang, Xiaoming

2018-01-01

This paper proposes a fast reliability assessing method for distribution grid with distributed renewable energy generation. First, the Weibull distribution and the Beta distribution are used to describe the probability distribution characteristics of wind speed and solar irradiance respectively, and the models of wind farm, solar park and local load are built for reliability assessment. Then based on power system production cost simulation probability discretization and linearization power flow, a optimal power flow objected with minimum cost of conventional power generation is to be resolved. Thus a reliability assessment for distribution grid is implemented fast and accurately. The Loss Of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) are selected as the reliability index, a simulation for IEEE RBTS BUS6 system in MATLAB indicates that the fast reliability assessing method calculates the reliability index much faster with the accuracy ensured when compared with Monte Carlo method.

Statistical analysis of the distribution of critical current and the correlation of n value to the critical current of bent Bi2223 composite tape

International Nuclear Information System (INIS)

Ochiai, S; Matsubayashi, H; Okuda, H; Osamura, K; Otto, A; Malozemoff, A

2009-01-01

Distributions of local and overall critical currents and correlation of n value to the critical current of bent Bi2223 composite tape were studied from the statistical viewpoint. The data of the local and overall transport critical currents and n values of the Bi2223 composite tape specimens were collected experimentally for a wide range of bending strain (0-1.1%) by using the specimens, designed so as to characterize the local and overall critical currents and n values. The measured local and overall critical currents were analyzed with various types of Weibull distribution function. Which of the Weibull distribution functions is suitable for the description of the distribution of local and overall critical currents at each bending strain, and also how much the Weibull parameter values characterizing the distribution vary with bending strain, were revealed. Then we attempted to reproduce the overall critical current distribution and correlation of the overall n value to the overall critical current from the distribution of local critical currents and the correlation of the local n value to the local critical current by a Monte Carlo simulation. The measured average values of critical current and n value at each bending strain and the correlation of n value to critical current were reproduced well by the present simulation, while the distribution of critical current values was reproduced fairly well but not fully. The reason for this is discussed.

On Selection of the Probability Distribution for Representing the Maximum Annual Wind Speed in East Cairo, Egypt

International Nuclear Information System (INIS)

El-Shanshoury, Gh. I.; El-Hemamy, S.T.

2013-01-01

The main objective of this paper is to identify an appropriate probability model and best plotting position formula which represent the maximum annual wind speed in east Cairo. This model can be used to estimate the extreme wind speed and return period at a particular site as well as to determine the radioactive release distribution in case of accident occurrence at a nuclear power plant. Wind speed probabilities can be estimated by using probability distributions. An accurate determination of probability distribution for maximum wind speed data is very important in expecting the extreme value . The probability plots of the maximum annual wind speed (MAWS) in east Cairo are fitted to six major statistical distributions namely: Gumbel, Weibull, Normal, Log-Normal, Logistic and Log- Logistic distribution, while eight plotting positions of Hosking and Wallis, Hazen, Gringorten, Cunnane, Blom, Filliben, Benard and Weibull are used for determining exceedance of their probabilities. A proper probability distribution for representing the MAWS is selected by the statistical test criteria in frequency analysis. Therefore, the best plotting position formula which can be used to select appropriate probability model representing the MAWS data must be determined. The statistical test criteria which represented in: the probability plot correlation coefficient (PPCC), the root mean square error (RMSE), the relative root mean square error (RRMSE) and the maximum absolute error (MAE) are used to select the appropriate probability position and distribution. The data obtained show that the maximum annual wind speed in east Cairo vary from 44.3 Km/h to 96.1 Km/h within duration of 39 years . Weibull plotting position combined with Normal distribution gave the highest fit, most reliable, accurate predictions and determination of the wind speed in the study area having the highest value of PPCC and lowest values of RMSE, RRMSE and MAE

Determination of Reliability Index and Weibull Modulus as a Measure of Hypereutectic Silumins Survival

OpenAIRE

J. Szymszal; J. Piątkowski; J. Przondziono

2007-01-01

The first part of the study describes the methods used to determine Weibull modulus and the related reliability index of hypereutectic silumins containing about 17% Si, assigned for manufacture of high-duty castings to be used in automotive applications and aviation. The second part of the study discusses the importance of chemical composition, including the additions of 3% Cu, 1,5% Ni and 1,5% Mg, while in the third part attention was focussed on the effect of process history, including moul...

Stability of the laws for the distribution of the cumulative failures in railway transport

OpenAIRE

Kirill VOYNOV

2008-01-01

There are very many different laws of distribution (for example), bellshaped (Gaussian) distribution, lognormal, Weibull distribution, exponential, uniform, Poisson’s, Student’s distributions and so on, which help to describe the real picture of failures with elements in various mechanical systems, in locomotives and carriages, too. To diminish the possibility of getting the rough error in the output of maths data treatment the new method is demonstrated in this article. The task is solved bo...

Introducing a system of wind speed distributions for modeling properties of wind speed regimes around the world

International Nuclear Information System (INIS)

Jung, Christopher; Schindler, Dirk; Laible, Jessica; Buchholz, Alexander

2017-01-01

Highlights: • Evaluation of statistical properties of 10,016 empirical wind speed distributions. • Analysis of the shape of empirical wind speed distributions by L-moment ratios. • Introduction of a new system of wind speed distributions (Swd). • Random forests classification of the most appropriate distribution. • Comprehensive goodness of Swd fit evaluation on a global scale. - Abstract: Accurate modeling of empirical wind speed distributions is a crucial step in the estimation of average wind turbine power output. For this purpose, the Weibull distribution has often been fitted to empirical wind speed distributions. However, the Weibull distribution has been found to be insufficient to reproduce many wind speed regimes existing around the world. Results from previous studies demonstrate that numerous one-component distributions as well as mixture distributions provide a better goodness-of-fit to empirical wind speed distributions than the Weibull distribution. Moreover, there is considerable interest to apply a single system of distributions that can be utilized to reproduce the large majority of near-surface wind speed regimes existing around the world. Therefore, a system of wind speed distributions was developed that is capable of reproducing the main characteristics of existing wind speed regimes. The proposed system consists of two one-component distributions (Kappa and Wakeby) and one mixture distribution (Burr-Generalized Extreme Value). A random forests classifier was trained in order to select the most appropriate of these three distributions for each of 10,016 globally distributed empirical wind speed distributions. The shape of the empirical wind speed distributions was described by L-moment ratios. The L-moment ratios were used as predictor variables for the random forests classifier. The goodness-of-fit of the system of wind speed distributions was evaluated according to eleven goodness-of-fit metrics, which were merged into one

Weibull statistics effective area and volume in the ball-on-ring testing method

DEFF Research Database (Denmark)

Frandsen, Henrik Lund

2014-01-01

The ball-on-ring method is together with other biaxial bending methods often used for measuring the strength of plates of brittle materials, because machining defects are remote from the high stresses causing the failure of the specimens. In order to scale the measured Weibull strength...... to geometries relevant for the application of the material, the effective area or volume for the test specimen must be evaluated. In this work analytical expressions for the effective area and volume of the ball-on-ring test specimen is derived. In the derivation the multiaxial stress field has been accounted...

Stand diameter distribution modelling and prediction based on Richards function.

Directory of Open Access Journals (Sweden)

Ai-guo Duan

Full Text Available The objective of this study was to introduce application of the Richards equation on modelling and prediction of stand diameter distribution. The long-term repeated measurement data sets, consisted of 309 diameter frequency distributions from Chinese fir (Cunninghamia lanceolata plantations in the southern China, were used. Also, 150 stands were used as fitting data, the other 159 stands were used for testing. Nonlinear regression method (NRM or maximum likelihood estimates method (MLEM were applied to estimate the parameters of models, and the parameter prediction method (PPM and parameter recovery method (PRM were used to predict the diameter distributions of unknown stands. Four main conclusions were obtained: (1 R distribution presented a more accurate simulation than three-parametric Weibull function; (2 the parameters p, q and r of R distribution proved to be its scale, location and shape parameters, and have a deep relationship with stand characteristics, which means the parameters of R distribution have good theoretical interpretation; (3 the ordinate of inflection point of R distribution has significant relativity with its skewness and kurtosis, and the fitted main distribution range for the cumulative diameter distribution of Chinese fir plantations was 0.4∼0.6; (4 the goodness-of-fit test showed diameter distributions of unknown stands can be well estimated by applying R distribution based on PRM or the combination of PPM and PRM under the condition that only quadratic mean DBH or plus stand age are known, and the non-rejection rates were near 80%, which are higher than the 72.33% non-rejection rate of three-parametric Weibull function based on the combination of PPM and PRM.

Progressive failure site generation in AlGaN/GaN high electron mobility transistors under OFF-state stress: Weibull statistics and temperature dependence

International Nuclear Information System (INIS)

Sun, Huarui; Bajo, Miguel Montes; Uren, Michael J.; Kuball, Martin

2015-01-01

Gate leakage degradation of AlGaN/GaN high electron mobility transistors under OFF-state stress is investigated using a combination of electrical, optical, and surface morphology characterizations. The generation of leakage “hot spots” at the edge of the gate is found to be strongly temperature accelerated. The time for the formation of each failure site follows a Weibull distribution with a shape parameter in the range of 0.7–0.9 from room temperature up to 120 °C. The average leakage per failure site is only weakly temperature dependent. The stress-induced structural degradation at the leakage sites exhibits a temperature dependence in the surface morphology, which is consistent with a surface defect generation process involving temperature-associated changes in the breakdown sites

Ajustes de funções de distribuição de probabilidade à radiação solar global no Estado do Rio Grande do Sul Adjustments of probability distribution functions to global solar radiation in Rio Grande do Sul State

Directory of Open Access Journals (Sweden)

Alberto Cargnelutti Filho

2004-12-01

Full Text Available O objetivo deste trabalho foi verificar o ajuste das séries de dados de radiação solar global média decendial, de 22 municípios do Estado do Rio Grande do Sul, às funções de distribuições de probabilidade normal, log-normal, gama, gumbel e weibull. Aplicou-se o teste de aderência de Kolmogorov-Smirnov, nas 792 séries de dados (22 municípios x 36 decêndios de radiação solar global média decendial, para verificar o ajuste dos dados às distribuições normal, log-normal, gama, gumbel e weibull, totalizando 3.960 testes. Os dados decendiais de radiação solar global média se ajustam às funções de distribuições de probabilidade normal, log-normal, gama, gumbel e weibull, e apresentam melhor ajuste à função de distribuição de probabilidade normal.The objective of this work was to verify the adjustment of data series for average global solar radiation to the normal, log-normal, gamma, gumbel and weibull probability distribution functions. Data were collected from 22 cities in Rio Grande do Sul State, Brazil. The Kolmogorov-Smirnov test was applied in the 792 series of data (22 localities x 36 periods of ten days of average global solar radiation to verify the adjustment of the data to the normal, log-normal, gamma, gumbel and weibull probability distribution functions, totalizing 3,960 tests. The data of average global solar radiation adjust to the normal, log-normal, gamma, gumbel and weibull probability distribution functions, and present a better adjustment to the normal probability function.

Stability of the laws for the distribution of the cumulative failures in railway transport

Directory of Open Access Journals (Sweden)

Kirill VOYNOV

2008-01-01

Full Text Available There are very many different laws of distribution (for example, bellshaped (Gaussian distribution, lognormal, Weibull distribution, exponential, uniform, Poisson’s, Student’s distributions and so on, which help to describe the real picture of failures with elements in various mechanical systems, in locomotives and carriages, too. To diminish the possibility of getting the rough error in the output of maths data treatment the new method is demonstrated in this article. The task is solved both to the discrete, and to the continuous distributions.

Statistical Distribution of Fatigue Life for Cast TiAl Alloy

Directory of Open Access Journals (Sweden)

WAN Wenjuan

2016-08-01

Full Text Available Statistic distribution of fatigue life data and its controls of cast Ti-47.5Al-2.5V-1.0Cr-0.2Zr (atom fraction/% alloy were investigated. Fatigue tests were operated by means of load-controlled rotating bending fatigue tests (R=-1 performed at a frequency of 100 Hz at 750 ℃ in air. The fracture mechanism was analyzed by observing the fracture surface morphologies through scanning electron microscope,and the achieved fatigue life data were analyzed by Weibull statistics. The results show that the fatigue life data present a remarkable scatter ranging from 103 to 106 cycles, and distribute mainly in short and long life regime. The reason for this phenomenon is that the fatigue crack initiators are different with different specimens. The crack initiators for short-life specimens are caused by shrinkage porosity, and for long-life ones are caused by bridged porosity interface and soft-oriented lamellar interface. Based on the observation results of fracture surface, two-parameter Weibull distribution model for fatigue life data can be used for the prediction of fatigue life at a certain failure probability. It has also shown that the shrinkage porosity causes the most detrimental effect to fatigue life.

A statistical investigation of wind characteristics and wind energy potential based on the Weibull and Rayleigh models in Rwanda

Energy Technology Data Exchange (ETDEWEB)

Safari, Bonfils; Gasore, Jimmy [Department of Physics, National University of Rwanda, P.O. Box 117, Huye, South Province (Rwanda)

2010-12-15

A wind energy system converts the kinetic energy of the wind into mechanical or electrical energy that can be harnessed for practical uses and transform the economy of rural areas where access to water and electricity is very restricted and industry is almost nonexistent in most of the developing countries like Rwanda. Assessing wind power potential for a location is an imperative requirement before making a decision for the installation of windmills or a wind electric generator and evaluating plans for relating projects. The aim of the present study was to evaluate the potential of wind resource in Rwanda and to constitute a database for the users of the wind power. A time series of hourly daily measured wind speed and wind direction for the period between 1974 and 1993 on five main Rwandan meteorological stations was provided by the National Meteorology Department. Statistical methods applying Weibull and Rayleigh distribution were presented to evaluate the wind speed characteristics and the wind power potential at a height of 10 m above ground level using hourly monthly average data. Those characteristics were extrapolated for higher levels in altitude. The results give a global picture of the distribution of the wind potential in different locations of Rwanda. (author)

Evaluation of wind power production prospective and Weibull parameter estimation methods for Babaurband, Sindh Pakistan

International Nuclear Information System (INIS)

Khahro, Shahnawaz Farhan; Tabbassum, Kavita; Soomro, Amir Mahmood; Dong, Lei; Liao, Xiaozhong

2014-01-01

Highlights: • Weibull scale and shape parameters are calculated using 5 numerical methods. • Yearly mean wind speed is 6.712 m/s at 80 m height with highest in May 9.595 m/s. • Yearly mean WPD is 310 W/m 2 and available energy density is 2716 kWh/m 2 at 80 m height. • Probability of higher wind speeds is more in spring and summer than in autumn and winter. • Estimated cost of per kWh of electricity from wind is calculated as 0.0263 US$/kWh. - Abstract: Pakistan is currently experiencing an acute shortage of energy and urgently needs new sources of affordable energy that could alleviate the misery of the energy starved masses. At present the government is increasing not only the conventional energy sources like hydel and thermal but also focusing on the immense potential of renewable energy sources like; solar, wind, biogas, waste-to-energy etc. The recent economic crisis worldwide, global warming and climate change have also emphasized the need for utilizing economic feasible energy sources having lowest carbon emissions. Wind energy, with its sustainability and low environmental impact, is highly prominent. The aim of this paper is to explore the wind power production prospective of one of the sites in south region of Pakistan. It is worth mentioning here that this type of detailed analysis is hardly done for any location in Pakistan. Wind power densities and frequency distributions of wind speed at four different altitudes along with estimated wind power expected to be generated through commercial wind turbines is calculated. Analysis and comparison of 5 numerical methods is presented in this paper to determine the Weibull scale and shape parameters for the available wind data. The yearly mean wind speed of the considered site is 6.712 m/s and has power density of 310 W/m 2 at 80 m height with high power density during April to August (highest in May with wind speed 9.595 m/s and power density 732 W/m 2 ). Economic evaluation, to exemplify feasibility

Modeling of speed distribution for mixed bicycle traffic flow

Directory of Open Access Journals (Sweden)

Cheng Xu

2015-11-01

Full Text Available Speed is a fundamental measure of traffic performance for highway systems. There were lots of results for the speed characteristics of motorized vehicles. In this article, we studied the speed distribution for mixed bicycle traffic which was ignored in the past. Field speed data were collected from Hangzhou, China, under different survey sites, traffic conditions, and percentages of electric bicycle. The statistics results of field data show that the total mean speed of electric bicycles is 17.09 km/h, 3.63 km/h faster and 27.0% higher than that of regular bicycles. Normal, log-normal, gamma, and Weibull distribution models were used for testing speed data. The results of goodness-of-fit hypothesis tests imply that the log-normal and Weibull model can fit the field data very well. Then, the relationships between mean speed and electric bicycle proportions were proposed using linear regression models, and the mean speed for purely electric bicycles or regular bicycles can be obtained. The findings of this article will provide effective help for the safety and traffic management of mixed bicycle traffic.

Approximation of the breast height diameter distribution of two-cohort stands by mixture models III Kernel density estimators vs mixture models

Science.gov (United States)

Rafal Podlaski; Francis A. Roesch

2014-01-01

Two-component mixtures of either the Weibull distribution or the gamma distribution and the kernel density estimator were used for describing the diameter at breast height (dbh) empirical distributions of two-cohort stands. The data consisted of study plots from the Å wietokrzyski National Park (central Poland) and areas close to and including the North Carolina section...

Modelling Wind for Wind Farm Layout Optimization Using Joint Distribution of Wind Speed and Wind Direction

DEFF Research Database (Denmark)

Feng, Ju; Shen, Wen Zhong

2015-01-01

Reliable wind modelling is of crucial importance for wind farm development. The common practice of using sector-wise Weibull distributions has been found inappropriate for wind farm layout optimization. In this study, we propose a simple and easily implementable method to construct joint distribu...

Statistical Evidence for the Preference of Frailty Distributions with Regularly-Varying-at-Zero Densities

DEFF Research Database (Denmark)

Missov, Trifon I.; Schöley, Jonas

to this criterion admissible distributions are, for example, the gamma, the beta, the truncated normal, the log-logistic and the Weibull, while distributions like the log-normal and the inverse Gaussian do not satisfy this condition. In this article we show that models with admissible frailty distributions...... and a Gompertz baseline provide a better fit to adult human mortality data than the corresponding models with non-admissible frailty distributions. We implement estimation procedures for mixture models with a Gompertz baseline and frailty that follows a gamma, truncated normal, log-normal, or inverse Gaussian...

Fitting diameter distribution models to data from forest inventories with concentric plot design

Energy Technology Data Exchange (ETDEWEB)

Nanos, N.; Sjöstedt de Luna, S.

2017-11-01

Aim: Several national forest inventories use a complex plot design based on multiple concentric subplots where smaller diameter trees are inventoried when lying in the smaller-radius subplots and ignored otherwise. Data from these plots are truncated with threshold (truncation) diameters varying according to the distance from the plot centre. In this paper we designed a maximum likelihood method to fit the Weibull diameter distribution to data from concentric plots. Material and methods: Our method (M1) was based on multiple truncated probability density functions to build the likelihood. In addition, we used an alternative method (M2) presented recently. We used methods M1 and M2 as well as two other reference methods to estimate the Weibull parameters in 40000 simulated plots. The spatial tree pattern of the simulated plots was generated using four models of spatial point patterns. Two error indices were used to assess the relative performance of M1 and M2 in estimating relevant stand-level variables. In addition, we estimated the Quadratic Mean plot Diameter (QMD) using Expansion Factors (EFs). Main results: Methods M1 and M2 produced comparable estimation errors in random and cluster tree spatial patterns. Method M2 produced biased parameter estimates in plots with inhomogeneous Poisson patterns. Estimation of QMD using EFs produced biased results in plots within inhomogeneous intensity Poisson patterns. Research highlights:We designed a new method to fit the Weibull distribution to forest inventory data from concentric plots that achieves high accuracy and precision in parameter estimates regardless of the within-plot spatial tree pattern.

Modeling the reliability and maintenance costs of wind turbines using Weibull analysis

Energy Technology Data Exchange (ETDEWEB)

Vachon, W.A. [W.A. Vachon & Associates, Inc., Manchester, MA (United States)

1996-12-31

A general description is provided of the basic mathematics and use of Weibull statistical models for modeling component failures and maintenance costs as a function of time. The applicability of the model to wind turbine components and subsystems is discussed with illustrative examples of typical component reliabilities drawn from actual field experiences. Example results indicate the dominant role of key subsystems based on a combination of their failure frequency and repair/replacement costs. The value of the model is discussed as a means of defining (1) maintenance practices, (2) areas in which to focus product improvements, (3) spare parts inventory, and (4) long-term trends in maintenance costs as an important element in project cash flow projections used by developers, investors, and lenders. 6 refs., 8 figs., 3 tabs.

Weibull Analysis of Electrical Breakdown Strength as an Effective Means of Evaluating Elastomer Thin Film Quality

DEFF Research Database (Denmark)

Silau, Harald; Stabell, Nicolai Bogø; Petersen, Frederik Riddersholm

2018-01-01

To realize the commercial potential of dielectric elastomers, reliable, large-scale film production is required. Ensuring proper mixing and subsequently avoiding demixing after, for example, pumping and coating of elastomer premix in an online process is not facile. Weibull analysis...... of the electrical breakdown strength of dielectric elastomer films is shown to be an effective means of evaluating the film quality. The analysis is shown to be capable of distinguishing between proper and improper mixing schemes where similar analysis of ultimate mechanical properties fails to distinguish....

Analysis of Statistical Distributions Used for Modeling Reliability and Failure Rate of Temperature Alarm Circuit

International Nuclear Information System (INIS)

EI-Shanshoury, G.I.

2011-01-01

Several statistical distributions are used to model various reliability and maintainability parameters. The applied distribution depends on the' nature of the data being analyzed. The presented paper deals with analysis of some statistical distributions used in reliability to reach the best fit of distribution analysis. The calculations rely on circuit quantity parameters obtained by using Relex 2009 computer program. The statistical analysis of ten different distributions indicated that Weibull distribution gives the best fit distribution for modeling the reliability of the data set of Temperature Alarm Circuit (TAC). However, the Exponential distribution is found to be the best fit distribution for modeling the failure rate

A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

Directory of Open Access Journals (Sweden)

Pelumi E. Oguntunde

2017-01-01

Full Text Available Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution.

Caracterização analítica e geométrica da metodologia geral de determinação de distribuições de Weibull para o regime eólico e suas aplicações Analytical and geometric characterization of general methodology of determination of Weibull distribution for wind regime and its applications

Directory of Open Access Journals (Sweden)

Luís R. A Gabriel Filho

2011-02-01

Full Text Available O regime eólico de uma região pode ser descrito por distribuição de frequências que fornecem informações e características extremamente necessárias para uma possível implantação de sistemas eólicos de captação de energia na região e consequentes aplicações no meio rural em regiões afastadas. Estas características, tais como a velocidade média anual, a variância das velocidades registradas e a densidade da potência eólica média horária, podem ser obtidas pela frequência de ocorrências de determinada velocidade, que por sua vez deve ser estudada através de expressões analíticas. A função analítica mais adequada para distribuições eólicas é a função de densidade de Weibull, que pode ser determinada por métodos numéricos e regressões lineares. O objetivo deste trabalho é caracterizar analítica e geometricamente todos os procedimentos metodológicos necessários para a realização de uma caracterização completa do regime eólico de uma região e suas aplicações na região de Botucatu - SP, visando a determinar o potencial energético para implementação de turbinas eólicas. Assim, foi possível estabelecer teoremas relacionados com a forma de caracterização do regime eólico, estabelecendo a metodologia concisa analiticamente para a definição dos parâmetros eólicos de qualquer região a ser estudada. Para o desenvolvimento desta pesquisa, utilizou-se um anemômetro da CAMPBELL.The wind regime of a region can be described by frequency distributions that provide information and features extremely necessary for a possible deployment of wind systems of energy capturing in the region and the resulting applications in rural areas in remote regions. These features, such as the annual average speed, variance of speed and hourly average of wind power density, can be obtained by the frequency of occurrences of certain speed, which in turn should be studied through analytical expressions. The analytic

Empleo de la función Weibull para evaluar la emergencia de las plántulas de Albizia lebbeck (L. Benth

Directory of Open Access Journals (Sweden)

Marlen Navarro

Full Text Available Con el objetivo de conocer el vigor de las semillas de Albizia lebbeck mediante la evaluación de la emergencia de plántulas, a través de la función Weibull modificada, se realizó la siembra en tres condiciones ambientales y en diferentes tiempos de almacenamiento de la semilla. El diseño fue completamente aleatorizado, con arreglo factorial. Se realizó análisis de varianza para los parámetros M (emergencia acumulada máxima, k (tasa de emergencia y Z (retraso para el inicio de la emergencia de la función Weibull modificada. A partir de los seis meses de iniciado el almacenamiento (44,1 % se observó la pérdida brusca del porcentaje de M en el vivero (A y ligeras variaciones en la cabina (C, en comparación con A y B (sombreador. El ámbito de dispersión del parámetro k osciló entre 0,4-2,6; 0,29-1,9 y 0,5-1,4 % emergencia d-1 para las evaluaciones realizadas en A, B y C, respectivamente. Del análisis de Z se interpretó que el tiempo para el inicio de la emergencia, sin distinción del ambiente de siembra, estuvo enmarcado entre los 3,0 y 7,3 días posteriores a la siembra. En el vivero a pleno sol, en la evaluación a 6 mdia (meses de iniciado el almacenamiento, se obtuvieron los mejores resultados de los parámetros biológicos de la ecuación de Weibull, lo cual permitió un análisis global que indicó un grado de vigor alto en las semillas de A. lebbeck, en comparación con las restantes evaluaciones

Effects of specimen size on the flexural strength and Weibull modulus of nuclear graphite IG-110, NBG-18, and PCEA

International Nuclear Information System (INIS)

Chi, Se-Hwan

2015-01-01

Changes in flexural strength and Weibull modulus due to specimen size were investigated for three nuclear graphite grades, IG-110, NBG-18, and PCEA, using four-point-1/3 point (4-1/3) loading with specimens of three different sizes: 3.18 (Thickness) × 6.35 (Width) × 50.8 (Length), 6.50 (T) × 12.0 (W) × 52.0 (L), 18.0 (T) × 16.0 (W) × 64 (L) (mm) (total: 210 specimens). Results showed some specimen size effects were grade dependent: While NBG-18 (a) showed rather significant specimen size effects (37% difference between the 3 T and 18 T), the differences in IG-110 and PCEA were 7.6–15%. The maximum differences in flexural strength due to specimen size were larger in the PCEA and NBG-18 having larger sized coke particles (medium grain size: >300 μm) than the IG-110 with super fine coke particle size (25 μm). The Weibull modulus showed a data population dependency, in that it decreased with increasing numbers of data used for modulus determination. A good correlation between the fracture surface roughness and the flexural strength was confirmed

WEIBULL MULTIPLICATIVE MODEL AND MACHINE LEARNING MODELS FOR FULL-AUTOMATIC DARK-SPOT DETECTION FROM SAR IMAGES

Directory of Open Access Journals (Sweden)

A. Taravat

2013-09-01

Full Text Available As a major aspect of marine pollution, oil release into the sea has serious biological and environmental impacts. Among remote sensing systems (which is a tool that offers a non-destructive investigation method, synthetic aperture radar (SAR can provide valuable synoptic information about the position and size of the oil spill due to its wide area coverage and day/night, and all-weather capabilities. In this paper we present a new automated method for oil-spill monitoring. A new approach is based on the combination of Weibull Multiplicative Model and machine learning techniques to differentiate between dark spots and the background. First, the filter created based on Weibull Multiplicative Model is applied to each sub-image. Second, the sub-image is segmented by two different neural networks techniques (Pulsed Coupled Neural Networks and Multilayer Perceptron Neural Networks. As the last step, a very simple filtering process is used to eliminate the false targets. The proposed approaches were tested on 20 ENVISAT and ERS2 images which contained dark spots. The same parameters were used in all tests. For the overall dataset, the average accuracies of 94.05 % and 95.20 % were obtained for PCNN and MLP methods, respectively. The average computational time for dark-spot detection with a 256 × 256 image in about 4 s for PCNN segmentation using IDL software which is the fastest one in this field at present. Our experimental results demonstrate that the proposed approach is very fast, robust and effective. The proposed approach can be applied to the future spaceborne SAR images.

Weibull Multiplicative Model and Machine Learning Models for Full-Automatic Dark-Spot Detection from SAR Images

Science.gov (United States)

Taravat, A.; Del Frate, F.

2013-09-01

As a major aspect of marine pollution, oil release into the sea has serious biological and environmental impacts. Among remote sensing systems (which is a tool that offers a non-destructive investigation method), synthetic aperture radar (SAR) can provide valuable synoptic information about the position and size of the oil spill due to its wide area coverage and day/night, and all-weather capabilities. In this paper we present a new automated method for oil-spill monitoring. A new approach is based on the combination of Weibull Multiplicative Model and machine learning techniques to differentiate between dark spots and the background. First, the filter created based on Weibull Multiplicative Model is applied to each sub-image. Second, the sub-image is segmented by two different neural networks techniques (Pulsed Coupled Neural Networks and Multilayer Perceptron Neural Networks). As the last step, a very simple filtering process is used to eliminate the false targets. The proposed approaches were tested on 20 ENVISAT and ERS2 images which contained dark spots. The same parameters were used in all tests. For the overall dataset, the average accuracies of 94.05 % and 95.20 % were obtained for PCNN and MLP methods, respectively. The average computational time for dark-spot detection with a 256 × 256 image in about 4 s for PCNN segmentation using IDL software which is the fastest one in this field at present. Our experimental results demonstrate that the proposed approach is very fast, robust and effective. The proposed approach can be applied to the future spaceborne SAR images.

Handling of computational in vitro/in vivo correlation problems by Microsoft Excel II. Distribution functions and moments.

Science.gov (United States)

Langenbucher, Frieder

2003-01-01

MS Excel is a useful tool to handle in vitro/in vivo correlation (IVIVC) distribution functions, with emphasis on the Weibull and the biexponential distribution, which are most useful for the presentation of cumulative profiles, e.g. release in vitro or urinary excretion in vivo, and differential profiles such as the plasma response in vivo. The discussion includes moments (AUC and mean) as summarizing statistics, and data-fitting algorithms for parameter estimation.

Multi-choice stochastic transportation problem involving general form of distributions.

Science.gov (United States)

Quddoos, Abdul; Ull Hasan, Md Gulzar; Khalid, Mohammad Masood

2014-01-01

Many authors have presented studies of multi-choice stochastic transportation problem (MCSTP) where availability and demand parameters follow a particular probability distribution (such as exponential, weibull, cauchy or extreme value). In this paper an MCSTP is considered where availability and demand parameters follow general form of distribution and a generalized equivalent deterministic model (GMCSTP) of MCSTP is obtained. It is also shown that all previous models obtained by different authors can be deduced with the help of GMCSTP. MCSTP with pareto, power function or burr-XII distributions are also considered and equivalent deterministic models are obtained. To illustrate the proposed model two numerical examples are presented and solved using LINGO 13.0 software package.

A Weibull model to describe antimicrobial kinetics of oregano and lemongrass essential oils against Salmonella Enteritidis in ground beef during refrigerated storage.

Science.gov (United States)

de Oliveira, Thales Leandro Coutinho; Soares, Rodrigo de Araújo; Piccoli, Roberta Hilsdorf

2013-03-01

The antimicrobial effect of oregano (Origanum vulgare L.) and lemongrass (Cymbopogon citratus (DC.) Stapf.) essential oils (EOs) against Salmonella enterica serotype Enteritidis in in vitro experiments, and inoculated in ground bovine meat during refrigerated storage (4±2 °C) for 6 days was evaluated. The Weibull model was tested to fit survival/inactivation bacterial curves (estimating of p and δ parameters). The minimum inhibitory concentration (MIC) value for both EOs on S. Enteritidis was 3.90 μl/ml. The EO concentrations applied in the ground beef were 3.90, 7.80 and 15.60 μl/g, based on MIC levels and possible activity reduction by food constituents. Both evaluated EOs in all tested levels, showed antimicrobial effects, with microbial populations reducing (p≤0.05) along time storage. Evaluating fit-quality parameters (RSS and RSE) Weibull models are able to describe the inactivation curves of EOs against S. Enteritidis. The application of EOs in processed meats can be used to control pathogens during refrigerated shelf-life. Copyright © 2012 Elsevier Ltd. All rights reserved.

Análise de distribuição de chuva para Santa Maria, RS Analysis of rainfall distribution for Santa Maria, RS, Brazil

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Joel C. da Silva

2007-02-01

Full Text Available O estudo em pauta teve como objetivo analisar a distribuição da quantidade diária de precipitação e do número de dias com chuva e determinar a variação da probabilidade de ocorrência de precipitação diária, durante os meses do ano, em Santa Maria, RS. Os dados de precipitação utilizados foram obtidos durante 36 anos de observação, na Estação Climatológica do 8º Distrito de Meteorologia, localizada na Universidade Federal de Santa Maria (29º 43' 23" de latitude Sul e 53º 43' 15" de longitude Oeste, altitude 95 m. Analisaram-se as seguintes funções de distribuição de probabilidade: gama, Weibull, normal, log-normal e exponencial. As funções que melhor descreveram a distribuição das probabilidades foram gama e Weibull. O maior número de dias com chuva ocorreu durante os meses de inverno porém o volume de precipitação é menor nesses dias, resultando em total mensal semelhante para todos os meses do ano.The objectives of this study were to analyze the distribution of total daily rainfall data and the number of rainy-days, and to determine the probability variation of daily precipitation during the months of the year in Santa Maria, Rio Grande do Sul State, Brazil. A 36-year rainfall database measured at the Climatological Station of 8th District of Meteorology, located in Santa Maria Federal University (29º 43' 23" S and 53º 43' 15" W were used in the study. The following probability distribution functions were tested: gamma, Weibull, normal, lognormal and exponential. The functions that best described the frequency distribution were gamma and Weibull. There were more number of rainy days in the winter, but with less amount of rainfall, resulting in similar monthly total precipitation for the twelve months of the year.

Optimal power flow for distribution networks with distributed generation

Directory of Open Access Journals (Sweden)

Radosavljević Jordan

2015-01-01

Full Text Available This paper presents a genetic algorithm (GA based approach for the solution of the optimal power flow (OPF in distribution networks with distributed generation (DG units, including fuel cells, micro turbines, diesel generators, photovoltaic systems and wind turbines. The OPF is formulated as a nonlinear multi-objective optimization problem with equality and inequality constraints. Due to the stochastic nature of energy produced from renewable sources, i.e. wind turbines and photovoltaic systems, as well as load uncertainties, a probabilisticalgorithm is introduced in the OPF analysis. The Weibull and normal distributions are employed to model the input random variables, namely the wind speed, solar irradiance and load power. The 2m+1 point estimate method and the Gram Charlier expansion theory are used to obtain the statistical moments and the probability density functions (PDFs of the OPF results. The proposed approach is examined and tested on a modified IEEE 34 node test feeder with integrated five different DG units. The obtained results prove the efficiency of the proposed approach to solve both deterministic and probabilistic OPF problems for different forms of the multi-objective function. As such, it can serve as a useful decision-making supporting tool for distribution network operators. [Projekat Ministarstva nauke Republike Srbije, br. TR33046

Handbook of exponential and related distributions for engineers and scientists

CERN Document Server

Pal, Nabendu; Lim, Wooi K

2005-01-01

The normal distribution is widely known and used by scientists and engineers. However, there are many cases when the normal distribution is not appropriate, due to the data being skewed. Rather than leaving you to search through journal articles, advanced theoretical monographs, or introductory texts for alternative distributions, the Handbook of Exponential and Related Distributions for Engineers and Scientists provides a concise, carefully selected presentation of the properties and principles of selected distributions that are most useful for application in the sciences and engineering.The book begins with all the basic mathematical and statistical background necessary to select the correct distribution to model real-world data sets. This includes inference, decision theory, and computational aspects including the popular Bootstrap method. The authors then examine four skewed distributions in detail: exponential, gamma, Weibull, and extreme value. For each one, they discuss general properties and applicabi...

The stochastic distribution of available coefficient of friction for human locomotion of five different floor surfaces.

Science.gov (United States)

Chang, Wen-Ruey; Matz, Simon; Chang, Chien-Chi

2014-05-01

The maximum coefficient of friction that can be supported at the shoe and floor interface without a slip is usually called the available coefficient of friction (ACOF) for human locomotion. The probability of a slip could be estimated using a statistical model by comparing the ACOF with the required coefficient of friction (RCOF), assuming that both coefficients have stochastic distributions. An investigation of the stochastic distributions of the ACOF of five different floor surfaces under dry, water and glycerol conditions is presented in this paper. One hundred friction measurements were performed on each floor surface under each surface condition. The Kolmogorov-Smirnov goodness-of-fit test was used to determine if the distribution of the ACOF was a good fit with the normal, log-normal and Weibull distributions. The results indicated that the ACOF distributions had a slightly better match with the normal and log-normal distributions than with the Weibull in only three out of 15 cases with a statistical significance. The results are far more complex than what had heretofore been published and different scenarios could emerge. Since the ACOF is compared with the RCOF for the estimate of slip probability, the distribution of the ACOF in seven cases could be considered a constant for this purpose when the ACOF is much lower or higher than the RCOF. A few cases could be represented by a normal distribution for practical reasons based on their skewness and kurtosis values without a statistical significance. No representation could be found in three cases out of 15. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Assessing the Adequacy of Probability Distributions for Estimating the Extreme Events of Air Temperature in Dabaa Region

International Nuclear Information System (INIS)

El-Shanshoury, Gh.I.

2015-01-01

Assessing the adequacy of probability distributions for estimating the extreme events of air temperature in Dabaa region is one of the pre-requisite s for any design purpose at Dabaa site which can be achieved by probability approach. In the present study, three extreme value distributions are considered and compared to estimate the extreme events of monthly and annual maximum and minimum temperature. These distributions include the Gumbel/Frechet distributions for estimating the extreme maximum values and Gumbel /Weibull distributions for estimating the extreme minimum values. Lieblein technique and Method of Moments are applied for estimating the distribution para meters. Subsequently, the required design values with a given return period of exceedance are obtained. Goodness-of-Fit tests involving Kolmogorov-Smirnov and Anderson-Darling are used for checking the adequacy of fitting the method/distribution for the estimation of maximum/minimum temperature. Mean Absolute Relative Deviation, Root Mean Square Error and Relative Mean Square Deviation are calculated, as the performance indicators, to judge which distribution and method of parameters estimation are the most appropriate one to estimate the extreme temperatures. The present study indicated that the Weibull distribution combined with Method of Moment estimators gives the highest fit, most reliable, accurate predictions for estimating the extreme monthly and annual minimum temperature. The Gumbel distribution combined with Method of Moment estimators showed the highest fit, accurate predictions for the estimation of the extreme monthly and annual maximum temperature except for July, August, October and November. The study shows that the combination of Frechet distribution with Method of Moment is the most accurate for estimating the extreme maximum temperature in July, August and November months while t he Gumbel distribution and Lieblein technique is the best for October

Assessment of wind characteristics for energy generation

Energy Technology Data Exchange (ETDEWEB)

Koray Ulgen [Ege University, Izmir (Turkey). Solar Energy Institute; Asir Genc [Selcuk University, Konya (Turkey). Dept. of Statistics; Arif Hepbasli [Ege University, Izmir (Turkey). Dept. of Mechanical Engineering; Galip Oturanc [Selcuk University, Konya (Turkey). Dept. of Mathematics

2004-11-15

Wind technology in Turkey has gained considerable maturity over the last five years, and wind energy projects are becoming commercially attractive in the country. In practice, it is essential to describe the variation of wind speeds for optimizing the design of the systems resulting in less energy generating costs. The wind variation for a typical site is usually described using the so-called Weibull distribution. In this study, the two Weibull parameters of the wind speed distribution function, the shape parameter k (dimensionless) and the scale parameter c (m/s), were computed from the wind speed data for Aksehir in Konya, located in Central Anatolia in Turkey (latitude: 38.35{sup o} and longitude: 31.42{sup o}). Wind data, consisting of hourly wind speed records over a 6 year period, 1997-2002, were obtained from the Aksehir State Meteorological Station. Based on the experimental data, it was found that the numerical values of both Weibull parameters (k and c) for Aksehir vary over a wide range. The yearly values of k range from 1.756 to 2.076, while those of c are in the range of 2.956 to 3.444. Average seasonal Weibull distributions for Aksehir are given. The wind speed distributions are represented by Weibull distribution and also by Rayleigh distribution with a special case of the Weibull distribution for k = 2. The Rayleigh distribution is found to be suitable to represent the actual probability of wind speed data for the site studied. (author)

A study of optimization problem for amplify-and-forward relaying over weibull fading channels

KAUST Repository

Ikki, Salama Said

2010-09-01

This paper addresses the power allocation and relay positioning problems in amplify-and-forward cooperative networks operating in Weibull fading environments. We study adaptive power allocation (PA) with fixed relay location, optimal relay location with fixed power allocation, and joint optimization of the PA and relay location under total transmit power constraint, in order to minimize the outage probability and average error probability at high signal-to-noise ratios (SNR). Analytical results are validated by numerical simulations and comparisons between the different optimization schemes and their performance are provided. Results show that optimum PA brings only coding gain, while optimum relay location yields, in addition to the latter, diversity gains as well. Also, joint optimization improves both, the diversity gain and coding gain. Furthermore, results illustrate that the analyzed adaptive algorithms outperform uniform schemes. ©2010 IEEE.

A distributed delay approach for modeling delayed outcomes in pharmacokinetics and pharmacodynamics studies.

Science.gov (United States)

Hu, Shuhua; Dunlavey, Michael; Guzy, Serge; Teuscher, Nathan

2018-04-01

A distributed delay approach was proposed in this paper to model delayed outcomes in pharmacokinetics and pharmacodynamics studies. This approach was shown to be general enough to incorporate a wide array of pharmacokinetic and pharmacodynamic models as special cases including transit compartment models, effect compartment models, typical absorption models (either zero-order or first-order absorption), and a number of atypical (or irregular) absorption models (e.g., parallel first-order, mixed first-order and zero-order, inverse Gaussian, and Weibull absorption models). Real-life examples were given to demonstrate how to implement distributed delays in Phoenix ® NLME™ 8.0, and to numerically show the advantages of the distributed delay approach over the traditional methods.

Evaluating the suitability of wind speed probability distribution models: A case of study of east and southeast parts of Iran

International Nuclear Information System (INIS)

Alavi, Omid; Mohammadi, Kasra; Mostafaeipour, Ali

2016-01-01

Highlights: • Suitability of different wind speed probability functions is assessed. • 5 stations distributed in east and south-east of Iran are considered as case studies. • Nakagami distribution is tested for first time and compared with 7 other functions. • Due to difference in wind features, best function is not similar for all stations. - Abstract: Precise information of wind speed probability distribution is truly significant for many wind energy applications. The objective of this study is to evaluate the suitability of different probability functions for estimating wind speed distribution at five stations, distributed in the east and southeast of Iran. Nakagami distribution function is utilized for the first time to estimate the distribution of wind speed. The performance of Nakagami function is compared with seven typically used distribution functions. The achieved results reveal that the more effective function is not similar among all stations. Wind speed characteristics, quantity and quality of the recorded wind speed data can be considered as influential parameters on the performance of the distribution functions. Also, the skewness of the recorded wind speed data may have influence on the accuracy of the Nakagami distribution. For Chabahar and Khaf stations the Nakagami distribution shows the highest performance while for Lutak, Rafsanjan and Zabol stations the Gamma, Generalized Extreme Value and Inverse-Gaussian distributions offer the best fits, respectively. Based on the analysis, the Nakagami distribution can generally be considered as an effective distribution since it provides the best fits in 2 stations and ranks 3rd to 5th in the remaining stations; however, due to the close performance of the Nakagami and Weibull distributions and also flexibility of the Weibull function as its widely proven feature, more assessments on the performance of the Nakagami distribution are required.

Statistical study on the strength of structural materials and elements

International Nuclear Information System (INIS)

Blume, J.A.; Dalal, J.S.; Honda, K.K.

1975-07-01

Strength data for structural materials and elements including concrete, reinforcing steel, structural steel, plywood elements, reinforced concrete beams, reinforced concrete columns, brick masonry elements, and concrete masonry walls were statistically analyzed. Sample statistics were computed for these data, and distribution parameters were derived for normal, lognormal, and Weibull distributions. Goodness-of-fit tests were performed on these distributions. Most data, except those for masonry elements, displayed fairly small dispersion. Dispersion in data for structural materials was generally found to be smaller than for structural elements. Lognormal and Weibull distributions displayed better overall fits to data than normal distribution, although either Weibull or lognormal distribution can be used to represent the data analyzed. (auth)

Hyperbolic Cosine–Exponentiated Exponential Lifetime Distribution and its Application in Reliability

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Omid Kharazmi

2017-02-01

Full Text Available Recently, Kharazmi and Saadatinik (2016 introduced a new family of lifetime distributions called hyperbolic cosine – F (HCF distribution. In the present paper, it is focused on a special case of HCF family with exponentiated exponential distribution as a baseline distribution (HCEE. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, mode, moment generating function, failure rate function, mean residual lifetime, order statistics and expression of the entropy are derived. Estimating parameters of HCEE distribution are obtained by eight estimation methods: maximum likelihood, Bayesian, maximum product of spacings, parametric bootstrap, non-parametric bootstrap, percentile, least-squares and weighted least-squares. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators. Finally, one real data set has been analyzed for illustrative purposes and it is observed that the proposed model fits better than Weibull, gamma and generalized exponential distributions.

Cell-size distribution and scaling in a one-dimensional Kolmogorov-Johnson-Mehl-Avrami lattice model with continuous nucleation

Science.gov (United States)

Néda, Zoltán; Járai-Szabó, Ferenc; Boda, Szilárd

2017-10-01

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can grow with constant speed and continuously nucleate on the empty sites. We offer an alternative mean-field-like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function. Our method reproduces the same scaling laws as the KJMA theory and has the advantage that it leads to a simple closed form for the cell-size distribution function. It is shown that a Weibull distribution is appropriate for describing the final cell-size distribution. The results are discussed in comparison with Monte Carlo simulation data.

Distribuição de frequência da chuva para região Centro-Sul do Ceará, Brasil Frequency distribution of rainfall for the South-Central region of Ceará, Brazil

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Ítalo Nunes Silva

2013-09-01

Full Text Available Foram analisadas sete distribuições de probabilidade Exponencial, Gama, Log-normal, Normal, Weibull, Gumbel e Beta para a chuva mensal e anual na região Centro-Sul do Ceará, Brasil. Para verificação dos ajustes dos dados às funções densidade de probabilidade foi utilizado o teste não-paramétrico de Kolmogorov-Smirnov com nível de 5% de significância. Os dados de chuva foram obtidos da base de dados da SUDENE registrados durante o período de 1913 a 1989. Para a chuva total anual teve ajuste satisfatório dos dados às distribuições Gama, Gumbel, Normal e Weibull e não ocorreu ajuste às distribuições Exponencial, Log-normal e Beta. Recomenda-se o uso da distribuição Normal para estimar valores de chuva provável anual para a região, por ser um procedimento de fácil aplicação e também pelo bom desempenho nos testes. A distribuição de frequência Gumbel foi a que melhor representou os dados de chuva para o período mensal, com o maior número de ajustes no período chuvoso. No período seco os dados de chuva foram melhores representados pela distribuição Exponencial.Seven probability distributions were analysed: Exponential, Gamma, Log-Normal, Normal, Weibull, Gumbel and Beta, for monthly and annual rainfall in the south-central region of Ceará, Brazil. In order to verify the adjustments of the data to the probability density functions, the non-parametric Kolmogorov-Smirnov test was used with a 5% level of significance. The rainfall data were obtained from the database at SUDENE, recorded from 1913 to 1989. For the total annual rainfall, adjustment of the data to the Gamma, Gumbel, Normal and Weibull distributions was satisfactory, and there was no adjustment to the Exponential, Log-normal and Beta distributions. Use of Normal distribution is recommended to estimate the values of probable annual rainfall in the region, this being a procedure of easy application, performing well in the tests. The Gumbel frequency

The statitistical evaluation of the uniaxial compressive strength of the Ruskov andesite

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Krepelka František

2002-03-01

Full Text Available The selection of a suitable model of the statistical distribution of the uniaxial compressive strength is discussed in the paper. The uniaxial compressive strength was studied on 180 specimens of the Ruskov andesite. The rate of loading was 1MPa.s-1. The experimental specimens had a prismatic form with a square base; the slightness ratio of specimens was 2:1. Three sets of specimens with a different length of the base edge were studied, namely 50, 30 and 10 mm. The result of the measurement were three sets with 60 values of the uniaxial compressive strength. The basic statistical parameters: the sample mean, the sample standard deviation, the variational interval, the minimum and maximum value, the sample obliqueness coefficient and the sharpness coefficient were evaluated for each collection. Two types of the distribution which can be joined with the real physical fundamentals of the desintegration of rocks ( the normal and the Weibull distribution were tested. The two-parametric Weibull distribution was tested. The basic characteristics of both distributions were evaluated for each set and the accordance of the model distribution with an experimental distribution was tested. The ÷2-test was used for testing. The two-parametric Weibull distribution was selected following the comparison of the test results of both model distributions as a suitable distribution model for the characterization of uniaxial compressive strength of the Ruskov andesite. The two-parametric Weibull distribution showed better results of the goodness-of-fit test. The normal distribution was suitable for two sets; one of the sets showed a negative result of the goodness-of-fit testing. At the uniaxial compressive strength of the Ruskov andesite, a scale effect was registered : the mean value of uniaxial compressive strength decreases with increasing the specimen base edge. This is another argument for using the Weibull distribution as a suitable statistical model of the

Distribution functions for the linear region of the S-N curve

Energy Technology Data Exchange (ETDEWEB)

Mueller, Christian; Waechter, Michael; Masendorf, Rainer; Esderts, Alfons [TU Clausthal, Clausthal-Zellerfeld (Germany). Inst. for Plant Engineering and Fatigue Analysis

2017-08-01

This study establishes a database containing the results of fatigue tests from the linear region of the S-N curve using sources from the literature. Each set of test results originates from testing metallic components on a single load level. Eighty-nine test series with sample sizes of 14 ≤ n ≤ 500 are included in the database, resulting in a sum of 6,086 individual test results. The test series are tested in terms of the type of distribution function (log-normal or 2-parameter Weibull) using the Shapiro-Wilk test, the Anderson-Darling test and probability plots. The majority of the tested individual test results follows a log-normal distribution.

Scaling strength distributions in quasi-brittle materials from micro-to macro-scales: A computational approach to modeling Nature-inspired structural ceramics

International Nuclear Information System (INIS)

Genet, Martin; Couegnat, Guillaume; Tomsia, Antoni P.; Ritchie, Robert O.

2014-01-01

This paper presents an approach to predict the strength distribution of quasi-brittle materials across multiple length-scales, with emphasis on Nature-inspired ceramic structures. It permits the computation of the failure probability of any structure under any mechanical load, solely based on considerations of the microstructure and its failure properties by naturally incorporating the statistical and size-dependent aspects of failure. We overcome the intrinsic limitations of single periodic unit-based approaches by computing the successive failures of the material components and associated stress redistributions on arbitrary numbers of periodic units. For large size samples, the microscopic cells are replaced by a homogenized continuum with equivalent stochastic and damaged constitutive behavior. After establishing the predictive capabilities of the method, and illustrating its potential relevance to several engineering problems, we employ it in the study of the shape and scaling of strength distributions across differing length-scales for a particular quasi-brittle system. We find that the strength distributions display a Weibull form for samples of size approaching the periodic unit; however, these distributions become closer to normal with further increase in sample size before finally reverting to a Weibull form for macroscopic sized samples. In terms of scaling, we find that the weakest link scaling applies only to microscopic, and not macroscopic scale, samples. These findings are discussed in relation to failure patterns computed at different size-scales. (authors)

Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling

Science.gov (United States)

Jeffrey H. Gove

2003-01-01

Many of the most popular sampling schemes used in forestry are probability proportional to size methods. These methods are also referred to as size biased because sampling is actually from a weighted form of the underlying population distribution. Length- and area-biased sampling are special cases of size-biased sampling where the probability weighting comes from a...

Empirical model based on Weibull distribution describing the destruction kinetics of natural microbiota in pineapple (Ananas comosus L.) puree during high-pressure processing.

Science.gov (United States)

Chakraborty, Snehasis; Rao, Pavuluri Srinivasa; Mishra, Hari Niwas

2015-10-15

High pressure inactivation of natural microbiota viz. aerobic mesophiles (AM), psychrotrophs (PC), yeasts and molds (YM), total coliforms (TC) and lactic acid bacteria (LAB) in pineapple puree was studied within the experimental domain of 0.1-600 MPa and 30-50 °C with a treatment time up to 20 min. A complete destruction of yeasts and molds was obtained at 500 MPa/50 °C/15 min; whereas no counts were detected for TC and LAB at 300 MPa/30 °C/15 min. A maximum of two log cycle reductions was obtained for YM during pulse pressurization at the severe process intensity of 600 MPa/50 °C/20 min. The Weibull model clearly described the non-linearity of the survival curves during the isobaric period. The tailing effect, as confirmed by the shape parameter (β) of the survival curve, was obtained in case of YM (β1) was observed for the other microbial groups. Analogous to thermal death kinetics, the activation energy (Ea, kJ·mol(-1)) and the activation volume (Va, mL·mol(-1)) values were computed further to describe the temperature and pressure dependencies of the scale parameter (δ, min), respectively. A higher δ value was obtained for each microbe at a lower temperature and it decreased with an increase in pressure. A secondary kinetic model was developed describing the inactivation rate (k, min(-1)) as a function of pressure (P, MPa) and temperature (T, K) including the dependencies of Ea and Va on P and T, respectively. Copyright © 2015 Elsevier B.V. All rights reserved.

Sunflower petals: Some physical properties and modeling distribution of their number, dimensions, and mass

Directory of Open Access Journals (Sweden)

Amir Hossein Mirzabe

2018-06-01

Full Text Available Sunflower petal is one of the parts of the sunflower which has drawn attention and has several applications these days. These applications justify getting information about physical properties, mechanical properties, drying trends, etc. in order to design new machines and use new methods to harvest or dry the sunflower petals. For three varieties of sunflower, picking force of petals was measured; number of petals of each head was counted; unit mass and 1000-unit mass of fresh petals were measured and length, width, and projected area of fresh petals were calculated based on image processing technique; frequency distributions of these parameters were modeled using statistical distribution models namely Gamma, Generalized Extreme Value (G. E. V, Lognormal, and Weibull. Results of picking force showed that with increasing number of days after appearing the first petal on each head from 5 to 14 and decreasing loading rate from 150 g min−1 to 50 g min−1 values of picking force were decreased for three varieties, but diameter of sunflower head had different effects on picking force for each variety. Length, width, and number of petals of Dorsefid variety ranged from 38.52 to 95.44 mm, 3.80 to 9.28 mm and 29 to 89, respectively. The corresponding values ranged from 34.19 to 88.18 mm, 4.28 to 10.60 mm and 21 to 89, respectively for Shamshiri variety and ranged from 44.47 to 114.63 mm, 7.03 to 20.31 mm and 29 to 89 for Sirena variety. Results of frequency distribution modeling indicated that in most cases, G. E. V and Weibull distributions had better performance than other distributions. Keywords: Sunflower (Helianthus annus L. petal, Picking force, Image processing, Fibonacci sequence, Lucas sequence

Reliability Engineering

International Nuclear Information System (INIS)

Lee, Sang Yong

1992-07-01

This book is about reliability engineering, which describes definition and importance of reliability, development of reliability engineering, failure rate and failure probability density function about types of it, CFR and index distribution, IFR and normal distribution and Weibull distribution, maintainability and movability, reliability test and reliability assumption in index distribution type, normal distribution type and Weibull distribution type, reliability sampling test, reliability of system, design of reliability and functionality failure analysis by FTA.

Gumbel Weibull distribution function for Sahel precipitation ...

African Journals Online (AJOL)

user

insecurity, migration, social conflicts, etc.). An efficient management of under and over ground water is a ... affects their incomes (Udual and Ini, 2012). Researches on modeling, prediction and forecasting ... Douentza in Mopti region, situated on the national road 15 highway linking Mopti to Gao and Kidal regions. This small ...

Fissure formation in coke. 3: Coke size distribution and statistical analysis

Energy Technology Data Exchange (ETDEWEB)

D.R. Jenkins; D.E. Shaw; M.R. Mahoney [CSIRO, North Ryde, NSW (Australia). Mathematical and Information Sciences

2010-07-15

A model of coke stabilization, based on a fundamental model of fissuring during carbonisation is used to demonstrate the applicability of the fissuring model to actual coke size distributions. The results indicate that the degree of stabilization is important in determining the size distribution. A modified form of the Weibull distribution is shown to provide a better representation of the whole coke size distribution compared to the Rosin-Rammler distribution, which is generally only fitted to the lump coke. A statistical analysis of a large number of experiments in a pilot scale coke oven shows reasonably good prediction of the coke mean size, based on parameters related to blend rank, amount of low rank coal, fluidity and ash. However, the prediction of measures of the spread of the size distribution is more problematic. The fissuring model, the size distribution representation and the statistical analysis together provide a comprehensive capability for understanding and predicting the mean size and distribution of coke lumps produced during carbonisation. 12 refs., 16 figs., 4 tabs.

Development of probabilistic fatigue curve for asphalt concrete based on viscoelastic continuum damage mechanics

Directory of Open Access Journals (Sweden)

Himanshu Sharma

2016-07-01

Full Text Available Due to its roots in fundamental thermodynamic framework, continuum damage approach is popular for modeling asphalt concrete behavior. Currently used continuum damage models use mixture averaged values for model parameters and assume deterministic damage process. On the other hand, significant scatter is found in fatigue data generated even under extremely controlled laboratory testing conditions. Thus, currently used continuum damage models fail to account the scatter observed in fatigue data. This paper illustrates a novel approach for probabilistic fatigue life prediction based on viscoelastic continuum damage approach. Several specimens were tested for their viscoelastic properties and damage properties under uniaxial mode of loading. The data thus generated were analyzed using viscoelastic continuum damage mechanics principles to predict fatigue life. Weibull (2 parameter, 3 parameter and lognormal distributions were fit to fatigue life predicted using viscoelastic continuum damage approach. It was observed that fatigue damage could be best-described using Weibull distribution when compared to lognormal distribution. Due to its flexibility, 3-parameter Weibull distribution was found to fit better than 2-parameter Weibull distribution. Further, significant differences were found between probabilistic fatigue curves developed in this research and traditional deterministic fatigue curve. The proposed methodology combines advantages of continuum damage mechanics as well as probabilistic approaches. These probabilistic fatigue curves can be conveniently used for reliability based pavement design. Keywords: Probabilistic fatigue curve, Continuum damage mechanics, Weibull distribution, Lognormal distribution

Probability distribution of pitting corrosion depth and rate in underground pipelines: A Monte Carlo study

International Nuclear Information System (INIS)

Caleyo, F.; Velazquez, J.C.; Valor, A.; Hallen, J.M.

2009-01-01

The probability distributions of external-corrosion pit depth and pit growth rate were investigated in underground pipelines using Monte Carlo simulations. The study combines a predictive pit growth model developed by the authors with the observed distributions of the model variables in a range of soils. Depending on the pipeline age, any of the three maximal extreme value distributions, i.e. Weibull, Frechet or Gumbel, can arise as the best fit to the pitting depth and rate data. The Frechet distribution best fits the corrosion data for long exposure periods. This can be explained by considering the long-term stabilization of the diffusion-controlled pit growth. The findings of the study provide reliability analysts with accurate information regarding the stochastic characteristics of the pitting damage in underground pipelines.

Probability distribution of pitting corrosion depth and rate in underground pipelines: A Monte Carlo study

Energy Technology Data Exchange (ETDEWEB)

Caleyo, F. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400, La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico)

2009-09-15

The probability distributions of external-corrosion pit depth and pit growth rate were investigated in underground pipelines using Monte Carlo simulations. The study combines a predictive pit growth model developed by the authors with the observed distributions of the model variables in a range of soils. Depending on the pipeline age, any of the three maximal extreme value distributions, i.e. Weibull, Frechet or Gumbel, can arise as the best fit to the pitting depth and rate data. The Frechet distribution best fits the corrosion data for long exposure periods. This can be explained by considering the long-term stabilization of the diffusion-controlled pit growth. The findings of the study provide reliability analysts with accurate information regarding the stochastic characteristics of the pitting damage in underground pipelines.

The probability distribution model of air pollution index and its dominants in Kuala Lumpur

Science.gov (United States)

AL-Dhurafi, Nasr Ahmed; Razali, Ahmad Mahir; Masseran, Nurulkamal; Zamzuri, Zamira Hasanah

2016-11-01

This paper focuses on the statistical modeling for the distributions of air pollution index (API) and its sub-indexes data observed at Kuala Lumpur in Malaysia. Five pollutants or sub-indexes are measured including, carbon monoxide (CO); sulphur dioxide (SO2); nitrogen dioxide (NO2), and; particulate matter (PM10). Four probability distributions are considered, namely log-normal, exponential, Gamma and Weibull in search for the best fit distribution to the Malaysian air pollutants data. In order to determine the best distribution for describing the air pollutants data, five goodness-of-fit criteria's are applied. This will help in minimizing the uncertainty in pollution resource estimates and improving the assessment phase of planning. The conflict in criterion results for selecting the best distribution was overcome by using the weight of ranks method. We found that the Gamma distribution is the best distribution for the majority of air pollutants data in Kuala Lumpur.

Comparison of ductile-to-brittle transition curve fitting approaches

International Nuclear Information System (INIS)

Cao, L.W.; Wu, S.J.; Flewitt, P.E.J.

2012-01-01

Ductile-to-brittle transition (DBT) curve fitting approaches are compared over the transition temperature range for reactor pressure vessel steels with different kinds of data, including Charpy-V notch impact energy data and fracture toughness data. Three DBT curve fitting methods have been frequently used in the past, including the Burr S-Weibull and tanh distributions. In general there is greater scatter associated with test data obtained within the transition region. Therefore these methods give results with different accuracies, especially when fitting to small quantities of data. The comparison shows that the Burr distribution and tanh distribution can almost equally fit well distributed and large data sets extending across the test temperature range to include the upper and lower shelves. The S-Weibull distribution fit is poor for the lower shelf of the DBT curve. Overall for both large and small quantities of measured data the Burr distribution provides the best description. - Highlights: ► Burr distribution offers a better fit than that of a S-Weibull and tanh fit. ► Burr and tanh methods show similar fitting ability for a large data set. ► Burr method can fit sparse data well distributed across the test temperature. ► S-Weibull method cannot fit the lower shelf well and show poor fitting quality.

Determination of the Mechanical Properties of Plasma-Sprayed Hydroxyapatite Coatings Using the Knoop Indentation Technique

Science.gov (United States)

Hasan, Md. Fahad; Wang, James; Berndt, Christopher

2015-06-01

The microhardness and elastic modulus of plasma-sprayed hydroxyapatite coatings were evaluated using Knoop indentation on the cross section and on the top surface. The effects of indentation angle, testing direction, measurement location and applied load on the microhardness and elastic modulus were investigated. The variability and distribution of the microhardness and elastic modulus data were statistically analysed using the Weibull modulus distribution. The results indicate that the dependence of microhardness and elastic modulus on the indentation angle exhibits a parabolic shape. Dependence of the microhardness values on the indentation angle follows Pythagoras's theorem. The microhardness, Weibull modulus of microhardness and Weibull modulus of elastic modulus reach their maximum at the central position (175 µm) on the cross section of the coatings. The Weibull modulus of microhardness revealed similar values throughout the thickness, and the Weibull modulus of elastic modulus shows higher values on the top surface compared to the cross section.

Evaluación poscosecha y estimación de vida útil de guayaba fresca utilizando el modelo de Weibull

Directory of Open Access Journals (Sweden)

Carlos García Mogollón

2010-07-01

Full Text Available La guayaba (Psidium guajava L. es una fruta tropical susceptible de sufrir alteraciones indeseables que afectan su vida útil debido a condiciones inadecuadas de almacenamiento y acondicionamiento. En este trabajo se estimó la vida útil de guayaba en fresco utilizando el modelo probabilístico de Weibull y se valuó la calidad de los frutos durante almacenamiento en diferentes condiciones de temperatura y empaque. La evaluación poscosecha se hizo por 15 días con guayabas variedad regional roja. Se utilizó un dise&#ntilde;o completamente al azar con arreglo factorial consistente en tres factores: tiempo de almacenamiento con seis niveles (0, 3, 6, 9, 12 y 15 días, temperatura de almacenamiento con dos niveles: ambiente (37 °C y humedad relativa (HR entre 85 y 90% y refrigeración (9±2 °C y HR de 85 - 90%; dos tipo de empaques: bandeja de poliestireno con film plástico de PVC y 'foil' de aluminio. Durante la evaluación sensorial en el periodo de almacenamiento se usó una escala estructurada de tres puntos grado de satisfacción. El modelo de Weibull demostró ser adecuado para predecir la vida útil de la guayaba fresca basados en los criterios de ajustes, límites de confianza de aceptación y fallo. Durante el periodo de almacenamiento se observó que el factor tiempo, la temperatura y el tipo de empaque tienen un efecto estadístico significativo (P < 0.05 sobre el diámetro equivalente, esfericidad, masa específica aparente, SST, pH, acidez y evaluación sensorial de los frutos. El producto puede ser consumido como fruta fresca hasta diez días de almacenamiento a temperatura ambiente y máximo quince días en almacenamiento refrigerado.

Comparison of the Gini and Zenga Indexes using Some Theoretical Income Distributions Abstract

Directory of Open Access Journals (Sweden)

Katarzyna Ostasiewicz

2013-01-01

Full Text Available The most common measure of inequality used in scientific research is the Gini index. In 2007, Zenga proposed a new index of inequality that has all the appropriate properties of an measure of equality. In this paper, we compared the Gini and Zenga indexes, calculating these quantities for the few distributions frequently used for approximating distributions of income, that is, the lognormal, gamma, inverse Gauss, Weibull and Burr distributions. Within this limited examination, we have observed three main differences. First, the Zenga index increases more rapidly for low values of the variation and decreases more slowly when the variation approaches intermediate values from above. Second, the Zenga index seems to be better predicted by the variation. Third, although the Zenga index is always higher than the Gini one, the ordering of some pairs of cases may be inverted. (original abstract

Statistical Analysis of Data for Timber Strengths

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Hoffmeyer, P.

Statistical analyses are performed for material strength parameters from approximately 6700 specimens of structural timber. Non-parametric statistical analyses and fits to the following distributions types have been investigated: Normal, Lognormal, 2 parameter Weibull and 3-parameter Weibull...

Wind distribution and capacity factor estimation for wind turbines in the coastal region of South Africa

International Nuclear Information System (INIS)

Ayodele, T.R.; Jimoh, A.A.; Munda, J.L.; Agee, J.T.

2012-01-01

Highlights: ► We evaluate capacity factor of some commercially available wind turbines. ► Wind speed in the sites studied can best be modelled using Weibull distribution. ► Site WM05 has the highest wind power potential while site WM02 has the lowest. ► More wind power can be harnessed during the day period compared to the night. ► Turbine K seems to be the best turbine for the coastal region of South Africa. - Abstract: The operating curve parameters of a wind turbine should match the local wind regime optimally to ensure maximum exploitation of available energy in a mass of moving air. This paper provides estimates of the capacity factor of 20 commercially available wind turbines, based on the local wind characteristics of ten different sites located in the Western Cape region of South Africa. Ten-min average time series wind-speed data for a period of 1 year are used for the study. First, the wind distribution that best models the local wind regime of the sites is determined. This is based on root mean square error (RMSE) and coefficient of determination (R 2 ) which are used to test goodness of fit. First, annual, seasonal, diurnal and peak period-capacity factor are estimated analytically. Then, the influence of turbine power curve parameters on the capacity factor is investigated. Some of the key results show that the wind distribution of the entire site can best be modelled statistically using the Weibull distribution. Site WM05 (Napier) presents the highest capacity factor for all the turbines. This indicates that this site has the highest wind power potential of all the available sites. Site WM02 (Calvinia) has the lowest capacity factor i.e. lowest wind power potential. This paper can assist in the planning and development of large-scale wind power-generating sites in South Africa.

Log-concavity property for some well-known distributions

Directory of Open Access Journals (Sweden)

G. R. Mohtashami Borzadaran

2011-12-01

Full Text Available Interesting properties and propositions, in many branches of science such as economics have been obtained according to the property of cumulative distribution function of a random variable as a concave function. Caplin and Nalebuff (1988,1989, Bagnoli and Khanna (1989 and Bagnoli and Bergstrom (1989 , 1989, 2005 have discussed the log-concavity property of probability distributions and their applications, especially in economics. Log-concavity concerns twice differentiable real-valued function g whose domain is an interval on extended real line. g as a function is said to be log-concave on the interval (a,b if the function ln(g is a concave function on (a,b. Log-concavity of g on (a,b is equivalent to g'/g being monotone decreasing on (a,b or (ln(g" 6] have obtained log-concavity for distributions such as normal, logistic, extreme-value, exponential, Laplace, Weibull, power function, uniform, gamma, beta, Pareto, log-normal, Student's t, Cauchy and F distributions. We have discussed and introduced the continuous versions of the Pearson family, also found the log-concavity for this family in general cases, and then obtained the log-concavity property for each distribution that is a member of Pearson family. For the Burr family these cases have been calculated, even for each distribution that belongs to Burr family. Also, log-concavity results for distributions such as generalized gamma distributions, Feller-Pareto distributions, generalized Inverse Gaussian distributions and generalized Log-normal distributions have been obtained.

On the performance of dual-hop mixed RF/FSO wireless communication system in urban area over aggregated exponentiated Weibull fading channels with pointing errors

Science.gov (United States)

Wang, Yue; Wang, Ping; Liu, Xiaoxia; Cao, Tian

2018-03-01

The performance of decode-and-forward dual-hop mixed radio frequency / free-space optical system in urban area is studied. The RF link is modeled by the Nakagami-m distribution and the FSO link is described by the composite exponentiated Weibull (EW) fading channels with nonzero boresight pointing errors (NBPE). For comparison, the ABER results without pointing errors (PE) and those with zero boresight pointing errors (ZBPE) are also provided. The closed-form expression for the average bit error rate (ABER) in RF link is derived with the help of hypergeometric function, and that in FSO link is obtained by Meijer's G and generalized Gauss-Laguerre quadrature functions. Then, the end-to-end ABERs with binary phase shift keying modulation are achieved on the basis of the computed ABER results of RF and FSO links. The end-to-end ABER performance is further analyzed with different Nakagami-m parameters, turbulence strengths, receiver aperture sizes and boresight displacements. The result shows that with ZBPE and NBPE considered, FSO link suffers a severe ABER degradation and becomes the dominant limitation of the mixed RF/FSO system in urban area. However, aperture averaging can bring significant ABER improvement of this system. Monte Carlo simulation is provided to confirm the validity of the analytical ABER expressions.

Protein dynamics and stability: The distribution of atomic fluctuations in thermophilic and mesophilic dihydrofolate reductase derived using elastic incoherent neutron scattering

International Nuclear Information System (INIS)

Meinhold, Lars; Clement, David; Tehei, M.; Daniel, R.M.; Finney, J.L.; Smith, Jeremy C.

2008-01-01

The temperature dependence of the dynamics of mesophilic and thermophilic dihydrofolate reductase is examined using elastic incoherent neutron scattering. It is demonstrated that the distribution of atomic displacement amplitudes can be derived from the elastic scattering data by assuming a (Weibull) functional form that resembles distributions seen in molecular dynamics simulations. The thermophilic enzyme has a significantly broader distribution than its mesophilic counterpart. Furthermore, although the rate of increase with temperature of the atomic mean-square displacements extracted from the dynamic structure factor is found to be comparable for both enzymes, the amplitudes are found to be slightly larger for the thermophilic enzyme. Therefore, these results imply that the thermophilic enzyme is the more flexible of the two

The effect of roughness model on scattering properties of ice crystals

International Nuclear Information System (INIS)

Geogdzhayev, Igor; Diedenhoven, Bastiaan van

2016-01-01

We compare stochastic models of microscale surface roughness assuming uniform and Weibull distributions of crystal facet tilt angles to calculate scattering by roughened hexagonal ice crystals using the geometric optics (GO) approximation. Both distributions are determined by similar roughness parameters, while the Weibull model depends on the additional shape parameter. Calculations were performed for two visible wavelengths (864 nm and 410 nm) for roughness values between 0.2 and 0.7 and Weibull shape parameters between 0 and 1.0 for crystals with aspect ratios of 0.21, 1 and 4.8. For this range of parameters we find that, for a given roughness level, varying the Weibull shape parameter can change the asymmetry parameter by up to about 0.05. The largest effect of the shape parameter variation on the phase function is found in the backscattering region, while the degree of linear polarization is most affected at the side-scattering angles. For high roughness, scattering properties calculated using the uniform and Weibull models are in relatively close agreement for a given roughness parameter, especially when a Weibull shape parameter of 0.75 is used. For smaller roughness values, a shape parameter close to unity provides a better agreement. Notable differences are observed in the phase function over the scattering angle range from 5° to 20°, where the uniform roughness model produces a plateau while the Weibull model does not. - Highlights: • We compare scattering by hexagonal crystals for uniform and Weibull roughness models. • The Weibull shape parameter has a stronger effect on the phase function at backscattering. • DoLP is mostly affected at the side-scattering angles. • For high roughness, the two models are in relatively close agreement for a given roughness. • A plateau from 5° to 20° is observed in the phase function when using the uniform model.

Do Insect Populations Die at Constant Rates as They Become Older? Contrasting Demographic Failure Kinetics with Respect to Temperature According to the Weibull Model.

Directory of Open Access Journals (Sweden)

Petros Damos

Full Text Available Temperature implies contrasting biological causes of demographic aging in poikilotherms. In this work, we used the reliability theory to describe the consistency of mortality with age in moth populations and to show that differentiation in hazard rates is related to extrinsic environmental causes such as temperature. Moreover, experiments that manipulate extrinsic mortality were used to distinguish temperature-related death rates and the pertinence of the Weibull aging model. The Newton-Raphson optimization method was applied to calculate parameters for small samples of ages at death by estimating the maximum likelihoods surfaces using scored gradient vectors and the Hessian matrix. The study reveals for the first time that the Weibull function is able to describe contrasting biological causes of demographic aging for moth populations maintained at different temperature regimes. We demonstrate that at favourable conditions the insect death rate accelerates as age advances, in contrast to the extreme temperatures in which each individual drifts toward death in a linear fashion and has a constant chance of passing away. Moreover, slope of hazard rates shifts towards a constant initial rate which is a pattern demonstrated by systems which are not wearing out (e.g. non-aging since the failure, or death, is a random event independent of time. This finding may appear surprising, because, traditionally, it was mostly thought as rule that in aging population force of mortality increases exponentially until all individuals have died. Moreover, in relation to other studies, we have not observed any typical decelerating aging patterns at late life (mortality leveling-off, but rather, accelerated hazard rates at optimum temperatures and a stabilized increase at the extremes.In most cases, the increase in aging-related mortality was simulated reasonably well according to the Weibull survivorship model that is applied. Moreover, semi log- probability hazard

Modeling wind speed and wind power distributions in Rwanda

Energy Technology Data Exchange (ETDEWEB)

Safari, Bonfils [Department of Physics, National University of Rwanda, P.O. Box 117, Huye District, South Province (Rwanda)

2011-02-15

Utilization of wind energy as an alternative energy source may offer many environmental and economical advantages compared to fossil fuels based energy sources polluting the lower layer atmosphere. Wind energy as other forms of alternative energy may offer the promise of meeting energy demand in the direct, grid connected modes as well as stand alone and remote applications. Wind speed is the most significant parameter of the wind energy. Hence, an accurate determination of probability distribution of wind speed values is very important in estimating wind speed energy potential over a region. In the present study, parameters of five probability density distribution functions such as Weibull, Rayleigh, lognormal, normal and gamma were calculated in the light of long term hourly observed data at four meteorological stations in Rwanda for the period of the year with fairly useful wind energy potential (monthly hourly mean wind speed anti v{>=}2 m s{sup -1}). In order to select good fitting probability density distribution functions, graphical comparisons to the empirical distributions were made. In addition, RMSE and MBE have been computed for each distribution and magnitudes of errors were compared. Residuals of theoretical distributions were visually analyzed graphically. Finally, a selection of three good fitting distributions to the empirical distribution of wind speed measured data was performed with the aid of a {chi}{sup 2} goodness-of-fit test for each station. (author)

On the Weibull distribution for wind energy assessment

DEFF Research Database (Denmark)

Batchvarova, Ekaterina; Gryning, Sven-Erik

2014-01-01

-term measurements performed by a wind lidar, the vertical profile of the shape parameter will be discussed for a sub-urban site, a coastal site and a marine site. The profile of the shape parameter was found to be substantially different over land and sea. A parameterization of the vertical behavior of the shape...

Percentile-based Weibull diameter distribution model for Pinus ...

African Journals Online (AJOL)

Using a site index equation and stem volume model developed for Pinus kesiya in the Philippines, a yield prediction system was created to predict the volume per ha (VPH) for each diameter class and, subsequently, the total volume of a stand. To evaluate the yield prediction system, the predicted mean VPH for each ...

Statistical study on applied stress dependence of failure time in stress corrosion cracking of Zircaloy-4 alloy

International Nuclear Information System (INIS)

Hirao, Keiichi; Yamane, Toshimi; Minamino, Yoritoshi; Tanaka, Akiei.

1988-01-01

Effects of applied stress on failure time in stress corrosion cracking of Zircaloy-4 alloy were investigated by Weibull distribution method. Test pieces in the evaculated silica tubes were annealed at 1,073 K for 7.2 x 10 3 s, and then quenched into ice-water. These species under constant applied stresses of 40∼90 % yield stress were immersed in CH 3 OH-1 w% I 2 solution at room temperature. The probability distribution of failure times under applied stress of 40 % of yield stress was described as single Weibull distribution, which had one shape parameter. The probability distributions of failure times under applied stress above 60 % of yield stress were described as composite and mixed Weibull distributions, which had the two shape parameters of Weibull distributions for the regions of the shorter time and longer one of failure. The values of these shape parameters in this study were larger than the value of 1 which corresponded to that of wear out failure. The observation of fracture surfaces and the stress dependence of the shape parameters indicated that the shape parameters both for the times of failure under 40 % of yield stress and for the longer ones above 60 % of yield stress corresponded to intergranular cracking, and that for shorter times of failure corresponded to transgranular cracking and dimple fracture. (author)

Universal behaviour in the stock market: Time dynamics of the electronic orderbook

Energy Technology Data Exchange (ETDEWEB)

Kızılersü, Ayşe, E-mail: ayse.kizilersu@adelaide.edu.au [Special Research Centre for the Subatomic Structure of Matter (CSSM), Department of Physics, School of Chemistry and Physics, Adelaide University, 5005 (Australia); Kreer, Markus [phi-t products & services, Karlsruher Strasse 88, 76139 Karlsruhe (Germany); Thomas, Anthony W. [CoEPP and CSSM, Department of Physics, Adelaide University, SA 5005 (Australia); Feindt, Michael [Blue Yonder GmbH, Ohiostraße 8, 756139 Karlsruhe (Germany)

2016-07-29

A consequence of the digital revolution is that share trading at the stock exchange takes place via electronic order books which are accessed by traders and investors via the internet. Our empirical findings of the London Stock Exchange demonstrate that once ultra-high frequency manipulation on time scales less than around ten milliseconds is excluded, all relevant changes in the order book happen with time differences that are randomly distributed and well described by a left-truncated Weibull distribution with universal shape parameter (independent of time and same for all stocks). The universal shape parameter corresponds to maximum entropy of the distribution. - Highlights: • After the ultra-high frequency manipulation is excluded, all the time differences in the EOB described by a left-truncated Weibull distribution. • The Weibull shape parameter is universal i.e. independent of time and same for all stocks and it is equal to Euler–Mascheroni constant. • The universal shape parameter corresponds to maximum entropy of the distribution.

Universal behaviour in the stock market: Time dynamics of the electronic orderbook

International Nuclear Information System (INIS)

Kızılersü, Ayşe; Kreer, Markus; Thomas, Anthony W.; Feindt, Michael

2016-01-01

A consequence of the digital revolution is that share trading at the stock exchange takes place via electronic order books which are accessed by traders and investors via the internet. Our empirical findings of the London Stock Exchange demonstrate that once ultra-high frequency manipulation on time scales less than around ten milliseconds is excluded, all relevant changes in the order book happen with time differences that are randomly distributed and well described by a left-truncated Weibull distribution with universal shape parameter (independent of time and same for all stocks). The universal shape parameter corresponds to maximum entropy of the distribution. - Highlights: • After the ultra-high frequency manipulation is excluded, all the time differences in the EOB described by a left-truncated Weibull distribution. • The Weibull shape parameter is universal i.e. independent of time and same for all stocks and it is equal to Euler–Mascheroni constant. • The universal shape parameter corresponds to maximum entropy of the distribution.

An eoq model for weibull deteriorating item with ramp type demand and salvage value under trade credit system

Directory of Open Access Journals (Sweden)

Lalit Mohan Pradhan

2014-03-01

Full Text Available Background: In the present competitive business scenario researchers have developed various inventory models for deteriorating items considering various practical situations for better inventory control. Permissible delay in payments with various demands and deteriorations is considerably a new concept introduced in developing various inventory models. These models are very useful for both the consumers and the manufacturer. Methods: In the present work an inventory model has been developed for a three parameter Weibull deteriorating item with ramp type demand and salvage value under trade credit system. Here we have considered a single item for developing the model. Results and conclusion: Optimal order quantity, optimal cycle time and total variable cost during a cycle have been derived for the proposed inventory model. The results obtained in this paper have been illustrated with the help of numerical examples and sensitivity analysis.   

Choosing an optimal model for failure data analysis by graphical approach

International Nuclear Information System (INIS)

Zhang, Tieling; Dwight, Richard

2013-01-01

Many models involving combination of multiple Weibull distributions, modification of Weibull distribution or extension of its modified ones, etc. have been developed to model a given set of failure data. The application of these models to modeling a given data set can be based on plotting the data on Weibull probability paper (WPP). Of them, two or more models are appropriate to model one typical shape of the fitting plot, whereas a specific model may be fit for analyzing different shapes of the plots. Hence, a problem arises, that is how to choose an optimal model for a given data set and how to model the data. The motivation of this paper is to address this issue. This paper summarizes the characteristics of Weibull-related models with more than three parameters including sectional models involving two or three Weibull distributions, competing risk model and mixed Weibull model. The models as discussed in this present paper are appropriate to model the data of which the shapes of plots on WPP can be concave, convex, S-shaped or inversely S-shaped. Then, the method for model selection is proposed, which is based on the shapes of the fitting plots. The main procedure for parameter estimation of the models is described accordingly. In addition, the range of data plots on WPP is clearly highlighted from the practical point of view. To note this is important as mathematical analysis of a model with neglecting the applicable range of the model plot will incur discrepancy or big errors in model selection and parameter estimates

Evaluación poscosecha y estimación de vida útil de guayaba fresca utilizando el modelo de Weibull

Directory of Open Access Journals (Sweden)

García Mogollón Carlos

2010-09-01

Full Text Available

La guayaba (Psidium guajava L. es una fruta tropical susceptible de sufrir alteraciones indeseables que afectan su vida útil debido a condiciones inadecuadas de almacenamiento y acondicionamiento. En este trabajo se estimó la vida útil de guayaba en fresco utilizando el modelo probabilístico de Weibull y se valuó la calidad de los frutos durante almacenamiento en diferentes condiciones de temperatura y empaque. La evaluación poscosecha se hizo por 15 días con guayabas variedad regional roja. Se utilizó un diseño completamente al azar con arreglo factorial consistente en tres factores: tiempo de almacenamiento con seis niveles (0, 3, 6, 9, 12 y 15 días, temperatura de almacenamiento con dos niveles: ambiente (37 °C y humedad relativa (HR entre 85 y 90% y refrigeración (9±2 °C y HR de 85 - 90%; dos tipo de empaques: bandeja de poliestireno con film plástico de PVC y 'foil' de aluminio. Durante la evaluación sensorial en el periodo de almacenamiento se usó una escala estructurada de tres puntos grado de satisfacción. El modelo de Weibull demostró ser adecuado para predecir la vida útil de la guayaba fresca basados en los criterios de ajustes, límites de confianza de aceptación y fallo. Durante el periodo de almacenamiento se observó que el factor tiempo, la temperatura y el tipo de empaque tienen un efecto estadístico significativo (P < 0.05 sobre el diámetro equivalente, esfericidad, masa específica aparente, SST, pH, acidez y evaluación sensorial de los frutos. El producto puede ser consumido como fruta fresca hasta diez días de almacenamiento a temperatura ambiente y máximo quince días en almacenamiento refrigerado.

Estimating the joint survival probabilities of married individuals

NARCIS (Netherlands)

Sanders, Lisanne; Melenberg, Bertrand

We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squared

Utilização da função pearson tipo V, Weibull e hiperbólica para modelagem da distribuição de diâmetros

Directory of Open Access Journals (Sweden)

Daniel Henrique Breda Binoti

2013-09-01

Full Text Available Objetivou-se neste estudo avaliar a eficiência da função log-Pearson tipo V para a descrição da estrutura diamétrica de povoamentos equiâneos de eucaliptos, bem como propor um modelo de distribuição diamétrica utilizando essa função. A modelagem realizada pela função log-Pearson tipo V foi comparada com a modelagem realizada com a função Weibull e hiperbólica. Para isso utilizou-se dados de parcelas permanentes de eucalipto, localizadas na região centro oeste do estado de Minas Gerais. A função Pearson tipo V foi testada em três diferentes configurações, com três e dois parâmetros, e tendo o parâmetro de locação substituído pelo diâmetro mínimo da parcela. A aderência das funções aos dados foi comprovada pela aplicação do teste Kolmogorov-Sminorv (K-S. Todos os ajustes apresentaram aderência aos dados pelo teste KS. As funções Weibull e hiperbólica apresentaram desempenho superior ao demonstrado pela função Pearson tipo V.

ASEP of MIMO System with MMSE-OSIC Detection over Weibull-Gamma Fading Channel Subject to AWGGN

Directory of Open Access Journals (Sweden)

Keerti Tiwari

2016-01-01

Full Text Available Ordered successive interference cancellation (OSIC is adopted with minimum mean square error (MMSE detection to enhance the multiple-input multiple-output (MIMO system performance. The optimum detection technique improves the error rate performance but increases system complexity. Therefore, MMSE-OSIC detection is used which reduces error rate compared to traditional MMSE with low complexity. The system performance is analyzed in composite fading environment that includes multipath and shadowing effects known as Weibull-Gamma (WG fading. Along with the composite fading, a generalized noise that is additive white generalized Gaussian noise (AWGGN is considered to show the impact of wireless scenario. This noise model includes various forms of noise as special cases such as impulsive, Gamma, Laplacian, Gaussian, and uniform. Consequently, generalized Q-function is used to model noise. The average symbol error probability (ASEP of MIMO system is computed for 16-quadrature amplitude modulation (16-QAM using MMSE-OSIC detection in WG fading perturbed by AWGGN. Analytical expressions are given in terms of Fox-H function (FHF. These expressions demonstrate the best fit to simulation results.

Optimal design of accelerated life tests for an extension of the exponential distribution

International Nuclear Information System (INIS)

Haghighi, Firoozeh

2014-01-01

Accelerated life tests provide information quickly on the lifetime distribution of the products by testing them at higher than usual levels of stress. In this paper, the lifetime of a product at any level of stress is assumed to have an extension of the exponential distribution. This new family has been recently introduced by Nadarajah and Haghighi (2011 [1]); it can be used as an alternative to the gamma, Weibull and exponentiated exponential distributions. The scale parameter of lifetime distribution at constant stress levels is assumed to be a log-linear function of the stress levels and a cumulative exposure model holds. For this model, the maximum likelihood estimates (MLEs) of the parameters, as well as the Fisher information matrix, are derived. The asymptotic variance of the scale parameter at a design stress is adopted as an optimization objective and its expression formula is provided using the maximum likelihood method. A Monte Carlo simulation study is carried out to examine the performance of these methods. The asymptotic confidence intervals for the parameters and hypothesis test for the parameter of interest are constructed

Bayesian analysis of general failure data from an ageing distribution: advances in numerical methods

International Nuclear Information System (INIS)

Procaccia, H.; Villain, B.; Clarotti, C.A.

1996-01-01

EDF and ENEA carried out a joint research program for developing the numerical methods and computer codes needed for Bayesian analysis of component-lives in the case of ageing. Early results of this study were presented at ESREL'94. Since then the following further steps have been gone: input data have been generalized to the case that observed lives are censored both on the right and on the left; allowable life distributions are Weibull and gamma - their parameters are both unknown and can be statistically dependent; allowable priors are histograms relative to different parametrizations of the life distribution of concern; first-and-second-order-moments of the posterior distributions can be computed. In particular the covariance will give some important information about the degree of the statistical dependence between the parameters of interest. An application of the code to the appearance of a stress corrosion cracking in a tube of the PWR Steam Generator system is presented. (authors)

The Distribution of Minimum of Ratios of Two Random Variables and Its Application in Analysis of Multi-hop Systems

Directory of Open Access Journals (Sweden)

A. Stankovic

2012-12-01

Full Text Available The distributions of random variables are of interest in many areas of science. In this paper, ascertaining on the importance of multi-hop transmission in contemporary wireless communications systems operating over fading channels in the presence of cochannel interference, the probability density functions (PDFs of minimum of arbitrary number of ratios of Rayleigh, Rician, Nakagami-m, Weibull and α-µ random variables are derived. These expressions can be used to study the outage probability as an important multi-hop system performance measure. Various numerical results complement the proposed mathematical analysis.

Experiment research on cognition reliability model of nuclear power plant

International Nuclear Information System (INIS)

Zhao Bingquan; Fang Xiang

1999-01-01

The objective of the paper is to improve the reliability of operation on real nuclear power plant of operators through the simulation research to the cognition reliability of nuclear power plant operators. The research method of the paper is to make use of simulator of nuclear power plant as research platform, to take present international research model of reliability of human cognition based on three-parameter Weibull distribution for reference, to develop and get the research model of Chinese nuclear power plant operators based on two-parameter Weibull distribution. By making use of two-parameter Weibull distribution research model of cognition reliability, the experiments about the cognition reliability of nuclear power plant operators have been done. Compared with the results of other countries such USA and Hungary, the same results can be obtained, which can do good to the safety operation of nuclear power plant

Fluctuations in a quasi-stationary shallow cumulus cloud ensemble

Directory of Open Access Journals (Sweden)

M. Sakradzija

2015-01-01

Full Text Available We propose an approach to stochastic parameterisation of shallow cumulus clouds to represent the convective variability and its dependence on the model resolution. To collect information about the individual cloud lifecycles and the cloud ensemble as a whole, we employ a large eddy simulation (LES model and a cloud tracking algorithm, followed by conditional sampling of clouds at the cloud-base level. In the case of a shallow cumulus ensemble, the cloud-base mass flux distribution is bimodal, due to the different shallow cloud subtypes, active and passive clouds. Each distribution mode can be approximated using a Weibull distribution, which is a generalisation of exponential distribution by accounting for the change in distribution shape due to the diversity of cloud lifecycles. The exponential distribution of cloud mass flux previously suggested for deep convection parameterisation is a special case of the Weibull distribution, which opens a way towards unification of the statistical convective ensemble formalism of shallow and deep cumulus clouds. Based on the empirical and theoretical findings, a stochastic model has been developed to simulate a shallow convective cloud ensemble. It is formulated as a compound random process, with the number of convective elements drawn from a Poisson distribution, and the cloud mass flux sampled from a mixed Weibull distribution. Convective memory is accounted for through the explicit cloud lifecycles, making the model formulation consistent with the choice of the Weibull cloud mass flux distribution function. The memory of individual shallow clouds is required to capture the correct convective variability. The resulting distribution of the subgrid convective states in the considered shallow cumulus case is scale-adaptive – the smaller the grid size, the broader the distribution.

Probabilistic distributions of wind velocity for the evaluation of the wind power potential; Distribuicoes probabilisticas de velocidades do vento para avaliacao do potencial energetico eolico

Energy Technology Data Exchange (ETDEWEB)

Vendramini, Elisa Zanuncio

1986-10-01

The theoretical model of wind speed distributions allow valuable information about the probability of events relative to the variable in study eliminating the necessity of a new experiment. The most used distributions has been the Weibull and the Rayleigh. These distributions are examined in the present investigation, as well as the exponential, gamma, chi square and lognormal distributions. Three years of hourly averages wind data recorded from a anemometer setting at the city of Ataliba Leonel, Sao Paulo State, Brazil, were used. Using wind speed distribution the theoretical relative frequency was calculated from the distributions which have been examined. Results from the Kolmogorov - Smirnov test allow to conclude that the lognormal distribution fit better the wind speed data, followed by the gamma and Rayleigh distributions. Using the lognormal probability density function the yearly energy output from a wind generator installed in the side was calculated. 30 refs, 4 figs, 14 tabs

基于韦伯模型的风场储能容量计算%Storage Capacity Calculation of Wind Power Based on Weibull Model

Institute of Scientific and Technical Information of China (English)

王树超

2013-01-01

Wind speed model and wind generator output model are analyzed by applying Weibull function to set up wind speed distribution model and the concept of probability theory to calculate the power capacity of energy storage system . The ratio of wind energy and storage capacity is reasonable and meets requirement of energy system by means of stimula -tion experiment .Under the condition of satisfying China ’ s wind power grid standard , the energy storage scale should be minimized and be verified by actual wind farm data .%分析了风电场风速的模型、风力发电机输出模型，运用韦伯函数建立风速分布模型，采用概率论期望的思想，计算储能系统功率容量。通过模拟仿真实验，得出满足电力系统要求的合理风储比。在满足我国风电并网标准的条件下，尽可能地减小储能系统规模，并利用实际风电场数据加以分析验证。

Stochastic distribution of the required coefficient of friction for level walking--an in-depth study.

Science.gov (United States)

Chang, Wen-Ruey; Matz, Simon; Chang, Chien-Chi

2012-01-01

This study investigated the stochastic distribution of the required coefficient of friction (RCOF) which is a critical element for estimating slip probability. Fifty participants walked under four walking conditions. The results of the Kolmogorov-Smirnov two-sample test indicate that 76% of the RCOF data showed a difference in distribution between both feet for the same participant under each walking condition; the data from both feet were kept separate. The results of the Kolmogorov-Smirnov goodness-of-fit test indicate that most of the distribution of the RCOF appears to have a good match with the normal (85.5%), log-normal (84.5%) and Weibull distributions (81.5%). However, approximately 7.75% of the cases did not have a match with any of these distributions. It is reasonable to use the normal distribution for representation of the RCOF distribution due to its simplicity and familiarity, but each foot had a different distribution from the other foot in 76% of cases. The stochastic distribution of the required coefficient of friction (RCOF) was investigated for use in a statistical model to improve the estimate of slip probability in risk assessment. The results indicate that 85.5% of the distribution of the RCOF appears to have a good match with the normal distribution.

Probability distributions of bed load particle velocities, accelerations, hop distances, and travel times informed by Jaynes's principle of maximum entropy

Science.gov (United States)

Furbish, David; Schmeeckle, Mark; Schumer, Rina; Fathel, Siobhan

2016-01-01

We describe the most likely forms of the probability distributions of bed load particle velocities, accelerations, hop distances, and travel times, in a manner that formally appeals to inferential statistics while honoring mechanical and kinematic constraints imposed by equilibrium transport conditions. The analysis is based on E. Jaynes's elaboration of the implications of the similarity between the Gibbs entropy in statistical mechanics and the Shannon entropy in information theory. By maximizing the information entropy of a distribution subject to known constraints on its moments, our choice of the form of the distribution is unbiased. The analysis suggests that particle velocities and travel times are exponentially distributed and that particle accelerations follow a Laplace distribution with zero mean. Particle hop distances, viewed alone, ought to be distributed exponentially. However, the covariance between hop distances and travel times precludes this result. Instead, the covariance structure suggests that hop distances follow a Weibull distribution. These distributions are consistent with high-resolution measurements obtained from high-speed imaging of bed load particle motions. The analysis brings us closer to choosing distributions based on our mechanical insight.

Compositional Analyses and Shelf-Life Modeling of Njangsa (Ricinodendron heudelotii) Seed Oil Using the Weibull Hazard Analysis.

Science.gov (United States)

Abaidoo-Ayin, Harold K; Boakye, Prince G; Jones, Kerby C; Wyatt, Victor T; Besong, Samuel A; Lumor, Stephen E

2017-08-01

This study investigated the compositional characteristics and shelf-life of Njangsa seed oil (NSO). Oil from Njangsa had a high polyunsaturated fatty acid (PUFA) content of which alpha eleostearic acid (α-ESA), an unusual conjugated linoleic acid was the most prevalent (about 52%). Linoleic acid was also present in appreciable amounts (approximately 34%). Our investigations also indicated that the acid-catalyzed transesterification of NSO resulted in lower yields of α-ESA methyl esters, due to isomerization, a phenomenon which was not observed under basic conditions. The triacylglycerol (TAG) profile analysis showed the presence of at least 1 α-ESA fatty acid chain in more than 95% of the oil's TAGs. Shelf-life was determined by the Weibull Hazard Sensory Method, where the end of shelf-life was defined as the time at which 50% of panelists found the flavor of NSO to be unacceptable. This was determined as 21 wk. Our findings therefore support the potential commercial viability of NSO as an important source of physiologically beneficial PUFAs. © 2017 Institute of Food Technologists®.

Comprehensive evaluation of wind speed distribution models: A case study for North Dakota sites

International Nuclear Information System (INIS)

Zhou Junyi; Erdem, Ergin; Li Gong; Shi Jing

2010-01-01

Accurate analysis of long term wind data is critical to the estimation of wind energy potential for a candidate location and its nearby area. Investigating the wind speed distribution is one critical task for this purpose. This paper presents a comprehensive evaluation on probability density functions for the wind speed data from five representative sites in North Dakota. Besides the popular Weibull and Rayleigh distributions, we also include other distributions such as gamma, lognormal, inverse Gaussian, and maximum entropy principle (MEP) derived probability density functions (PDFs). Six goodness-of-fit (GOF) statistics are used to determine the appropriate distributions for the wind speed data for each site. It is found that no particular distribution outperforms others for all five sites, while Rayleigh distribution performs poorly for most of the sites. Similar to other models, the performances of MEP-derived PDFs in fitting wind speed data varies from site to site. Also, the results demonstrate that MEP-derived PDFs are flexible and have the potential to capture other possible distribution patterns of wind speed data. Meanwhile, different GOF statistics may generate inconsistent ranking orders of fit performance among the candidate PDFs. In addition, one comprehensive metric that combines all individual statistics is proposed to rank the overall performance for the chosen statistical distributions.

Statistical investigation of the crack initiation lives of piping structural welded joint in low cycle fatigue test of 240 degree C

International Nuclear Information System (INIS)

Zhao Yongxiang; Gao Qing; Cai Lixun

1999-01-01

A statistical investigation into the fitting of four possible fatigue assumed distributions (three parameter Weibull, two parameter Weibull, lognormal and extreme maximum value distributions) for the crack initiation lives of piping structural welded joint in low cycle fatigue test of 240 degree C is performed by linear regression and least squares methods. The results reveal that the three parameters Weibull distribution may give misleading results in fatigue reliability analysis because the shape parameter is often less than 1. This means that the failure rate decreases with fatigue cycling which is contrary to the general understanding of the behaviour of welded joint. Reliability analyses may also affected by the slightly nonconservative evaluations in tail regions of this distribution. The other three distributions are slightly poor in the total fit effects, but they can be safety assumed in reliability analyses due to the non-conservative evaluations in tail regions mostly and the consistency with the fatigue physics of the structural behaviour of welded joint in the range of engineering practice. In addition, the extreme maximum value distribution is in good consists with the general physical understanding of the structural behaviour of welded joint

A statistical model for horizontal mass flux of erodible soil

International Nuclear Information System (INIS)

Babiker, A.G.A.G.; Eltayeb, I.A.; Hassan, M.H.A.

1986-11-01

It is shown that the mass flux of erodible soil transported horizontally by a statistically distributed wind flow has a statistical distribution. Explicit expression for the probability density function, p.d.f., of the flux is derived for the case in which the wind speed has a Weibull distribution. The statistical distribution for a mass flux characterized by a generalized Bagnold formula is found to be Weibull for the case of zero threshold speed. Analytic and numerical values for the average horizontal mass flux of soil are obtained for various values of wind parameters, by evaluating the first moment of the flux density function. (author)

Effect of particle size and distribution of the sizing agent on the carbon fibers surface and interfacial shear strength (IFSS) of its composites

International Nuclear Information System (INIS)

Zhang, R.L.; Liu, Y.; Huang, Y.D.; Liu, L.

2013-01-01

Effect of particle size and distribution of the sizing agent on the performance of carbon fiber and carbon fiber composites has been investigated. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) were used to characterize carbon fiber surface topographies. At the same time, the single fiber strength and Weibull distribution were also studied in order to investigate the effect of coatings on the fibers. The interfacial shear strength and hygrothermal aging of the carbon fiber/epoxy resin composites were also measured. The results indicated that the particle size and distribution is important for improving the surface of carbon fibers and its composites performance. Different particle size and distribution of sizing agent has different contribution to the wetting performance of carbon fibers. The fibers sized with P-2 had higher value of IFSS and better hygrothermal aging resistant properties.

Study on constant-step stress accelerated life tests in white organic light-emitting diodes.

Science.gov (United States)

Zhang, J P; Liu, C; Chen, X; Cheng, G L; Zhou, A X

2014-11-01

In order to obtain reliability information for a white organic light-emitting diode (OLED), two constant and one step stress tests were conducted with its working current increased. The Weibull function was applied to describe the OLED life distribution, and the maximum likelihood estimation (MLE) and its iterative flow chart were used to calculate shape and scale parameters. Furthermore, the accelerated life equation was determined using the least squares method, a Kolmogorov-Smirnov test was performed to assess if the white OLED life follows a Weibull distribution, and self-developed software was used to predict the average and the median lifetimes of the OLED. The numerical results indicate that white OLED life conforms to a Weibull distribution, and that the accelerated life equation completely satisfies the inverse power law. The estimated life of a white OLED may provide significant guidelines for its manufacturers and customers. Copyright © 2014 John Wiley & Sons, Ltd.

On dielectric breakdown statistics

International Nuclear Information System (INIS)

Tuncer, Enis; James, D Randy; Sauers, Isidor; Ellis, Alvin R; Pace, Marshall O

2006-01-01

In this paper, we investigate the dielectric breakdown data of some insulating materials and focus on the applicability of the two- and three-parameter Weibull distributions. A new distribution function is also proposed. In order to assess the model distribution's trustworthiness, we employ the Monte Carlo technique and, randomly selecting data-subsets from the whole dielectric breakdown data, determine whether the selected probability functions accurately describe the breakdown data. The utility and strength of the proposed expression are illustrated distinctly by the numerical procedure. The proposed expression is shown to be a valuable alternative to the Weibull ones

Monitoring and quantifying future climate projections of dryness and wetness extremes: SPI bias

Directory of Open Access Journals (Sweden)

F. Sienz

2012-07-01

Full Text Available The adequacy of the gamma distribution (GD for monthly precipitation totals is reconsidered. The motivation for this study is the observation that the GD fails to represent precipitation in considerable areas of global observed and simulated data. This misrepresentation may lead to erroneous estimates of the Standardised Precipitation Index (SPI, evaluations of models, and assessments of climate change. In this study, the GD is compared to the Weibull (WD, Burr Type III (BD, exponentiated Weibull (EWD and generalised gamma (GGD distribution. These distributions extend the GD in terms of possible shapes (skewness and kurtosis and the behaviour for large arguments. The comparison is based on the Akaike information criterion, which maximises information entropy and reveals a trade-off between deviation and the numbers of parameters used. We use monthly sums of observed and simulated precipitation for 12 calendar months of the year. Assessing observed and simulated data, (i the Weibull type distributions give distinctly improved fits compared to the GD and (ii the SPI resulting from the GD overestimates (underestimates extreme dryness (wetness.

Wind climate modeling using Weibull and extreme value distribution ...

African Journals Online (AJOL)

It is very much important to fit wind speed data into some suitable statistical model for two aspects. One is fatigue failure due to periodic vortex shedding and the other is to estimate the wind energy potential of a particular location. For the fatigue failure due to periodic vortex shedding, it is important to analyse the load cycle.

Temporal distribution of earthquakes using renewal process in the Dasht-e-Bayaz region

Science.gov (United States)

Mousavi, Mehdi; Salehi, Masoud

2018-01-01

Temporal distribution of earthquakes with M w > 6 in the Dasht-e-Bayaz region, eastern Iran has been investigated using time-dependent models. Based on these types of models, it is assumed that the times between consecutive large earthquakes follow a certain statistical distribution. For this purpose, four time-dependent inter-event distributions including the Weibull, Gamma, Lognormal, and the Brownian Passage Time (BPT) are used in this study and the associated parameters are estimated using the method of maximum likelihood estimation. The suitable distribution is selected based on logarithm likelihood function and Bayesian Information Criterion. The probability of the occurrence of the next large earthquake during a specified interval of time was calculated for each model. Then, the concept of conditional probability has been applied to forecast the next major ( M w > 6) earthquake in the site of our interest. The emphasis is on statistical methods which attempt to quantify the probability of an earthquake occurring within a specified time, space, and magnitude windows. According to obtained results, the probability of occurrence of an earthquake with M w > 6 in the near future is significantly high.

Nonparametric Fine Tuning of Mixtures: Application to Non-Life Insurance Claims Distribution Estimation

Science.gov (United States)

Sardet, Laure; Patilea, Valentin

When pricing a specific insurance premium, actuary needs to evaluate the claims cost distribution for the warranty. Traditional actuarial methods use parametric specifications to model claims distribution, like lognormal, Weibull and Pareto laws. Mixtures of such distributions allow to improve the flexibility of the parametric approach and seem to be quite well-adapted to capture the skewness, the long tails as well as the unobserved heterogeneity among the claims. In this paper, instead of looking for a finely tuned mixture with many components, we choose a parsimonious mixture modeling, typically a two or three-component mixture. Next, we use the mixture cumulative distribution function (CDF) to transform data into the unit interval where we apply a beta-kernel smoothing procedure. A bandwidth rule adapted to our methodology is proposed. Finally, the beta-kernel density estimate is back-transformed to recover an estimate of the original claims density. The beta-kernel smoothing provides an automatic fine-tuning of the parsimonious mixture and thus avoids inference in more complex mixture models with many parameters. We investigate the empirical performance of the new method in the estimation of the quantiles with simulated nonnegative data and the quantiles of the individual claims distribution in a non-life insurance application.

Minimum K-S estimator using PH-transform technique

Directory of Open Access Journals (Sweden)

Somchit Boonthiem

2016-07-01

Full Text Available In this paper, we propose an improvement of the Minimum Kolmogorov-Smirnov (K-S estimator using proportional hazards transform (PH-transform technique. The data of experiment is 47 fire accidents data of an insurance company in Thailand. This experiment has two operations, the first operation, we minimize K-S statistic value using grid search technique for nine distributions; Rayleigh distribution, gamma distribution, Pareto distribution, log-logistic distribution, logistic distribution, normal distribution, Weibull distribution, lognormal distribution, and exponential distribution and the second operation, we improve K-S statistic using PHtransform. The result appears that PH-transform technique can improve the Minimum K-S estimator. The algorithms give better the Minimum K-S estimator for seven distributions; Rayleigh distribution, logistic distribution, gamma distribution, Pareto distribution, log-logistic distribution, normal distribution, Weibull distribution, log-normal distribution, and exponential distribution while the Minimum K-S estimators of normal distribution and logistic distribution are unchanged

Sensitivity Weaknesses in Application of some Statistical Distribution in First Order Reliability Methods

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Enevoldsen, I.

1993-01-01

It has been observed and shown that in some examples a sensitivity analysis of the first order reliability index results in increasing reliability index, when the standard deviation for a stochastic variable is increased while the expected value is fixed. This unfortunate behaviour can occur when...... a stochastic variable is modelled by an asymmetrical density function. For lognormally, Gumbel and Weibull distributed stochastic variables it is shown for which combinations of the/3-point, the expected value and standard deviation the weakness can occur. In relation to practical application the behaviour...... is probably rather infrequent. A simple example is shown as illustration and to exemplify that for second order reliability methods and for exact calculations of the probability of failure this behaviour is much more infrequent....

The time interval distribution of sand–dust storms in theory: testing with observational data for Yanchi, China

International Nuclear Information System (INIS)

Liu, Guoliang; Zhang, Feng; Hao, Lizhen

2012-01-01

We previously introduced a time record model for use in studying the duration of sand–dust storms. In the model, X is the normalized wind speed and Xr is the normalized wind speed threshold for the sand–dust storm. X is represented by a random signal with a normal Gaussian distribution. The storms occur when X ≥ Xr. From this model, the time interval distribution of N = Aexp(−bt) can be deduced, wherein N is the number of time intervals with length greater than t, A and b are constants, and b is related to Xr. In this study, sand–dust storm data recorded in spring at the Yanchi meteorological station in China were analysed to verify whether the time interval distribution of the sand–dust storms agrees with the above time interval distribution. We found that the distribution of the time interval between successive sand–dust storms in April agrees well with the above exponential equation. However, the interval distribution for the sand–dust storm data for the entire spring period displayed a better fit to the Weibull equation and depended on the variation of the sand–dust storm threshold wind speed. (paper)

Weibull modulus of hardness, bend strength, and tensile strength of Ni−Ta−Co−X metallic glass ribbons

Energy Technology Data Exchange (ETDEWEB)

Neilson, Henry J., E-mail: hjn2@case.edu [Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH (United States); Petersen, Alex S.; Cheung, Andrew M.; Poon, S. Joseph; Shiflet, Gary J. [University of Virginia, 395 McCormick Road, P.O. Box 400745, Charlottesville, VA 22904 (United States); Widom, Mike [Carnegie Mellon University, 5000 Forbes Avenue, Wean Hall 3325, Pittsburgh, PA 15213 (United States); Lewandowski, John J. [Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH (United States)

2015-05-14

In this study, the variations in mechanical properties of Ni−Co−Ta-based metallic glasses have been analyzed. Three different chemistries of metallic glass ribbons were analyzed: Ni{sub 45}Ta{sub 35}Co{sub 20}, Ni{sub 40}Ta{sub 35}Co{sub 20}Nb{sub 5}, and Ni{sub 30}Ta{sub 35}Co{sub 30}Nb{sub 5}. These alloys possess very high density (approximately 12.5 g/cm{sup 3}) and very high strength (e.g. >3 GPa). Differential scanning calorimetry (DSC) and x-ray diffraction (XRD) were used to characterize the amorphicity of the ribbons. Mechanical properties were measured via a combination of Vickers hardness, bending strength, and tensile strength for each chemistry. At least 50 tests were conducted for each chemistry and each test technique in order to quantify the variability of properties using both 2- and 3-parameter Weibull statistics. The variability in properties and their source(s) were compared to that of other engineering materials, while the nature of deformation via shear bands as well as fracture surface features have been determined using scanning electron microscopy (SEM). Toughness, the role of defects, and volume effects are also discussed.

Statistical Analysis of Data for Timber Strengths

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard

2003-01-01

Statistical analyses are performed for material strength parameters from a large number of specimens of structural timber. Non-parametric statistical analysis and fits have been investigated for the following distribution types: Normal, Lognormal, 2 parameter Weibull and 3-parameter Weibull...... fits to the data available, especially if tail fits are used whereas the Log Normal distribution generally gives a poor fit and larger coefficients of variation, especially if tail fits are used. The implications on the reliability level of typical structural elements and on partial safety factors...... for timber are investigated....

Increase in the accuracy of approximating the profile of the erosion zone in planar magnetrons

Science.gov (United States)

Rogov, A. V.; Kapustin, Yu. V.

2017-09-01

It has been shown that the use of the survival function of the Weibull distribution shifted along the ordinate axis allows one to increase the accuracy of the approximation of the normalized profile of an erosion zone in the area from the axis to the maximum sputtering region compared with the previously suggested distribution function of the extremum values. The survival function of the Weibull distribution is used in the area from the maximum to the outer boundary of an erosion zone. The major advantage of using the new approximation is observed for magnetrons with a large central nonsputtered spot and for magnetrons with substantial sputtering in the paraxial zone.

Development of Testing Methodologies for the Mechanical Properties of MEMS

Science.gov (United States)

Ekwaro-Osire, Stephen

2003-01-01

This effort is to investigate and design testing strategies to determine the mechanical properties of MicroElectroMechanical Systems (MEMS) as well as investigate the development of a MEMS Probabilistic Design Methodology (PDM). One item of potential interest is the design of a test for the Weibull size effect in pressure membranes. The Weibull size effect is a consequence of a stochastic strength response predicted from the Weibull distribution. Confirming that MEMS strength is controlled by the Weibull distribution will enable the development of a probabilistic design methodology for MEMS - similar to the GRC developed CARES/Life program for bulk ceramics. However, the primary area of investigation will most likely be analysis and modeling of material interfaces for strength as well as developing a strategy to handle stress singularities at sharp corners, filets, and material interfaces. This will be a continuation of the previous years work. The ultimate objective of this effort is to further develop and verify the ability of the Ceramics Analysis and Reliability Evaluation of Structures Life (CARES/Life) code to predict the time-dependent reliability of MEMS structures subjected to multiple transient loads.

Leveraging comprehensive baseline datasets to quantify property variability in nuclear-grade graphites

Energy Technology Data Exchange (ETDEWEB)

Carroll, Mark C., E-mail: mark.carroll@inl.gov [Idaho National Laboratory, PO Box 1625, Idaho Falls, ID 83415-2213 (United States); Windes, William E.; Rohrbaugh, David T. [Idaho National Laboratory, PO Box 1625, Idaho Falls, ID 83415-2213 (United States); Strizak, Joseph P.; Burchell, Timothy D. [Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, TN 37831-6088 (United States)

2016-10-15

Highlights: • An effort is underway to fully quantify the properties of nuclear-grade graphites. • Physical and mechanical properties of graphite are best characterized by distributions. • The Weibull distribution is most representative of graphite based on goodness-of-fit. • Fine-grained isomolded grades exhibit higher Weibull modulus values, indicative of more homogeneous properties. - Abstract: The full characterization of the physical and mechanical properties of candidate nuclear-grade graphites is highly dependent upon an understanding of the distribution of values that are inherent to graphite. Not only do the material properties of graphites vary considerably between grades owing to the raw materials sources, filler particle type and size, methods of compaction, and production process parameters, but variability is observed between billets of the same grade from a single batch and even across spatial positions within a single billet. Properly enveloping the expected properties of interest requires both a substantial amount of data to statistically capture this variability and a representative distribution capable of accurately describing the range of values. A two-parameter Weibull distribution is confirmed to be representative of the distribution of physical (density, modulus) and mechanical (compressive, flexure, and tensile strength) values in five different nuclear-grades of graphite. The fine-grained isomolded grades tend toward higher Weibull modulus and characteristic strength values, while the extruded grade being examined exhibits relatively large distributions in property values. With the number of candidate graphite specimens that can undergo full irradiation exposure and subsequent testing having limited feasibility with regard to economics and timely evaluations, a proper capture of the raw material variability in an unirradiated state can provide crucial supplementary resolution to the limited amount of available data on irradiated

Automatic Threshold Detector Techniques

Science.gov (United States)

1976-07-15

Averaging CFAR in Non- Stationary Weibull Clutter, " L. Novak, (1974 IEEE Symposium on Information Theory ). 8. "The Weibull Distribution Applied to the... UGTS (K) ,Kml NPTS) 140 DO 153 K~lvNPT9 IF(SIGCSO(K) .LT.0. )SIOCSO(K).1 .E-50 IF(SIOWSO(K) .LT.0. )SIGWSQ(K)-1 .E-50 IF(SIONSG(K) .LT.O. )SIG3NSQCIO-1.E

Statistical aspects of fatigue crack growth life of base metal, weld metal and heat affected zone in FSWed 7075-T651aluminum alloy

International Nuclear Information System (INIS)

Sohn, Hye Jeong; Haryadi, Gunawan Dwi; Kim, Seon Jin

2014-01-01

The statistical aspects of fatigue crack growth life of base metal (BM), weld metal (WM) and heat affected zone (HAZ) in friction stir welded (FSWed) 7075-T651 aluminum alloy has been studied by Weibull statistical analysis. The fatigue crack growth tests were performed at room temperature on ASTM standard CT specimens under three different constant stress intensity factor range controls. The main objective of this paper is to investigate the effects of statistical aspects of fatigue crack growth life on stress intensity factor ranges and material properties, namely BM, WM and HAZ specimens. In this work, the Weibull distribution was employed to estimate the statistical aspects of fatigue crack growth life. The shape parameter of Weibull distribution for fatigue crack growth life was significantly affected by material properties and the stress intensity factor range. The scale parameter of WM specimen exhibited the lowest value at all stress intensity factor ranges.

Diameter distribution in a Brazilian tropical dry forest domain: predictions for the stand and species.

Science.gov (United States)

Lima, Robson B DE; Bufalino, Lina; Alves, Francisco T; Silva, José A A DA; Ferreira, Rinaldo L C

2017-01-01

Currently, there is a lack of studies on the correct utilization of continuous distributions for dry tropical forests. Therefore, this work aims to investigate the diameter structure of a brazilian tropical dry forest and to select suitable continuous distributions by means of statistic tools for the stand and the main species. Two subsets were randomly selected from 40 plots. Diameter at base height was obtained. The following functions were tested: log-normal; gamma; Weibull 2P and Burr. The best fits were selected by Akaike's information validation criterion. Overall, the diameter distribution of the dry tropical forest was better described by negative exponential curves and positive skewness. The forest studied showed diameter distributions with decreasing probability for larger trees. This behavior was observed for both the main species and the stand. The generalization of the function fitted for the main species show that the development of individual models is needed. The Burr function showed good flexibility to describe the diameter structure of the stand and the behavior of Mimosa ophthalmocentra and Bauhinia cheilantha species. For Poincianella bracteosa, Aspidosperma pyrifolium and Myracrodum urundeuva better fitting was obtained with the log-normal function.

Statistical wind analysis for near-space applications

Science.gov (United States)

Roney, Jason A.

2007-09-01

Statistical wind models were developed based on the existing observational wind data for near-space altitudes between 60 000 and 100 000 ft (18 30 km) above ground level (AGL) at two locations, Akon, OH, USA, and White Sands, NM, USA. These two sites are envisioned as playing a crucial role in the first flights of high-altitude airships. The analysis shown in this paper has not been previously applied to this region of the stratosphere for such an application. Standard statistics were compiled for these data such as mean, median, maximum wind speed, and standard deviation, and the data were modeled with Weibull distributions. These statistics indicated, on a yearly average, there is a lull or a “knee” in the wind between 65 000 and 72 000 ft AGL (20 22 km). From the standard statistics, trends at both locations indicated substantial seasonal variation in the mean wind speed at these heights. The yearly and monthly statistical modeling indicated that Weibull distributions were a reasonable model for the data. Forecasts and hindcasts were done by using a Weibull model based on 2004 data and comparing the model with the 2003 and 2005 data. The 2004 distribution was also a reasonable model for these years. Lastly, the Weibull distribution and cumulative function were used to predict the 50%, 95%, and 99% winds, which are directly related to the expected power requirements of a near-space station-keeping airship. These values indicated that using only the standard deviation of the mean may underestimate the operational conditions.

Determining the best population-level alcohol consumption model and its impact on estimates of alcohol-attributable harms

Directory of Open Access Journals (Sweden)

Kehoe Tara

2012-04-01

Full Text Available Abstract Background The goals of our study are to determine the most appropriate model for alcohol consumption as an exposure for burden of disease, to analyze the effect of the chosen alcohol consumption distribution on the estimation of the alcohol Population- Attributable Fractions (PAFs, and to characterize the chosen alcohol consumption distribution by exploring if there is a global relationship within the distribution. Methods To identify the best model, the Log-Normal, Gamma, and Weibull prevalence distributions were examined using data from 41 surveys from Gender, Alcohol and Culture: An International Study (GENACIS and from the European Comparative Alcohol Study. To assess the effect of these distributions on the estimated alcohol PAFs, we calculated the alcohol PAF for diabetes, breast cancer, and pancreatitis using the three above-named distributions and using the more traditional approach based on categories. The relationship between the mean and the standard deviation from the Gamma distribution was estimated using data from 851 datasets for 66 countries from GENACIS and from the STEPwise approach to Surveillance from the World Health Organization. Results The Log-Normal distribution provided a poor fit for the survey data, with Gamma and Weibull distributions providing better fits. Additionally, our analyses showed that there were no marked differences for the alcohol PAF estimates based on the Gamma or Weibull distributions compared to PAFs based on categorical alcohol consumption estimates. The standard deviation of the alcohol distribution was highly dependent on the mean, with a unit increase in alcohol consumption associated with a unit increase in the mean of 1.258 (95% CI: 1.223 to 1.293 (R2 = 0.9207 for women and 1.171 (95% CI: 1.144 to 1.197 (R2 = 0. 9474 for men. Conclusions Although the Gamma distribution and the Weibull distribution provided similar results, the Gamma distribution is recommended to model alcohol

Computer Model to Estimate Reliability Engineering for Air Conditioning Systems

International Nuclear Information System (INIS)

Afrah Al-Bossly, A.; El-Berry, A.; El-Berry, A.

2012-01-01

Reliability engineering is used to predict the performance and optimize design and maintenance of air conditioning systems. Air conditioning systems are expose to a number of failures. The failures of an air conditioner such as turn on, loss of air conditioner cooling capacity, reduced air conditioning output temperatures, loss of cool air supply and loss of air flow entirely can be due to a variety of problems with one or more components of an air conditioner or air conditioning system. Forecasting for system failure rates are very important for maintenance. This paper focused on the reliability of the air conditioning systems. Statistical distributions that were commonly applied in reliability settings: the standard (2 parameter) Weibull and Gamma distributions. After distributions parameters had been estimated, reliability estimations and predictions were used for evaluations. To evaluate good operating condition in a building, the reliability of the air conditioning system that supplies conditioned air to the several The company's departments. This air conditioning system is divided into two, namely the main chilled water system and the ten air handling systems that serves the ten departments. In a chilled-water system the air conditioner cools water down to 40-45 degree F (4-7 degree C). The chilled water is distributed throughout the building in a piping system and connected to air condition cooling units wherever needed. Data analysis has been done with support a computer aided reliability software, this is due to the Weibull and Gamma distributions indicated that the reliability for the systems equal to 86.012% and 77.7% respectively. A comparison between the two important families of distribution functions, namely, the Weibull and Gamma families was studied. It was found that Weibull method performed for decision making.

Wind energy potential in Peshawar, Pakistan

International Nuclear Information System (INIS)

Nasir, S.M.; Raza, S.M.

1994-01-01

Hourly wind data at Peshawar airport, received from the Headquarters, Pakistan Air Force, has been used to determine the diurnal variations, speed duration and speed frequency curves. The applicability of Weibull distribution is then tested over probability density function, which shows that weibull distribution fits the wind data satisfactorily and with a good precision, provided the observations of calm spells are omitted. Our analysis shows that monthly mean wind speed and wind power varies from 0.6 to 2.0 m/s and 0.2 to 4.0 wm-2, respectively, giving fair prospects for wind owe applications over the summer months. (author)

Statistical analysis of the ASME KIc database

International Nuclear Information System (INIS)

Sokolov, M.A.

1998-01-01

The American Society of Mechanical Engineers (ASME) K Ic curve is a function of test temperature (T) normalized to a reference nil-ductility temperature, RT NDT , namely, T-RT NDT . It was constructed as the lower boundary to the available K Ic database. Being a lower bound to the unique but limited database, the ASME K Ic curve concept does not discuss probability matters. However, a continuing evolution of fracture mechanics advances has led to employment of the Weibull distribution function to model the scatter of fracture toughness values in the transition range. The Weibull statistic/master curve approach was applied to analyze the current ASME K Ic database. It is shown that the Weibull distribution function models the scatter in K Ic data from different materials very well, while the temperature dependence is described by the master curve. Probabilistic-based tolerance-bound curves are suggested to describe lower-bound K Ic values

Observations in the statistical analysis of NBG-18 nuclear graphite strength tests

International Nuclear Information System (INIS)

Hindley, Michael P.; Mitchell, Mark N.; Blaine, Deborah C.; Groenwold, Albert A.

2012-01-01

Highlights: ► Statistical analysis of NBG-18 nuclear graphite strength test. ► A Weibull distribution and normal distribution is tested for all data. ► A Bimodal distribution in the CS data is confirmed. ► The CS data set has the lowest variance. ► A Combined data set is formed and has Weibull distribution. - Abstract: The purpose of this paper is to report on the selection of a statistical distribution chosen to represent the experimental material strength of NBG-18 nuclear graphite. Three large sets of samples were tested during the material characterisation of the Pebble Bed Modular Reactor and Core Structure Ceramics materials. These sets of samples are tensile strength, flexural strength and compressive strength (CS) measurements. A relevant statistical fit is determined and the goodness of fit is also evaluated for each data set. The data sets are also normalised for ease of comparison, and combined into one representative data set. The validity of this approach is demonstrated. A second failure mode distribution is found on the CS test data. Identifying this failure mode supports the similar observations made in the past. The success of fitting the Weibull distribution through the normalised data sets allows us to improve the basis for the estimates of the variability. This could also imply that the variability on the graphite strength for the different strength measures is based on the same flaw distribution and thus a property of the material.

Estimation of design wave heights based on exterme value statistics for Kakinada coast, Bay of Bengal

Digital Repository Service at National Institute of Oceanography (India)

Chandramohan, P.; Nayak, B.U.; Raju, N.S.N.

Statistical analyses for longterm distribution of significant wave heights were performed using Lognormal, Weibull, Gumbel and Fretcher distributions for waves measured off Kakinada, Andhra Pradesh, India from June 1983 to May 1984. Fretcher...

Assessing biomass based on canopy height profiles using airborne laser scanning data in eucalypt plantations

Directory of Open Access Journals (Sweden)

André Gracioso Peres Silva

2015-12-01

Full Text Available This study aimed to map the stem biomass of an even-aged eucalyptus plantation in southeastern Brazil based on canopy height profile (CHPs statistics using wall-to-wall discrete return airborne laser scanning (ALS, and compare the results with alternative maps generated by ordinary kriging interpolation from field-derived measurements. The assessment of stem biomass with ALS data was carried out using regression analysis methods. Initially, CHPs were determined to express the distribution of laser point heights in the ALS cloud for each sample plot. The probability density function (pdf used was the Weibull distribution, with two parameters that in a secondary task, were used as explanatory variables to model stem biomass. ALS metrics such as height percentiles, dispersion of heights, and proportion of points were also investigated. A simple linear regression model of stem biomass as a function of the Weibull scale parameter showed high correlation (adj.R2 = 0.89. The alternative model considering the 30th percentile and the Weibull shape parameter slightly improved the quality of the estimation (adj.R2 = 0.93. Stem biomass maps based on the Weibull scale parameter doubled the accuracy of the ordinary kriging approach (relative root mean square error = 6 % and 13 %, respectively.

Evaluation of the climate change impact on wind resources in Taiwan Strait

International Nuclear Information System (INIS)

Chang, Tsang-Jung; Chen, Chun-Lung; Tu, Yi-Long; Yeh, Hung-Te; Wu, Yu-Ting

2015-01-01

Highlights: • We propose a new statistical downscaling framework to evaluate the climate change impact on wind resources in Taiwan Strait. • The statistical model relates Weibull distribution parameters to output of a GCM model and regression coefficients. • Validation of the simulated wind speed distribution presents an acceptable agreement with meteorological data. • Three chosen GCMs show the same tendency that the eastern half of Taiwan Strait stores higher wind resources. - Abstract: A new statistical downscaling framework is proposed to evaluate the climate change impact on wind resources in Taiwan Strait. In this framework, a two-parameter Weibull distribution function is used to estimate the wind energy density distribution in the strait. An empirically statistical downscaling model that relates the Weibull parameters to output of a General Circulation Model (GCM) and regression coefficients is adopted. The regression coefficients are calculated using wind speed results obtained from a past climate (1981–2000) simulation reconstructed by a Weather Research and Forecasting (WRF) model. These WRF-reconstructed wind speed results are validated with data collected at a weather station on an islet inside the strait. The comparison shows that the probability distributions of the monthly wind speeds obtained from WRF-reconstructed and measured wind speed data are in acceptable agreement, with small discrepancies of 10.3% and 7.9% for the shape and scale parameters of the Weibull distribution, respectively. The statistical downscaling framework with output from three chosen GCMs (i.e., ECHAM5, CM2.1 and CGCM2.3.2) is applied to evaluate the wind energy density distribution in Taiwan Strait for three future climate periods of 2011–2040, 2041–2070, and 2071–2100. The results show that the wind energy density distributions in the future climate periods are higher in the eastern half of Taiwan Strait, but reduce slightly by 3% compared with that in the

Stochastic Analysis of Wind Energy for Wind Pump Irrigation in Coastal Andhra Pradesh, India

Science.gov (United States)

Raju, M. M.; Kumar, A.; Bisht, D.; Rao, D. B.

2014-09-01

The rapid escalation in the prices of oil and gas as well as increasing demand for energy has attracted the attention of scientists and researchers to explore the possibility of generating and utilizing the alternative and renewable sources of wind energy in the long coastal belt of India with considerable wind energy resources. A detailed analysis of wind potential is a prerequisite to harvest the wind energy resources efficiently. Keeping this in view, the present study was undertaken to analyze the wind energy potential to assess feasibility of the wind-pump operated irrigation system in the coastal region of Andhra Pradesh, India, where high ground water table conditions are available. The stochastic analysis of wind speed data were tested to fit a probability distribution, which describes the wind energy potential in the region. The normal and Weibull probability distributions were tested; and on the basis of Chi square test, the Weibull distribution gave better results. Hence, it was concluded that the Weibull probability distribution may be used to stochastically describe the annual wind speed data of coastal Andhra Pradesh with better accuracy. The size as well as the complete irrigation system with mass curve analysis was determined to satisfy various daily irrigation demands at different risk levels.

Predicting The Exit Time Of Employees In An Organization Using Statistical Model

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Ahmed Al Kuwaiti

2015-08-01

Full Text Available Employees are considered as an asset to any organization and each organization provide a better and flexible working environment to retain its best and resourceful workforce. As such continuous efforts are being taken to avoid or extend the exitwithdrawal of employees from the organization. Human resource managers are facing a challenge to predict the exit time of employees and there is no precise model existing at present in the literature. This study has been conducted to predict the probability of exit of an employee in an organization using appropriate statistical model. Accordingly authors designed a model using Additive Weibull distribution to predict the expected exit time of employee in an organization. In addition a Shock model approach is also executed to check how well the Additive Weibull distribution suits in an organization. The analytical results showed that when the inter-arrival time increases the expected time for the employees to exit also increases. This study concluded that Additive Weibull distribution can be considered as an alternative in the place of Shock model approach to predict the exit time of employee in an organization.

Study on the product estimation of small wind turbines; Kogata fusha no hatsudenryo yosoku ni kansuru kenkyu

Energy Technology Data Exchange (ETDEWEB)

Matsuzawa, K.; Kimura, Y.; Ushiyama, I. [Ashikaga Institute of Technology, Tochigi (Japan); Nagai, H. [Nihon Univ., Chiba (Japan). Coll. of Industrial Technology

1998-09-01

In order to clarify problems involved in application of Weibull probability distribution used for estimation of power production by a large wind turbine to a small wind turbine, and solutions thereof, the estimated results are compared with the observed ones. The conventional estimation method, when applied to a small wind turbine, tends to overestimate production of power, because of overestimated production in a high wind velocity range which occurs less frequently. Estimation of power produced by a wind turbine is based on working wind velocity range, determined from the furling mechanism for the power generation characteristics of the wind turbine concerned. In the case of a small wind turbine, on the other hand, better estimates are obtained from the working wind velocity range in which Weibull wind velocity distribution is used to determine probability of occurrence. For wind turbines working at low to medium wind velocities, such as Savonius wind turbine, the estimates are in fairly good agreement with the observed results, by which is meant that the conventional estimation method aided by Weibull distribution can be directly applicable to small wind turbines. 4 refs., 3 figs., 3 tabs.

Failure rate and reliability of the KOMATSU hydraulic excavator in surface limestone mine

Science.gov (United States)

Harish Kumar N., S.; Choudhary, R. P.; Murthy, Ch. S. N.

2018-04-01

The model with failure rate function of bathtub-shaped is helpful in reliability analysis of any system and particularly in reliability associated privative maintenance. The usual Weibull distribution is, however, not capable to model the complete lifecycle of the any with a bathtub-shaped failure rate function. In this paper, failure rate and reliability analysis of the KOMATSU hydraulic excavator/shovel in surface mine is presented and also to improve the reliability and decrease the failure rate of each subsystem of the shovel based on the preventive maintenance. The model of the bathtub-shaped for shovel can also be seen as a simplification of the Weibull distribution.

statistical analysis of wind speed for electrical power generation

African Journals Online (AJOL)

HOD

In order to predict and model the potential of any site, ... gamma, and Raleigh distributions for 8 locations in. Nigeria. ... probability density function is used to model the average power in ... mathematical expression of the Weibull distribution is.

Wind Resource Assessment in Abadan Airport in Iran

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Mojtaba Nedaei

2012-11-01

Full Text Available Renewable energies have potential for supplying of relatively clean and mostly local energy. Wind energy generation is expected to increase in the near future and has experienced dramatic growth over the past decade in many countries. Wind speed is the most important parameter in the design and study of wind energy conversion systems. Probability density functions such as Weibull and Rayleigh are often used in wind speed and wind energy analyses. This paper presents an assessment of wind energy at three heights during near two years based on Weibull distribution function in Abadan Airport. Extrapolation of the 10 m and 40 m data, using the power law, has been used to determine the wind speed at height of 80 m. According to the results wind speed at 80 m height in Abadan is ranged from 5.8 m/s in Nov to 8.5 m/s in Jun with average value of 7.15 m/s. In this study, different parameters such as Weibull parameters, diurnal and monthly wind speeds, cumulative distribution and turbulence intensity have been estimated and analyzed. In addition Energy production of different wind turbines at different heights was estimated. The results show that the studied site has good potential for Installation of large and commercial wind turbines at height of 80 m or higher. Keywords: Abadan, Iran, wind energy, wind resource, wind turbine, Weibull

Use of Frequency Distribution Functions to Establish Safe Conditions in Relation to the Foodborne Pathogen Bacillus cereus

Directory of Open Access Journals (Sweden)

Begoña Delgado

2005-01-01

Full Text Available Minimal processing implementation greatly depends on a detailed knowledge of the effects of preservation factors and their combinations on the spoilage and foodborne pathogenic microorganisms. The effectiveness of mild preservation conditions will become increasingly dependent on a more stochastic approach linking microbial physiological factors with product preservation factors. In this study, the validity of frequency distributions to efficiently describe the inactivation and growth of Bacillus cereus in the presence of natural antimicrobials (essential oils has been studied. For this purpose, vegetative cells were exposed to 0.6 mM of thymol or cymene, obtaining survival curves that were best described by the distribution of Weibull, since a tailing effect was observed. B. cereus was also exposed in a growth medium to a low concentration (0.1 mM of both antimicrobials, separately or combined, and the lag times obtained were fitted to a normal distribution, which allowed a description of dispersion of the start of growth. This allowed a more efficient evaluation of the experimental data to establish safe processing conditions according to accurate parameters and their implementation in risk assessment.

A Stand-Class Growth and Yield Model for Mexico’s Northern Temperate, Mixed and Multiaged Forests

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José Návar

2014-12-01

Full Text Available The aim of this research was to develop a stand-class growth and yield model based on the diameter growth dynamics of Pinus spp. and Quercus spp. of Mexico’s mixed temperate forests. Using a total of 2663 temporary, circular-sampling plots of 1000 m2 each, nine Weibull distribution techniques of parameter estimation were fitted to the diameter structures of pines and oaks. Statistical equations using stand attributes and the first three moments of the diameter distribution predicted and recovered the Weibull parameters. Using nearly 1200 and 100 harvested trees for pines and oaks, respectively, I developed the total height versus diameter at breast height relationship by fitting three non-linear functions. The Newnham model predicted stem taper and numerical integration was done to estimate merchantable timber volume for all trees in the stand for each diameter class. The independence of the diameter structures of pines and oaks was tested by regressing the Weibull parameters and projecting diameter structures. The model predicts diameter distributions transition from exponential (J inverse, logarithmic to well-balanced distributions with increasing mean stand diameter at breast height. Pine diameter distributions transition faster and the model predicts independent growth rates between pines and oaks. The stand-class growth and yield model must be completed with the diameter-age relationship for oaks in order to carry a full optimization procedure to find stand density and genera composition to maximize forest growth.

Variation of local critical current and its influence on overall current of bent multifilamentary Bi2223/Ag tape

International Nuclear Information System (INIS)

Ochiai, S.; Doko, D.; Rokkaku, H.; Fujimoto, M.; Okuda, H.; Hojo, M.; Tanaka, M.; Sugano, M.; Osamura, K.; Mimura, M.

2006-01-01

The correlation between the local and overall currents in a multifilamentary Bi2223/Ag/Ag alloy composite tape under bending strain was studied. The correlation of the measured distributed local critical current and n-value to overall critical current was described comprehensively with a voltage summation model that regards the overall sample to be composed of a series circuit. The analysis of the measured critical current and n-value revealed that the distribution of local critical current could be described with the Weibull distribution function and the n-value could be expressed as a function of critical current as a first approximation. By combining the Weibull distribution function of the local critical current, the empirical formula of the n-value as a function of critical current, voltage summation model and Monte Carlo method, the overall current and n-value could be predicted fairly well from those of local elements

How Many Model Evaluations Are Required To Predict The AEP Of A Wind Power Plant?

DEFF Research Database (Denmark)

Murcia Leon, Juan Pablo; Réthoré, Pierre-Elouan; Natarajan, Anand

2015-01-01

(AEP) predictions expensive. The objective of the present paper is to minimize the number of model evaluations required to capture the wind power plant's AEP using stationary wind farm flow models. Polynomial chaos techniques are proposed based on arbitrary Weibull distributed wind speed and Von Misses...... distributed wind direction. The correlation between wind direction and wind speed are captured by defining Weibull-parameters as functions of wind direction. In order to evaluate the accuracy of these methods the expectation and variance of the wind farm power distributions are compared against...... the traditional binning method with trapezoidal and Simpson's integration rules. The wind farm flow model used in this study is the semi-empirical wake model developed by Larsen [1]. Three test cases are studied: a single turbine, a simple and a real offshore wind power plant. A reduced number of model...

Analysis of Flexural Fatigue Strength of Self Compacting Fibre Reinforced Concrete Beams

Science.gov (United States)

Murali, G.; Sudar Celestina, J. P. Arul; Subhashini, N.; Vigneshwari, M.

2017-07-01

This study presents the extensive statistical investigation ofvariations in flexural fatigue life of self-compacting Fibrous Concrete (FC) beams. For this purpose, the experimental data of earlier researchers were examined by two parameter Weibull distribution.Two methods namely Graphical and moment wereused to analyse the variations in experimental data and the results have been presented in the form of probability of survival. The Weibull parameters values obtained from graphical and method of moments are precise. At 0.7 stress level, the fatigue life shows 59861 cyclesfor areliability of 90%.

New considerations on variability of creep rupture data and life prediction

International Nuclear Information System (INIS)

Kim, Seon Jin; Jeong, Won Taek; Kong, Yu Sik

2009-01-01

This paper deals with the variability analysis of short term creep rupture test data based on the previous creep rupture tests and the possibility of the creep life prediction. From creep tests performed by constant uniaxial stresses at 600, 650 and 700 .deg. C elevated temperature, in order to investigate the variability of short-term creep rupture data, the creep curves were analyzed for normalized creep strain divided by initial strain. There are some variability in thee creep rupture data. And, the difference between general creep curves and normalized creep curves were obtained. The effects of the creep rupture time and state steady creep rate on the Weibull distribution parameters were investigated. There were good relation between normal Weibull parameters and normalized Weibull parameters. Finally, the predicted creep life were compared with the Monkman-Grant model.

New Considerations on Variability of Creep Rupture Data and Life Prediction

International Nuclear Information System (INIS)

Jung, Won Taek; Kong, Yu Sik; Kim, Seon Jin

2009-01-01

This paper deals with the variability analysis of short term creep rupture test data based on the previous creep rupture tests and the possibility of the creep life prediction. From creep tests performed by constant uniaxial stresses at 600, 650 and 700 .deg. C elevated temperature, in order to investigate the variability of short-term creep rupture data, the creep curves were analyzed for normalized creep strain divided by initial strain. There are some variability in the creep rupture data. And, the difference between general creep curves and normalized creep curves were obtained. The effects of the creep rupture time (RT) and steady state creep rate (SSCR) on the Weibull distribution parameters were investigated. There were good relation between normal Weibull parameters and normalized Weibull parameters. Finally, the predicted creep life were compared with the Monkman-Grant model

Theory model and experiment research about the cognition reliability of nuclear power plant operators

International Nuclear Information System (INIS)

Fang Xiang; Zhao Bingquan

2000-01-01

In order to improve the reliability of NPP operation, the simulation research on the reliability of nuclear power plant operators is needed. Making use of simulator of nuclear power plant as research platform, and taking the present international reliability research model-human cognition reliability for reference, the part of the model is modified according to the actual status of Chinese nuclear power plant operators and the research model of Chinese nuclear power plant operators obtained based on two-parameter Weibull distribution. Experiments about the reliability of nuclear power plant operators are carried out using the two-parameter Weibull distribution research model. Compared with those in the world, the same results are achieved. The research would be beneficial to the operation safety of nuclear power plant

Effect of nonlinear stress-strain relationship on bending strength of isotropic graphite

International Nuclear Information System (INIS)

Arai, Taketoshi; Oku, Tatsuo

1978-05-01

Four-point bending tests were made on rectangular isotropic 7477PT graphite specimens of different sizes to observe the relation between load and outermost fiber strain. Analytical methods, allowing for nonlinear stress-strain relationships different between tension and compression, were developed for calculating the fiber stress distribution in a beam and the failure probability based on the Weibull statistical theory for bending fracture. With increase of the stress, the stress-strain curves for tension deviate from the linearity and also from those for compression. The true bending strengths of the rectangular bars are 10 -- 20 percent lower than elastic bending strengths. Revised Weibull theory gives failure probability distributions agreeing with measured ones, compared with the theory based on elastic behavior. (auth.)

Prediction of Mean and Design Fatigue Lives of Self Compacting Concrete Beams in Flexure

Science.gov (United States)

Goel, S.; Singh, S. P.; Singh, P.; Kaushik, S. K.

2012-02-01

In this paper, result of an investigation conducted to study the flexural fatigue characteristics of self compacting concrete (SCC) beams in flexure are presented. An experimental programme was planned in which approximately 60 SCC beam specimens of size 100 × 100 × 500 mm were tested under flexural fatigue loading. Approximately 45 static flexural tests were also conducted to facilitate fatigue testing. The flexural fatigue and static flexural strength tests were conducted on a 100 kN servo-controlled actuator. The fatigue life data thus obtained have been used to establish the probability distributions of fatigue life of SCC using two-parameter Weibull distribution. The parameters of the Weibull distribution have been obtained by different methods of analysis. Using the distribution parameters, the mean and design fatigue lives of SCC have been estimated and compared with Normally vibrated concrete (NVC), the data for which have been taken from literature. It has been observed that SCC exhibits higher mean and design fatigue lives compared to NVC.

Characteristics of service requests and service processes of fire and rescue service dispatch centers: analysis of real world data and the underlying probability distributions.

Science.gov (United States)

Krueger, Ute; Schimmelpfeng, Katja

2013-03-01

A sufficient staffing level in fire and rescue dispatch centers is crucial for saving lives. Therefore, it is important to estimate the expected workload properly. For this purpose, we analyzed whether a dispatch center can be considered as a call center. Current call center publications very often model call arrivals as a non-homogeneous Poisson process. This bases on the underlying assumption of the caller's independent decision to call or not to call. In case of an emergency, however, there are often calls from more than one person reporting the same incident and thus, these calls are not independent. Therefore, this paper focuses on the dependency of calls in a fire and rescue dispatch center. We analyzed and evaluated several distributions in this setting. Results are illustrated using real-world data collected from a typical German dispatch center in Cottbus ("Leitstelle Lausitz"). We identified the Pólya distribution as being superior to the Poisson distribution in describing the call arrival rate and the Weibull distribution to be more suitable than the exponential distribution for interarrival times and service times. However, the commonly used distributions offer acceptable approximations. This is important for estimating a sufficient staffing level in practice using, e.g., the Erlang-C model.

Analytical method for optimization of maintenance policy based on available system failure data

International Nuclear Information System (INIS)

Coria, V.H.; Maximov, S.; Rivas-Dávalos, F.; Melchor, C.L.; Guardado, J.L.

2015-01-01

An analytical optimization method for preventive maintenance (PM) policy with minimal repair at failure, periodic maintenance, and replacement is proposed for systems with historical failure time data influenced by a current PM policy. The method includes a new imperfect PM model based on Weibull distribution and incorporates the current maintenance interval T 0 and the optimal maintenance interval T to be found. The Weibull parameters are analytically estimated using maximum likelihood estimation. Based on this model, the optimal number of PM and the optimal maintenance interval for minimizing the expected cost over an infinite time horizon are also analytically determined. A number of examples are presented involving different failure time data and current maintenance intervals to analyze how the proposed analytical optimization method for periodic PM policy performances in response to changes in the distribution of the failure data and the current maintenance interval. - Highlights: • An analytical optimization method for preventive maintenance (PM) policy is proposed. • A new imperfect PM model is developed. • The Weibull parameters are analytically estimated using maximum likelihood. • The optimal maintenance interval and number of PM are also analytically determined. • The model is validated by several numerical examples

Stochastic modeling of pitting corrosion: A new model for initiation and growth of multiple corrosion pits

International Nuclear Information System (INIS)

Valor, A.; Caleyo, F.; Alfonso, L.; Rivas, D.; Hallen, J.M.

2007-01-01

In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion

Stochastic modeling of pitting corrosion: A new model for initiation and growth of multiple corrosion pits

Energy Technology Data Exchange (ETDEWEB)

Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 Havana (Cuba); Caleyo, F. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)]. E-mail: fcaleyo@gmail.com; Alfonso, L. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Rivas, D. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Hallen, J.M. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)

2007-02-15

In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion.

Challenges in risk estimation using routinely collected clinical data: The example of estimating cervical cancer risks from electronic health-records.

Science.gov (United States)

Landy, Rebecca; Cheung, Li C; Schiffman, Mark; Gage, Julia C; Hyun, Noorie; Wentzensen, Nicolas; Kinney, Walter K; Castle, Philip E; Fetterman, Barbara; Poitras, Nancy E; Lorey, Thomas; Sasieni, Peter D; Katki, Hormuzd A

2018-06-01

Electronic health-records (EHR) are increasingly used by epidemiologists studying disease following surveillance testing to provide evidence for screening intervals and referral guidelines. Although cost-effective, undiagnosed prevalent disease and interval censoring (in which asymptomatic disease is only observed at the time of testing) raise substantial analytic issues when estimating risk that cannot be addressed using Kaplan-Meier methods. Based on our experience analysing EHR from cervical cancer screening, we previously proposed the logistic-Weibull model to address these issues. Here we demonstrate how the choice of statistical method can impact risk estimates. We use observed data on 41,067 women in the cervical cancer screening program at Kaiser Permanente Northern California, 2003-2013, as well as simulations to evaluate the ability of different methods (Kaplan-Meier, Turnbull, Weibull and logistic-Weibull) to accurately estimate risk within a screening program. Cumulative risk estimates from the statistical methods varied considerably, with the largest differences occurring for prevalent disease risk when baseline disease ascertainment was random but incomplete. Kaplan-Meier underestimated risk at earlier times and overestimated risk at later times in the presence of interval censoring or undiagnosed prevalent disease. Turnbull performed well, though was inefficient and not smooth. The logistic-Weibull model performed well, except when event times didn't follow a Weibull distribution. We have demonstrated that methods for right-censored data, such as Kaplan-Meier, result in biased estimates of disease risks when applied to interval-censored data, such as screening programs using EHR data. The logistic-Weibull model is attractive, but the model fit must be checked against Turnbull non-parametric risk estimates. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

5_29 - 37_Dikko et al.,_A New Generalized-Exponential-Weibull ...

African Journals Online (AJOL)

user pc

ction, survival and hazard function, order statistics of the distribution. were estimated using ... he mathematical properties eibull distribution .... 2 December, 2017. Applying binomial expansion and further simplification, equation (15) become.

Determination of utilizable wind energy for indoor ventilation in ...

African Journals Online (AJOL)

Journal of the Nigerian Association of Mathematical Physics ... Determination of utilizable wind energy for indoor ventilation in buildings across selected locations in Nigeria ... Weibull's distribution function was used for modeling of wind speed ...

New method of safety assessment for pressure vessel of nuclear power plant--brief introduction of master curve approach

International Nuclear Information System (INIS)

Yang Wendou

2011-01-01

The new Master Curve Method is called as a revolutionary advance to the assessment of- reactor pressure vessel integrity in USA. This paper explains the origin, basis and standard of the Master Curve from the reactor pressure-temperature limit curve which assures the safety of nuclear power plant. According to the characteristics of brittle fracture which is greatly susceptible to the microstructure, the theory and the test method of the Master Curve as well as its statistical law which can be modeled using Weibull distribution are described in this paper. The meaning, advantage, application and importance of the Master Curve as well as the relation between the Master Curve and nuclear power safety are understood from the fitting formula for the fracture toughness database by Weibull distribution model. (author)

Reliability analysis of component of affination centrifugal 1 machine by using reliability engineering

Science.gov (United States)

Sembiring, N.; Ginting, E.; Darnello, T.

2017-12-01

Problems that appear in a company that produces refined sugar, the production floor has not reached the level of critical machine availability because it often suffered damage (breakdown). This results in a sudden loss of production time and production opportunities. This problem can be solved by Reliability Engineering method where the statistical approach to historical damage data is performed to see the pattern of the distribution. The method can provide a value of reliability, rate of damage, and availability level, of an machine during the maintenance time interval schedule. The result of distribution test to time inter-damage data (MTTF) flexible hose component is lognormal distribution while component of teflon cone lifthing is weibull distribution. While from distribution test to mean time of improvement (MTTR) flexible hose component is exponential distribution while component of teflon cone lifthing is weibull distribution. The actual results of the flexible hose component on the replacement schedule per 720 hours obtained reliability of 0.2451 and availability 0.9960. While on the critical components of teflon cone lifthing actual on the replacement schedule per 1944 hours obtained reliability of 0.4083 and availability 0.9927.

Wind power statistics and an evaluation of wind energy density

Energy Technology Data Exchange (ETDEWEB)

Jamil, M.; Parsa, S.; Majidi, M. [Materials and Energy Research Centre, Tehran (Iran, Islamic Republic of)

1995-11-01

In this paper the statistical data of fifty days` wind speed measurements at the MERC- solar site are used to find out the wind energy density and other wind characteristics with the help of the Weibull probability distribution function. It is emphasized that the Weibull and Rayleigh probability functions are useful tools for wind energy density estimation but are not quite appropriate for properly fitting the actual wind data of low mean speed, short-time records. One has to use either the actual wind data (histogram) or look for a better fit by other models of the probability function. (Author)

Example of a Non-standard Extreme Value Law

Czech Academy of Sciences Publication Activity Database

Haydn, N.; Kupsa, Michal

2015-01-01

Roč. 35, č. 6 (2015), s. 1902-1912 ISSN 0143-3857 Institutional support: RVO:67985556 Keywords : extreme-value law * rotations of unit circle * non-mixing systems * discrete law * Gumbel distribution * Weibull distribution * Frechet distribution * return times Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.983, year: 2015 http://library.utia.cas.cz/separaty/2014/SI/kupsa-0434480.pdf

Application of Weibull analysis and artificial neural networks to predict the useful life of the vacuum packed soft cheese

Directory of Open Access Journals (Sweden)

Jesús Alexander Sánchez-González

2017-01-01

Full Text Available El objetivo de este trabajo fue evaluar la capacidad de las redes neuronales artificiales (RNA para predecir la vida útil y la acidez en el queso fresco envasado al vacío. En primer lugar, se prepararon muestras de queso de 200 g por unidad. Luego estas muestras se almacenaron en un intervalo de 2 a 4 días a temperaturas de 4, 10 y 16 ° C y humedad relativa del 67,5%. A lo largo del almacenamiento se determinaron la acidez (AC y la aceptabilidad sensorial. Esta aceptabilidad se utilizó para determinar el tiempo de vida útil (TVU por el método de riesgo sensorial Weibull modificado. Se creó y entrenó un conjunto de redes neuronales artificiales (RNA; como entradas se utilizaron la temperatura (T, tiempo de maduración (M y posibilidad de fallo (F (x y TVU y AC como salidas. A partir de este conjunto, se seleccionaron las redes con el menor error cuadrático medio (ECM y el mejor ajuste (R2. Estas redes mostraron coeficientes de correlación (R2 de 0,9996 y 0,6897 para TVU y AC respectivamente y buena precisión en comparación con modelos de regresión. Se muestra que la RNA puede usarse para modelar adecuadamente TVU y en menor grado AC de quesos frescos envasados al vacío.

comparison of accuracies in techniques for evaluating wind power ...

African Journals Online (AJOL)

Dk.kainkwa

Johnson functions (Conradsen et al. 1984). Several non normal distributions have been suggested as ... Vf exp. 1. (4). The mean wind speed of the Weibull distribution is expressed as (Johnson 2006):. dV c. V c. V c. Vk. V .... Electricity Supply Company (TANESCO). The meteorological parameters namely wind speed and ...

A methodology to quantify the stochastic distribution of friction coefficient required for level walking.

Science.gov (United States)

Chang, Wen-Ruey; Chang, Chien-Chi; Matz, Simon; Lesch, Mary F

2008-11-01

The required friction coefficient is defined as the minimum friction needed at the shoe and floor interface to support human locomotion. The available friction is the maximum friction coefficient that can be supported without a slip at the shoe and floor interface. A statistical model was recently introduced to estimate the probability of slip and fall incidents by comparing the available friction with the required friction, assuming that both the available and required friction coefficients have stochastic distributions. This paper presents a methodology to investigate the stochastic distributions of the required friction coefficient for level walking. In this experiment, a walkway with a layout of three force plates was specially designed in order to capture a large number of successful strikes without causing fatigue in participants. The required coefficient of friction data of one participant, who repeatedly walked on this walkway under four different walking conditions, is presented as an example of the readiness of the methodology examined in this paper. The results of the Kolmogorov-Smirnov goodness-of-fit test indicated that the required friction coefficient generated from each foot and walking condition by this participant appears to fit the normal, log-normal or Weibull distributions with few exceptions. Among these three distributions, the normal distribution appears to fit all the data generated with this participant. The average of successful strikes for each walk achieved with three force plates in this experiment was 2.49, ranging from 2.14 to 2.95 for each walking condition. The methodology and layout of the experimental apparatus presented in this paper are suitable for being applied to a full-scale study.

Characteristics for wind energy and wind turbines by considering vertical wind shear

Institute of Scientific and Technical Information of China (English)

郑玉巧; 赵荣珍

2015-01-01

The probability distributions of wind speeds and the availability of wind turbines were investigated by considering the vertical wind shear. Based on the wind speed data at the standard height observed at a wind farm, the power-law process was used to simulate the wind speeds at a hub height of 60 m. The Weibull and Rayleigh distributions were chosen to express the wind speeds at two different heights. The parameters in the model were estimated via the least square (LS) method and the maximum likelihood estimation (MLE) method, respectively. An adjusted MLE approach was also presented for parameter estimation. The main indices of wind energy characteristics were calculated based on observational wind speed data. A case study based on the data of Hexi area, Gansu Province of China was given. The results show that MLE method generally outperforms LS method for parameter estimation, and Weibull distribution is more appropriate to describe the wind speed at the hub height.

Reliability Characteristics of Power Plants

Directory of Open Access Journals (Sweden)

Zbynek Martinek

2017-01-01

Full Text Available This paper describes the phenomenon of reliability of power plants. It gives an explanation of the terms connected with this topic as their proper understanding is important for understanding the relations and equations which model the possible real situations. The reliability phenomenon is analysed using both the exponential distribution and the Weibull distribution. The results of our analysis are specific equations giving information about the characteristics of the power plants, the mean time of operations and the probability of failure-free operation. Equations solved for the Weibull distribution respect the failures as well as the actual operating hours. Thanks to our results, we are able to create a model of dynamic reliability for prediction of future states. It can be useful for improving the current situation of the unit as well as for creating the optimal plan of maintenance and thus have an impact on the overall economics of the operation of these power plants.

ZERODUR: deterministic approach for strength design

Science.gov (United States)

Hartmann, Peter

2012-12-01

There is an increasing request for zero expansion glass ceramic ZERODUR substrates being capable of enduring higher operational static loads or accelerations. The integrity of structures such as optical or mechanical elements for satellites surviving rocket launches, filigree lightweight mirrors, wobbling mirrors, and reticle and wafer stages in microlithography must be guaranteed with low failure probability. Their design requires statistically relevant strength data. The traditional approach using the statistical two-parameter Weibull distribution suffered from two problems. The data sets were too small to obtain distribution parameters with sufficient accuracy and also too small to decide on the validity of the model. This holds especially for the low failure probability levels that are required for reliable applications. Extrapolation to 0.1% failure probability and below led to design strengths so low that higher load applications seemed to be not feasible. New data have been collected with numbers per set large enough to enable tests on the applicability of the three-parameter Weibull distribution. This distribution revealed to provide much better fitting of the data. Moreover it delivers a lower threshold value, which means a minimum value for breakage stress, allowing of removing statistical uncertainty by introducing a deterministic method to calculate design strength. Considerations taken from the theory of fracture mechanics as have been proven to be reliable with proof test qualifications of delicate structures made from brittle materials enable including fatigue due to stress corrosion in a straight forward way. With the formulae derived, either lifetime can be calculated from given stress or allowable stress from minimum required lifetime. The data, distributions, and design strength calculations for several practically relevant surface conditions of ZERODUR are given. The values obtained are significantly higher than those resulting from the two

A review and comparison of methods for recreating individual patient data from published Kaplan-Meier survival curves for economic evaluations: a simulation study.

Science.gov (United States)

Wan, Xiaomin; Peng, Liubao; Li, Yuanjian

2015-01-01

In general, the individual patient-level data (IPD) collected in clinical trials are not available to independent researchers to conduct economic evaluations; researchers only have access to published survival curves and summary statistics. Thus, methods that use published survival curves and summary statistics to reproduce statistics for economic evaluations are essential. Four methods have been identified: two traditional methods 1) least squares method, 2) graphical method; and two recently proposed methods by 3) Hoyle and Henley, 4) Guyot et al. The four methods were first individually reviewed and subsequently assessed regarding their abilities to estimate mean survival through a simulation study. A number of different scenarios were developed that comprised combinations of various sample sizes, censoring rates and parametric survival distributions. One thousand simulated survival datasets were generated for each scenario, and all methods were applied to actual IPD. The uncertainty in the estimate of mean survival time was also captured. All methods provided accurate estimates of the mean survival time when the sample size was 500 and a Weibull distribution was used. When the sample size was 100 and the Weibull distribution was used, the Guyot et al. method was almost as accurate as the Hoyle and Henley method; however, more biases were identified in the traditional methods. When a lognormal distribution was used, the Guyot et al. method generated noticeably less bias and a more accurate uncertainty compared with the Hoyle and Henley method. The traditional methods should not be preferred because of their remarkable overestimation. When the Weibull distribution was used for a fitted model, the Guyot et al. method was almost as accurate as the Hoyle and Henley method. However, if the lognormal distribution was used, the Guyot et al. method was less biased compared with the Hoyle and Henley method.

Reliability Analysis and Overload Capability Assessment of Oil-Immersed Power Transformers

Directory of Open Access Journals (Sweden)

Chen Wang

2016-01-01

Full Text Available Smart grids have been constructed so as to guarantee the security and stability of the power grid in recent years. Power transformers are a most vital component in the complicated smart grid network. Any transformer failure can cause damage of the whole power system, within which the failures caused by overloading cannot be ignored. This research gives a new insight into overload capability assessment of transformers. The hot-spot temperature of the winding is the most critical factor in measuring the overload capacity of power transformers. Thus, the hot-spot temperature is calculated to obtain the duration running time of the power transformers under overloading conditions. Then the overloading probability is fitted with the mature and widely accepted Weibull probability density function. To guarantee the accuracy of this fitting, a new objective function is proposed to obtain the desired parameters in the Weibull distributions. In addition, ten different mutation scenarios are adopted in the differential evolutionary algorithm to optimize the parameter in the Weibull distribution. The final comprehensive overload capability of the power transformer is assessed by the duration running time as well as the overloading probability. Compared with the previous studies that take no account of the overloading probability, the assessment results obtained in this research are much more reliable.

Experimental Study on Fatigue Performance of Foamed Lightweight Soil

Science.gov (United States)

Qiu, Youqiang; Yang, Ping; Li, Yongliang; Zhang, Liujun

2017-12-01

In order to study fatigue performance of foamed lightweight soil and forecast its fatigue life in the supporting project, on the base of preliminary tests, beam fatigue tests on foamed lightweight soil is conducted by using UTM-100 test system. Based on Weibull distribution and lognormal distribution, using the mathematical statistics method, fatigue equations of foamed lightweight soil are obtained. At the same time, according to the traffic load on real road surface of the supporting project, fatigue life of formed lightweight soil is analyzed and compared with the cumulative equivalent axle loads during the design period of the pavement. The results show that even the fatigue life of foamed lightweight soil has discrete property, the linear relationship between logarithmic fatigue life and stress ratio still performs well. Especially, the fatigue life of Weibull distribution is more close to that derived from the lognormal distribution, in the instance of 50% guarantee ratio. In addition, the results demonstrated that foamed lightweight soil as subgrade filler has good anti-fatigue performance, which can be further adopted by other projects in the similar research domain.

Estimation of some stochastic models used in reliability engineering

International Nuclear Information System (INIS)

Huovinen, T.

1989-04-01

The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a beta-binomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gamma-poisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilizing point processes. Here we consider the statistical analysis of non-homogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method

Reliability analysis of nuclear component cooling water system using semi-Markov process model

International Nuclear Information System (INIS)

Veeramany, Arun; Pandey, Mahesh D.

2011-01-01

Research highlights: → Semi-Markov process (SMP) model is used to evaluate system failure probability of the nuclear component cooling water (NCCW) system. → SMP is used because it can solve reliability block diagram with a mixture of redundant repairable and non-repairable components. → The primary objective is to demonstrate that SMP can consider Weibull failure time distribution for components while a Markov model cannot → Result: the variability in component failure time is directly proportional to the NCCW system failure probability. → The result can be utilized as an initiating event probability in probabilistic safety assessment projects. - Abstract: A reliability analysis of nuclear component cooling water (NCCW) system is carried out. Semi-Markov process model is used in the analysis because it has potential to solve a reliability block diagram with a mixture of repairable and non-repairable components. With Markov models it is only possible to assume an exponential profile for component failure times. An advantage of the proposed model is the ability to assume Weibull distribution for the failure time of components. In an attempt to reduce the number of states in the model, it is shown that usage of poly-Weibull distribution arises. The objective of the paper is to determine system failure probability under these assumptions. Monte Carlo simulation is used to validate the model result. This result can be utilized as an initiating event probability in probabilistic safety assessment projects.

On the non-Poissonian repetition pattern of FRB121102

Science.gov (United States)

Oppermann, Niels; Yu, Hao-Ran; Pen, Ue-Li

2018-04-01

The Fast Radio Burst FRB121102 has been observed to repeat in an irregular fashion. Using published timing data of the observed bursts, we show that Poissonian statistics are not a good description of this random process. As an alternative, we suggest to describe the intervals between bursts with a Weibull distribution with a shape parameter smaller than one, which allows for the clustered nature of the bursts. We quantify the amount of clustering using the parameters of the Weibull distribution and discuss the consequences that it has for the detection probabilities of future observations and for the optimization of observing strategies. Allowing for this generalization, we find a mean repetition rate of r=5.7^{+3.0}_{-2.0} per day and index k=0.34^{+0.06}_{-0.05} for a correlation function ξ(t) = (t/t0)k - 1.

Sadhana | Indian Academy of Sciences

Indian Academy of Sciences (India)

In this study, corrosion test-data of steel-rebar in concrete were subjected to the fittings of the Normal, Gumbel and the Weibull probability distribution functions. This was done to investigate the suitability of the results of the fitted test-data, by these distributions, for modelling the effectiveness of C6H15NO3, triethanolamine ...

Group SkSP-R sampling plan for accelerated life tests

Indian Academy of Sciences (India)

Muhammad Aslam

2017-09-15

Sep 15, 2017 ... SkSP-R sampling; life test; Weibull distribution; producer's risk; ... designed a sampling plan under a time-truncated life test .... adjusted using an acceleration factor. ... where P is the probability of lot acceptance for a single.

Some challenges of wind modelling for modern wind turbines: The Weibull distribution

DEFF Research Database (Denmark)

Gryning, Sven-Erik; Batchvarova, Ekatarina; Floors, Rogier

2012-01-01

Wind power assessments, as well as forecast of wind energy production, are key issues in wind energy and grid related studies. However the hub height of today’s wind turbines is well above the surface layer. Wind profiles studies based on mast data show that the wind profile above the surface layer...

Transformation and Self-Similarity Properties of Gamma and Weibull Fragment Size Distributions

Science.gov (United States)

2015-12-01

the spatial dimension ( 31 m ). For classic aerosols with nearly-spherical droplets, 3m and 6/s . Alternatively, Wittel et. al. (2006...which come from the definitions of )(DFM , )(MFM , )(DF , and )(MF . The fourth transformation equation is as follows: )(~)( DfDDf mM... dimension defined by Equation (2), )(x is the gamma function, and ),( xs is the upper incomplete gamma function. Table 1a. Rosin-Rammler (a.k.a

determination of weibull parameters and analysis of wind power

African Journals Online (AJOL)

HOD

shape parameter (k) and the scale factor(c) were obtained to be 6.7 m/s and 4.3 m/s, 0.91 MW and 0.25 MW, K~ 5.4 and. 2.1, and c ... China, the forecast is not different as the report of the ..... Distribution for Wind Energy Analysis”, J. Wind Eng.

Modelling of extreme minimum rainfall using generalised extreme value distribution for Zimbabwe

Directory of Open Access Journals (Sweden)

Delson Chikobvu

2015-09-01

Full Text Available We modelled the mean annual rainfall for data recorded in Zimbabwe from 1901 to 2009. Extreme value theory was used to estimate the probabilities of meteorological droughts. Droughts can be viewed as extreme events which go beyond and/or below normal rainfall occurrences, such as exceptionally low mean annual rainfall. The duality between the distribution of the minima and maxima was exploited and used to fit the generalised extreme value distribution (GEVD to the data and hence find probabilities of extreme low levels of mean annual rainfall. The augmented Dickey Fuller test confirmed that rainfall data were stationary, while the normal quantile-quantile plot indicated that rainfall data deviated from the normality assumption at both ends of the tails of the distribution. The maximum likelihood estimation method and the Bayesian approach were used to find the parameters of the GEVD. The Kolmogorov-Smirnov and Anderson-Darling goodnessof- fit tests showed that the Weibull class of distributions was a good fit to the minima mean annual rainfall using the maximum likelihood estimation method. The mean return period estimate of a meteorological drought using the threshold value of mean annual rainfall of 473 mm was 8 years. This implies that if in the year there is a meteorological drought then another drought of the same intensity or greater is expected after 8 years. It is expected that the use of Bayesian inference may better quantify the level of uncertainty associated with the GEVD parameter estimates than with the maximum likelihood estimation method. The Markov chain Monte Carlo algorithm for the GEVD was applied to construct the model parameter estimates using the Bayesian approach. These findings are significant because results based on non-informative priors (Bayesian method and the maximum likelihood method approach are expected to be similar.

The comparative kinetic analysis of Acetocell and Lignoboost® lignin pyrolysis: the estimation of the distributed reactivity models.

Science.gov (United States)

Janković, Bojan

2011-10-01

The non-isothermal pyrolysis kinetics of Acetocell (the organosolv) and Lignoboost® (kraft) lignins, in an inert atmosphere, have been studied by thermogravimetric analysis. Using isoconversional analysis, it was concluded that the apparent activation energy for all lignins strongly depends on conversion, showing that the pyrolysis of lignins is not a single chemical process. It was identified that the pyrolysis process of Acetocell and Lignoboost® lignin takes place over three reaction steps, which was confirmed by appearance of the corresponding isokinetic relationships (IKR). It was found that major pyrolysis stage of both lignins is characterized by stilbene pyrolysis reactions, which were subsequently followed by decomposition reactions of products derived from the stilbene pyrolytic process. It was concluded that non-isothermal pyrolysis of Acetocell and Lignoboost® lignins can be best described by n-th (n>1) reaction order kinetics, using the Weibull mixture model (as distributed reactivity model) with alternating shape parameters. Copyright © 2011 Elsevier Ltd. All rights reserved.

Stochastic model of texture dependence of iodine SCC susceptibility of a zircaloy-2 alloy

International Nuclear Information System (INIS)

Hirao, Keiichi; Yamane, Toshimi; Nakajima, Shinichi; Node, Shunsaku; Fujisawa, Takashi; Minamino, Yoritoshi

1991-01-01

Effects of textures on statistical parameters of tensile elongations in stress corrosion cracking (SCC) of zircaloy-2 using a slow strain rate test (SSRT) method have been investigated by Weibull distribution method based on stochastic process theory. The SCC is analyzed by assuming a probabilistic state transition model. Tensile directions of test pieces were prepared parallel, 45deg and perpendicular to rolling direction of the sheet. The test pieces in evacuated silica tubes were annealed at 1073K for 7.2x10 3 s, and then quenched into ice water. The annealed pieces with tilt angle α between tensile direction and a basal plane {0001} were 0, 18 and 25deg respectively. The tensile elongations of zircaloy-2 in SCC using the SSRT method are found to obey the single Weibull distribution with location parameters, and the SCC phenomena can be described by the Weibull distribution based on the stochastic process. The values of scale parameter η decrease with the tilt angle α, and the SCC susceptibility can be indicated by the values of scale parameter η. The texture dependence of the values of shape parameters m shows the changes of corrosion process in iodine solution and deformation system in air which are observed in the SSRT. The mechanism of decrement in the SCC susceptibility changes with the tilt angle α. The SCC under SSRT method is found to obey the model of probabilistic state transition. The constant load SCC process which obey the model of probabilistic state transition, is found to be effective for estimation of accelerated SCC condition. (author)

An Advanced Bayesian Method for Short-Term Probabilistic Forecasting of the Generation of Wind Power

Directory of Open Access Journals (Sweden)

Antonio Bracale

2015-09-01

Full Text Available Currently, among renewable distributed generation systems, wind generators are receiving a great deal of interest due to the great economic, technological, and environmental incentives they involve. However, the uncertainties due to the intermittent nature of wind energy make it difficult to operate electrical power systems optimally and make decisions that satisfy the needs of all the stakeholders of the electricity energy market. Thus, there is increasing interest determining how to forecast wind power production accurately. Most the methods that have been published in the relevant literature provided deterministic forecasts even though great interest has been focused recently on probabilistic forecast methods. In this paper, an advanced probabilistic method is proposed for short-term forecasting of wind power production. A mixture of two Weibull distributions was used as a probability function to model the uncertainties associated with wind speed. Then, a Bayesian inference approach with a particularly-effective, autoregressive, integrated, moving-average model was used to determine the parameters of the mixture Weibull distribution. Numerical applications also are presented to provide evidence of the forecasting performance of the Bayesian-based approach.

Environmental indicators for the wind power generation in Mato Grosso do Sul; Indicadores ambientais para a geracao de energia eolica em Mato Grosso do Sul

Energy Technology Data Exchange (ETDEWEB)

Souza, Amaury de; Fernandes, Widinei Alves; Pavao, Hamilton Germano; Lastoria, Giancarlo; Gabas, Sandra Garcia; Paranhos Filho, Antonio Conceicao; Zampieri, Alexandra [Universidade Federal de Mato Grosso do Sul (UFRGS), Campo Grande, MS (Brazil). Centro de Ciencias Exatas e Tecnologia], E-mails: amaury.de@uol.com.br, wafer@hotmail.com, pavao@dfi.ufms.br, g.lastoria@.ufms.br; sandragabas@ufms.br, antonio.paranhos@pq.cnpq.br, alexandrazampieri@gmail.com

2011-10-15

In this study, we used data of wind speed, from Universal Records anemograph Fuess, 10 m high, from 19 meteorological stations belonging to the National Institute of Meteorology (INMET), from January 2008 to December 2010. The research objective was to determine the wind power in selected stations. To do so, estimated the parameters of the Weibull distribution, by which it calculated the wind power. The least squares method applied to the frequency distribution of wind speed is a good option for calculating the parameters of Weibull distribution and the estimated parameters c and k, represent satisfactorily, the monthly frequencies of wind speed in the locations studied. The methods in the characterization of wind power in the state of Mato Grosso do Sul, according to the spatial and temporal variability of daily average wind speeds and classification of wind speeds, using the agglomerative Wards at the discretion of inertia, allowed to obtain three homogeneous groups in the study area and the regions that showed higher average daily wind speed was the area of Campo Grande and Sete Quedas. (author)

Optimal methods for fitting probability distributions to propagule retention time in studies of zoochorous dispersal.

Science.gov (United States)

Viana, Duarte S; Santamaría, Luis; Figuerola, Jordi

2016-02-01

Propagule retention time is a key factor in determining propagule dispersal distance and the shape of "seed shadows". Propagules dispersed by animal vectors are either ingested and retained in the gut until defecation or attached externally to the body until detachment. Retention time is a continuous variable, but it is commonly measured at discrete time points, according to pre-established sampling time-intervals. Although parametric continuous distributions have been widely fitted to these interval-censored data, the performance of different fitting methods has not been evaluated. To investigate the performance of five different fitting methods, we fitted parametric probability distributions to typical discretized retention-time data with known distribution using as data-points either the lower, mid or upper bounds of sampling intervals, as well as the cumulative distribution of observed values (using either maximum likelihood or non-linear least squares for parameter estimation); then compared the estimated and original distributions to assess the accuracy of each method. We also assessed the robustness of these methods to variations in the sampling procedure (sample size and length of sampling time-intervals). Fittings to the cumulative distribution performed better for all types of parametric distributions (lognormal, gamma and Weibull distributions) and were more robust to variations in sample size and sampling time-intervals. These estimated distributions had negligible deviations of up to 0.045 in cumulative probability of retention times (according to the Kolmogorov-Smirnov statistic) in relation to original distributions from which propagule retention time was simulated, supporting the overall accuracy of this fitting method. In contrast, fitting the sampling-interval bounds resulted in greater deviations that ranged from 0.058 to 0.273 in cumulative probability of retention times, which may introduce considerable biases in parameter estimates. We

Author Details

African Journals Online (AJOL)

Multivariate Exponential Autoregressive and Autoregressive Moving Average Models Abstract · Vol 16 (2010) - Articles Multivariate Pareto Minification Processes Abstract · Vol 18 (2011) - Articles Methods of Parameter Addition to a Family of Multivariate Exponential and Weibull Distributions Abstract · Vol 20, No 1 (2012) - ...

The Wandering of Corn

OpenAIRE

Salov, Valerii

2017-01-01

Time and Sales of corn futures traded electronically on the CME Group Globex are studied. Theories of continuous prices turn upside down reality of intra-day trading. Prices and their increments are discrete and obey lattice probability distributions. A function for systematic evolution of futures trading volume is proposed. Dependence between sample skewness and kurtosis of waiting times does not support hypothesis of Weibull distribution. Kumaraswamy distribution is more suitable for waitin...

Modeling size effects on fatigue life of a zirconium-based bulk metallic glass under bending

International Nuclear Information System (INIS)

Yuan Tao; Wang Gongyao; Feng Qingming; Liaw, Peter K.; Yokoyama, Yoshihiko; Inoue, Akihisa

2013-01-01

A size effect on the fatigue-life cycles of a Zr 50 Cu 30 Al 10 Ni 10 (at.%) bulk metallic glass has been observed in the four-point-bending fatigue experiment. Under the same bending-stress condition, large-sized samples tend to exhibit longer fatigue lives than small-sized samples. This size effect on the fatigue life cannot be satisfactorily explained by the flaw-based Weibull theories. Based on the experimental results, this study explores possible approaches to modeling the size effects on the bending-fatigue life of bulk metallic glasses, and proposes two fatigue-life models based on the Weibull distribution. The first model assumes, empirically, log-linear effects of the sample thickness on the Weibull parameters. The second model incorporates the mechanistic knowledge of the fatigue behavior of metallic glasses, and assumes that the shear-band density, instead of the flaw density, has significant influence on the bending fatigue-life cycles. Promising predictive results provide evidence of the potential validity of the models and their assumptions.

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Science.gov (United States)

Le, Jia-Liang; Bažant, Zdeněk P.; Bazant, Martin Z.

2011-07-01

Engineering structures must be designed for an extremely low failure probability such as 10 -6, which is beyond the means of direct verification by histogram testing. This is not a problem for brittle or ductile materials because the type of probability distribution of structural strength is fixed and known, making it possible to predict the tail probabilities from the mean and variance. It is a problem, though, for quasibrittle materials for which the type of strength distribution transitions from Gaussian to Weibullian as the structure size increases. These are heterogeneous materials with brittle constituents, characterized by material inhomogeneities that are not negligible compared to the structure size. Examples include concrete, fiber composites, coarse-grained or toughened ceramics, rocks, sea ice, rigid foams and bone, as well as many materials used in nano- and microscale devices. This study presents a unified theory of strength and lifetime for such materials, based on activation energy controlled random jumps of the nano-crack front, and on the nano-macro multiscale transition of tail probabilities. Part I of this study deals with the case of monotonic and sustained (or creep) loading, and Part II with fatigue (or cyclic) loading. On the scale of the representative volume element of material, the probability distribution of strength has a Gaussian core onto which a remote Weibull tail is grafted at failure probability of the order of 10 -3. With increasing structure size, the Weibull tail penetrates into the Gaussian core. The probability distribution of static (creep) lifetime is related to the strength distribution by the power law for the static crack growth rate, for which a physical justification is given. The present theory yields a simple relation between the exponent of this law and the Weibull moduli for strength and lifetime. The benefit is that the lifetime distribution can be predicted from short-time tests of the mean size effect on

Pocket Handbook on Reliability

Science.gov (United States)

1975-09-01

exponencial distributions Weibull distribution, -xtimating reliability, confidence intervals, relia- bility growth, 0. P- curves, Bayesian analysis. 20 A S...introduction for those not familiar with reliability and a good refresher for those who are currently working in the area. LEWIS NERI, CHIEF...includes one or both of the following objectives: a) prediction of the current system reliability, b) projection on the system reliability for someI future

Optimal siting and sizing of wind farms

NARCIS (Netherlands)

Cetinay-Iyicil, H.; Kuipers, F.A.; Guven, A. Nezih

2017-01-01

In this paper, we propose a novel technique to determine the optimal placement of wind farms, thereby taking into account wind characteristics and electrical grid constraints. We model the long-term variability of wind speed using a Weibull distribution according to wind direction intervals, and

One Year of Vertical Wind Profiles Measurements at a Mediterranean Coastal Site of South Italy

DEFF Research Database (Denmark)

Calidonna, Claudia Roberta; Gullì, Daniel; Avolio, Elenio

2015-01-01

To exploit wind energy both onshore and offshore in coastal area the effect of the coastal discontinuity is important. The shape of the vertical wind profiles and the related c parameter of the Weibull distribution are impacted by the atmospheric internal boundary layers developing from the coast...

Determination of Critical Conditions for Puncturing Almonds Using Coupled Response Surface Methodology and Genetic Algorithm

Directory of Open Access Journals (Sweden)

Mahmood Mahmoodi-Eshkaftaki

2013-01-01

Full Text Available In this study, the effect of seed moisture content, probe diameter and loading velocity (puncture conditions on some mechanical properties of almond kernel and peeled almond kernel is considered to model a relationship between the puncture conditions and rupture energy. Furthermore, distribution of the mechanical properties is determined. The main objective is to determine the critical values of mechanical properties significant for peeling machines. The response surface methodology was used to find the relationship between the input parameters and the output responses, and the fitness function was applied to measure the optimal values using the genetic algorithm. Two-parameter Weibull function was used to describe the distribution of mechanical properties. Based on the Weibull parameter values, i.e. shape parameter (β and scale parameter (η calculated for each property, the mechanical distribution variations were completely described and it was confirmed that the mechanical properties are rule governed, which makes the Weibull function suitable for estimating their distributions. The energy model estimated using response surface methodology shows that the mechanical properties relate exponentially to the moisture, and polynomially to the loading velocity and probe diameter, which enabled successful estimation of the rupture energy (R²=0.94. The genetic algorithm calculated the critical values of seed moisture, probe diameter, and loading velocity to be 18.11 % on dry mass basis, 0.79 mm, and 0.15 mm/min, respectively, and optimum rupture energy of 1.97·10-³ J. These conditions were used for comparison with new samples, where the rupture energy was experimentally measured to be 2.68 and 2.21·10-³ J for kernel and peeled kernel, respectively, which was nearly in agreement with our model results.

Residence times and alluvial architecture of a sediment superslug in response to different flow regimes

Science.gov (United States)

Moody, John A.

2017-10-01

A superslug was deposited in a basin in the Colorado Front Range Mountains as a consequence of an extreme flood following a wildfire disturbance in 1996. The subsequent evolution of this superslug was measured by repeat topographic surveys (31 surveys from 1996 through 2014) of 18 cross sections approximately uniformly spaced over 1500 m immediately above the basin outlet. These surveys allowed the identification within the superslug of chronostratigraphic units deposited and eroded by different geomorphic processes in response to different flow regimes. Over the time period of the study, the superslug went through aggradation, incision, and stabilization phases that were controlled by a shift in geomorphic processes from generally short-duration, episodic, large-magnitude floods that deposited new chronostratigraphic units to long-duration processes that eroded units. These phases were not contemporaneous at each channel cross section, which resulted in a complex response that preserved different chronostratigraphic units at each channel cross section having, in general, two dominant types of alluvial architecture-laminar and fragmented. Age and transit-time distributions for these two alluvial architectures evolved with time since the extreme flood. Because of the complex shape of the distributions they were best modeled by two-parameter Weibull functions. The Weibull scale parameter approximated the median age of the distributions, and the Weibull shape parameter generally had a linear relation that increased with time since the extreme flood. Additional results indicated that deposition of new chronostratigraphic units can be represented by a power-law frequency distribution, and that the erosion of units decreases with depth of burial to a limiting depth. These relations can be used to model other situations with different flow regimes where vertical aggradation and incision are dominant processes, to predict the residence time of possible contaminated

Normal and Extreme Wind Conditions for Power at Coastal Locations in China.

Science.gov (United States)

Gao, Meng; Ning, Jicai; Wu, Xiaoqing

2015-01-01

In this paper, the normal and extreme wind conditions for power at 12 coastal locations along China's coastline were investigated. For this purpose, the daily meteorological data measured at the standard 10-m height above ground for periods of 40-62 years are statistically analyzed. The East Asian Monsoon that affects almost China's entire coastal region is considered as the leading factor determining wind energy resources. For most stations, the mean wind speed is higher in winter and lower in summer. Meanwhile, the wind direction analysis indicates that the prevalent winds in summer are southerly, while those in winter are northerly. The air densities at different coastal locations differ significantly, resulting in the difference in wind power density. The Weibull and lognormal distributions are applied to fit the yearly wind speeds. The lognormal distribution performs better than the Weibull distribution at 8 coastal stations according to two judgement criteria, the Kolmogorov-Smirnov test and absolute error (AE). Regarding the annual maximum extreme wind speed, the generalized extreme value (GEV) distribution performs better than the commonly-used Gumbel distribution. At these southeastern coastal locations, strong winds usually occur in typhoon season. These 4 coastal provinces, that is, Guangdong, Fujian, Hainan, and Zhejiang, which have abundant wind resources, are also prone to typhoon disasters.

Brownian gas models for extreme-value laws

International Nuclear Information System (INIS)

Eliazar, Iddo

2013-01-01

In this paper we establish one-dimensional Brownian gas models for the extreme-value laws of Gumbel, Weibull, and Fréchet. A gas model is a countable collection of independent particles governed by common diffusion dynamics. The extreme-value laws are the universal probability distributions governing the affine scaling limits of the maxima and minima of ensembles of independent and identically distributed one-dimensional random variables. Using the recently introduced concept of stationary Poissonian intensities, we construct two gas models whose global statistical structures are stationary, and yield the extreme-value laws: a linear Brownian motion gas model for the Gumbel law, and a geometric Brownian motion gas model for the Weibull and Fréchet laws. The stochastic dynamics of these gas models are studied in detail, and closed-form analytical descriptions of their temporal correlation structures, their topological phase transitions, and their intrinsic first-passage-time fluxes are presented. (paper)

Survival Analysis of Patients with End Stage Renal Disease

Science.gov (United States)

Urrutia, J. D.; Gayo, W. S.; Bautista, L. A.; Baccay, E. B.

2015-06-01

This paper provides a survival analysis of End Stage Renal Disease (ESRD) under Kaplan-Meier Estimates and Weibull Distribution. The data were obtained from the records of V. L. MakabaliMemorial Hospital with respect to time t (patient's age), covariates such as developed secondary disease (Pulmonary Congestion and Cardiovascular Disease), gender, and the event of interest: the death of ESRD patients. Survival and hazard rates were estimated using NCSS for Weibull Distribution and SPSS for Kaplan-Meier Estimates. These lead to the same conclusion that hazard rate increases and survival rate decreases of ESRD patient diagnosed with Pulmonary Congestion, Cardiovascular Disease and both diseases with respect to time. It also shows that female patients have a greater risk of death compared to males. The probability risk was given the equation R = 1 — e-H(t) where e-H(t) is the survival function, H(t) the cumulative hazard function which was created using Cox-Regression.

Reliability Overhaul Model

Science.gov (United States)

1989-08-01

Random variables for the conditional exponential distribution are generated using the inverse transform method. C1) Generate U - UCO,i) (2) Set s - A ln...e - [(x+s - 7)/ n] 0 + [Cx-T)/n]0 c. Random variables from the conditional weibull distribution are generated using the inverse transform method. C1...using a standard normal transformation and the inverse transform method. B - 3 APPENDIX 3 DISTRIBUTIONS SUPPORTED BY THE MODEL (1) Generate Y - PCX S

Global sensitivity analysis in wind energy assessment

Science.gov (United States)

Tsvetkova, O.; Ouarda, T. B.

2012-12-01

research show that the brute force method is best for wind assessment purpose, SBSS outperforms other sampling strategies in the majority of cases. The results indicate that the Weibull scale parameter, turbine lifetime and Weibull shape parameter are the three most influential variables in the case study setting. The following conclusions can be drawn from these results: 1) SBSS should be recommended for use in Monte Carlo experiments, 2) The brute force method should be recommended for conducting sensitivity analysis in wind resource assessment, and 3) Little variation in the Weibull scale causes significant variation in energy production. The presence of the two distribution parameters in the top three influential variables (the Weibull shape and scale) emphasizes the importance of accuracy of (a) choosing the distribution to model wind regime at a site and (b) estimating probability distribution parameters. This can be labeled as the most important conclusion of this research because it opens a field for further research, which the authors see could change the wind energy field tremendously.

Numerical and machine learning simulation of parametric distributions of groundwater residence time in streams and wells

Science.gov (United States)

Starn, J. J.; Belitz, K.; Carlson, C.

2017-12-01

Groundwater residence-time distributions (RTDs) are critical for assessing susceptibility of water resources to contamination. This novel approach for estimating regional RTDs was to first simulate groundwater flow using existing regional digital data sets in 13 intermediate size watersheds (each an average of 7,000 square kilometers) that are representative of a wide range of glacial systems. RTDs were simulated with particle tracking. We refer to these models as "general models" because they are based on regional, as opposed to site-specific, digital data. Parametric RTDs were created from particle RTDs by fitting 1- and 2-component Weibull, gamma, and inverse Gaussian distributions, thus reducing a large number of particle travel times to 3 to 7 parameters (shape, location, and scale for each component plus a mixing fraction) for each modeled area. The scale parameter of these distributions is related to the mean exponential age; the shape parameter controls departure from the ideal exponential distribution and is partly a function of interaction with bedrock and with drainage density. Given the flexible shape and mathematical similarity of these distributions, any of them are potentially a good fit to particle RTDs. The 1-component gamma distribution provided a good fit to basin-wide particle RTDs. RTDs at monitoring wells and streams often have more complicated shapes than basin-wide RTDs, caused in part by heterogeneity in the model, and generally require 2-component distributions. A machine learning model was trained on the RTD parameters using features derived from regionally available watershed characteristics such as recharge rate, material thickness, and stream density. RTDs appeared to vary systematically across the landscape in relation to watershed features. This relation was used to produce maps of useful metrics with respect to risk-based thresholds, such as the time to first exceedance, time to maximum concentration, time above the threshold

Wind profile modelling using WAsP and "tall" wind measurements

DEFF Research Database (Denmark)

Floors, Rogier Ralph; Kelly, Mark C.; Troen, Ib

2015-01-01

extrapolations (the wind profile) this is done using the Weibull distribution and the geostrophic drag law. Wind lidar measurements obtained during the ’Tall wind’ campaign at three different sites are used to evaluate the assumptions and equations that are used in the WAsP vertical extrapolation strategy...

Variations in long term wind speed during different decades in ...

Indian Academy of Sciences (India)

A study has been carried out by comparing the extreme wind speeds estimated based on NCEP/NCAR reanalysis data for 100 years return period using Fischer Tippet-1 (commonly known as Gumbel)and Weibull distributions for three locations (off Goa,Visakhapatnam and Machilipatnam)in the north Indian Ocean.

Statistical behavior of the tensile property of heated cotton fiber

Science.gov (United States)

The temperature dependence of the tensile property of single cotton fiber was studied in the range of 160-300°C using Favimat test, and its statistical behavior was interpreted in terms of structural changes. The tenacity of control cotton fiber was well described by the single Weibull distribution,...

Ceramics Analysis and Reliability Evaluation of Structures (CARES). Users and programmers manual

Science.gov (United States)

Nemeth, Noel N.; Manderscheid, Jane M.; Gyekenyesi, John P.

1990-01-01

This manual describes how to use the Ceramics Analysis and Reliability Evaluation of Structures (CARES) computer program. The primary function of the code is to calculate the fast fracture reliability or failure probability of macroscopically isotropic ceramic components. These components may be subjected to complex thermomechanical loadings, such as those found in heat engine applications. The program uses results from MSC/NASTRAN or ANSYS finite element analysis programs to evaluate component reliability due to inherent surface and/or volume type flaws. CARES utilizes the Batdorf model and the two-parameter Weibull cumulative distribution function to describe the effect of multiaxial stress states on material strength. The principle of independent action (PIA) and the Weibull normal stress averaging models are also included. Weibull material strength parameters, the Batdorf crack density coefficient, and other related statistical quantities are estimated from four-point bend bar or unifrom uniaxial tensile specimen fracture strength data. Parameter estimation can be performed for single or multiple failure modes by using the least-square analysis or the maximum likelihood method. Kolmogorov-Smirnov and Anderson-Darling goodness-of-fit tests, ninety percent confidence intervals on the Weibull parameters, and Kanofsky-Srinivasan ninety percent confidence band values are also provided. The probabilistic fast-fracture theories used in CARES, along with the input and output for CARES, are described. Example problems to demonstrate various feature of the program are also included. This manual describes the MSC/NASTRAN version of the CARES program.

Probability Analysis of the Wave-Slamming Pressure Values of the Horizontal Deck with Elastic Support

Science.gov (United States)

Zuo, Weiguang; Liu, Ming; Fan, Tianhui; Wang, Pengtao

2018-06-01

This paper presents the probability distribution of the slamming pressure from an experimental study of regular wave slamming on an elastically supported horizontal deck. The time series of the slamming pressure during the wave impact were first obtained through statistical analyses on experimental data. The exceeding probability distribution of the maximum slamming pressure peak and distribution parameters were analyzed, and the results show that the exceeding probability distribution of the maximum slamming pressure peak accords with the three-parameter Weibull distribution. Furthermore, the range and relationships of the distribution parameters were studied. The sum of the location parameter D and the scale parameter L was approximately equal to 1.0, and the exceeding probability was more than 36.79% when the random peak was equal to the sample average during the wave impact. The variation of the distribution parameters and slamming pressure under different model conditions were comprehensively presented, and the parameter values of the Weibull distribution of wave-slamming pressure peaks were different due to different test models. The parameter values were found to decrease due to the increased stiffness of the elastic support. The damage criterion of the structure model caused by the wave impact was initially discussed, and the structure model was destroyed when the average slamming time was greater than a certain value during the duration of the wave impact. The conclusions of the experimental study were then described.

A stochastic model for hybrid off-grid wind power systems

Energy Technology Data Exchange (ETDEWEB)

Fouladgar, Javad [Inst. de Recherche en Electronique et en Electrotechnique de Nantes Atlantique (IREENA), Saint-Nazaire (France)

2008-07-01

Long-term wind speed and wind power forecasting of a hybrid installation are studied. A statistical approach based on Weibull distribution is used to predict the auxiliary power required or the exceeding power produced for an isolated site. The presence of a suitable storage system has been taken into account. (orig.)

A Damage Constitutive Model for the Effects of CO2-Brine-Rock Interactions on the Brittleness of a Low-Clay Shale

Directory of Open Access Journals (Sweden)

Qiao Lyu

2018-01-01

Full Text Available CO2 is a very promising fluid for drilling and nonaqueous fracturing, especially for CO2-enhanced shale gas recovery. Brittleness is a very important characteristic to evaluate the drillability and fracability. However, there is not much relevant research works on the influence of CO2 and CO2-based fluids on shale’s brittleness been carried out. Therefore, a series of strength tests were conducted to obtain the stress-strain characteristics of shale soaked in different phases of CO2 including subcritical or supercritical CO2 with formation of water for different time intervals (10 days, 20 days, and 30 days. Two damage constitutive equations based on the power function distribution and Weibull distribution were established to predict the threshold stress for both intact and soaked shale samples. Based on the results, physical and chemical reactions during the imbibition cause reductions of shales’ peak axial strength (20.79%~61.52% and Young’s modulus (13.14%~62.44%. Weibull distribution-based constitutive model with a damage threshold value of 0.8 has better agreement with the experiments than that of the power function distribution-based constitutive model. The energy balance method together with the Weibull distribution-based constitutive model is applied to calculate the brittleness values of samples with or without soaking. The intact shale sample has the highest BI value of 0.9961, which is in accordance with the high percentage of brittleness minerals of the shale samples. The CO2-NaCl-shale interactions during the imbibition decrease the brittleness values. Among the three soaking durations, the minimum brittleness values occur on samples with 20 days’ imbibition in subcritical and supercritical CO2 + NaCl solutions and the reductions of which are 2.08% and 2.49%, respectively. Subcritical/supercritical CO2 + NaCl imbibition has higher effect on shale’s strength and Young’s modulus than on the brittleness. The

Master equation approach to the intra-urban passenger flow and application to the Metropolitan Seoul Subway system

Energy Technology Data Exchange (ETDEWEB)

Lee, Keumsook [Department of Geography, Sungshin University, Seoul 136-742 (Korea, Republic of); Goh, Segun; Choi, M Y [Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University, Seoul 151-747 (Korea, Republic of); Park, Jong Soo [School of Information Technology, Sungshin University, Seoul 136-742 (Korea, Republic of); Jung, Woo-Sung, E-mail: kslee@sungshin.ac.kr, E-mail: mychoi@snu.ac.kr [Department of Physics and Basic Science Research Institute, Pohang University of Science and Technology, Pohang 790-784 (Korea, Republic of)

2011-03-18

The master equation approach is proposed to describe the evolution of passengers in a subway system. With the transition rate constructed from simple geographical consideration, the evolution equation for the distribution of subway passengers is found to bear skew distributions including log-normal, Weibull, and power-law distributions. This approach is then applied to the Metropolitan Seoul Subway system: analysis of the trip data of all passengers in a day reveals that the data in most cases fit well to the log-normal distributions. Implications of the results are also discussed.

Master equation approach to the intra-urban passenger flow and application to the Metropolitan Seoul Subway system

International Nuclear Information System (INIS)

Lee, Keumsook; Goh, Segun; Choi, M Y; Park, Jong Soo; Jung, Woo-Sung

2011-01-01

The master equation approach is proposed to describe the evolution of passengers in a subway system. With the transition rate constructed from simple geographical consideration, the evolution equation for the distribution of subway passengers is found to bear skew distributions including log-normal, Weibull, and power-law distributions. This approach is then applied to the Metropolitan Seoul Subway system: analysis of the trip data of all passengers in a day reveals that the data in most cases fit well to the log-normal distributions. Implications of the results are also discussed.

Improvement of a method for predicting failure rates of coated particles during irradiation

International Nuclear Information System (INIS)

Bongartz, K.

1977-01-01

A method for calculating the coating stress distribution resulting from the statistical spread of geometrical parameters in irradiated fuel particle batches has been developed by Gulden et al. The existing method utilizing coated particles is extended in two ways: 1. A more realistic treatment of the buffer layer is adopted, taking into account its physical properties. 2. A statistical distribution according to Weibull has been adopted for the silicon carbide layer strength. Calculations with both the new and the old assumptions were performed on one feed particle and one breed particle type. It is shown that the two modifications influence the results of the original method. It was found that the extension of the first assumption has no influence on the stress distribution and the fraction of breaking feed particles, but it changes the stress distribution of the breed particles significantly. The fraction of broken particles at end burnup is increased by a factor of approximately 10. The extension of the second assumption affects the fraction of broken feed as well as that of the breed particles. Depending on the Weibull parameter, m, the number of failed feed particles increases by a factor of 1.3 to 2; the corresponding factor for breed particles is between 3.5 and 60

Assessment of wind speed and wind power through three stations in Egypt, including air density variation and analysis results with rough set theory

International Nuclear Information System (INIS)

Essa, K.S.M.; Embaby, M.; Marrouf, A.A.; Koza, A.M.; Abd El-Monsef, M.E.

2007-01-01

It is well known that the wind energy potential is proportional to both air density and the third power of the wind speed average over a suitable time period. The wind speed and air density have random variables depending on both time and location. The main objective of this work is to derive the most general wind energy potential of the wind formulation putting into consideration the time variable in both wind speed and air density. The correction factor is derived explicitly in terms of the cross-correlation and the coefficients of variation.The application is performed for environmental and wind speed measurements at the Cairo Airport, Kosseir and Hurguada, Egypt. Comparisons are made between Weibull, Rayleigh, and actual data distributions of wind speed and wind power of one year 2005. A Weibull distribution is the best match to the actual probability distribution of wind speed data for most stations. The maximum wind energy potential was 373 W/m 2 in June at Hurguada (Red Sea coast) where the annual mean value was 207 W/m 2 . By Using Rough Set Theory, We Find That the Wind Power Depends on the Wind Speed with greater than air density

Human disease mortality kinetics are explored through a chain model embodying principles of extreme value theory and competing risks.

Science.gov (United States)

Juckett, D A; Rosenberg, B

1992-04-21

The distributions for human disease-specific mortality exhibit two striking characteristics: survivorship curves that intersect near the longevity limit; and, the clustering of best-fitting Weibull shape parameter values into groups centered on integers. Correspondingly, we have hypothesized that the distribution intersections result from either competitive processes or population partitioning and the integral clustering in the shape parameter results from the occurrence of a small number of rare, rate-limiting events in disease progression. In this report we initiate a theoretical examination of these questions by exploring serial chain model dynamics and parameteric competing risks theory. The links in our chain models are composed of more than one bond, where the number of bonds in a link are denoted the link size and are the number of events necessary to break the link and, hence, the chain. We explored chains with all links of the same size or with segments of the chain composed of different size links (competition). Simulations showed that chain breakage dynamics depended on the weakest-link principle and followed kinetics of extreme-values which were very similar to human mortality kinetics. In particular, failure distributions for simple chains were Weibull-type extreme-value distributions with shape parameter values that were identifiable with the integral link size in the limit of infinite chain length. Furthermore, for chains composed of several segments of differing link size, the survival distributions for the various segments converged at a point in the S(t) tails indistinguishable from human data. This was also predicted by parameteric competing risks theory using Weibull underlying distributions. In both the competitive chain simulations and the parametric competing risks theory, however, the shape values for the intersecting distributions deviated from the integer values typical of human data. We conclude that rare events can be the source of

The correct "ball bearings" data.

Science.gov (United States)

Caroni, C

2002-12-01

The famous data on fatigue failure times of ball bearings have been quoted incorrectly from Lieblein and Zelen's original paper. The correct data include censored values, as well as non-fatigue failures that must be handled appropriately. They could be described by a mixture of Weibull distributions, corresponding to different modes of failure.

Author Details

African Journals Online (AJOL)

Kaoga, DK. Vol 6, No 2 (2014) - Articles Performance Analysis of Methods for Estimating Weibull Parameters for Wind Speed Distribution in the District of Maroua Abstract PDF. ISSN: 1112-9867. AJOL African Journals Online. HOW TO USE AJOL... for Researchers · for Librarians · for Authors · FAQ's · More about AJOL ...

Four theorems on the psychometric function.

Science.gov (United States)

May, Keith A; Solomon, Joshua A

2013-01-01

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus

TEORIA DA CONFIABILIDADE APLICADA NA AVALIAÇÃO DA VIDA EM FADIGA-DE-CONTATO THEORY OF RELIABILITY APPLIED IN THE EVALUATION OF THE LIFE IN CONTACT FATIGUE

Directory of Open Access Journals (Sweden)

Nelson Vanegas M

2009-12-01

Full Text Available A confiabilidade é uma ferramenta fundamental no desenvolvimento de projetos cuja aplicação visa a melhoria do desempenho através da redução da probabilidade de falha dos mesmos. Neste estudo empregou-se a teoria de confiabilidade nos critérios de projeto e seleção de ferros fundidos com matrizes de elevada dureza utilizados em diversas aplicações. A partir destes conceitos e das informações geradas em laboratório, em equipamento para ensaios de fadiga de contato de rolamento, avaliou-se a confiabilidade empregando-se os métodos não paramétrico e o paramétrico (com o emprego da distribuição de Weibull, a fim de caracterizar o comportamento da confiabilidade, da probabilidade de falha e da taxa de falha dos dois materiais estudados (ferro fundido cinzento e ferro fundido nodular. Os métodos foram comparados obtendo-se resultados semelhantes, mas foi o método paramétrico (distribuição de Weibull que melhor modelou o fenômeno em estudo.Reliability is a fundamental tool in the development of projects since it allows the improvement of performance through the reduction of the failure probability of the products. In this study the reliability theory was applied as the criteria for design and selection of cast irons with high hardness matrix used in different applications. Based on these concepts and from information generated in laboratory tests, in a rolling contact fatigue testing machine, reliability analysis using non parametric approaches and the Weibull´s distribution is developed, in order to characterize reliability, probability of failure, and the rate of failure of both materials (gray cast iron and ductile cast iron. When comparing both methods, similar results were obtained, but the parametric approach (Weibull distribution has better represented the phenomenon under analysis.

Four theorems on the psychometric function.

Directory of Open Access Journals (Sweden)

Keith A May

Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is

Estimation of the lifetime distribution of mechatronic systems in the presence of a covariate: A comparison among parametric, semiparametric and nonparametric models

International Nuclear Information System (INIS)

Bobrowski, Sebastian; Chen, Hong; Döring, Maik; Jensen, Uwe; Schinköthe, Wolfgang

2015-01-01

In practice manufacturers may have lots of failure data of similar products using the same technology basis under different operating conditions. Thus, one can try to derive predictions for the distribution of the lifetime of newly developed components or new application environments through the existing data using regression models based on covariates. Three categories of such regression models are considered: a parametric, a semiparametric and a nonparametric approach. First, we assume that the lifetime is Weibull distributed, where its parameters are modelled as linear functions of the covariate. Second, the Cox proportional hazards model, well-known in Survival Analysis, is applied. Finally, a kernel estimator is used to interpolate between empirical distribution functions. In particular the last case is new in the context of reliability analysis. We propose a goodness of fit measure (GoF), which can be applied to all three types of regression models. Using this GoF measure we discuss a new model selection procedure. To illustrate this method of reliability prediction, the three classes of regression models are applied to real test data of motor experiments. Further the performance of the approaches is investigated by Monte Carlo simulations. - Highlights: • We estimate the lifetime distribution in the presence of a covariate. • Three types of regression models are considered and compared. • A new nonparametric estimator based on our particular data structure is introduced. • We propose a goodness of fit measure and show a new model selection procedure. • A case study with real data and Monte Carlo simulations are performed

Descrição da distribuição diamétrica de sistemas agrossilvipastoris utilizando as funções Weibull e hiperbólica

Directory of Open Access Journals (Sweden)

Daniel Henrique Breda Binoti

2012-04-01

Full Text Available Foram objetivos deste estudo ajustar e avaliar diferentes formas da função Weibull e hiperbólica para descrição da estrutura diamétrica de sistemas agrossilvipastoris. O componente florestal foi estabelecido com clones de híbridos de eucalipto no espaçamento 10 x 4 m, visando à produção de madeira para energia e serraria. Nas entrelinhas houve o plantio de culturas anuais, como o arroz no primeiro ano e a soja no segundo. A partir do ano seguinte ocorreu a formação de pastagens de braquiária, manejadas para engorda de gado de corte. Testaram-se as duas funções com três parâmetros, dois parâmetros e parâmetro de locação como diâmetro mínimo e truncada à direita. A aderência da função aos dados foi avaliada pelo teste de Kolmogorov-Smirnorv. As funções também foram avaliadas pela Soma de Quadrados de Desvios (SQD e pela análise gráfica entre valores observados e estimados. Os resultados indicaram a possibilidade do uso das funções para descrição da distribuição diamétrica de povoamentos desbastados.

Modelización de la antigüedad de las citas en la literatura científica con datos censurados a la derecha

Directory of Open Access Journals (Sweden)

Basulto Santos, Jesús

2002-06-01

Full Text Available We explore the application of Weibull model in age distribution of citations in scientific articles references, when this age is censored at the right side. The Weibull model has been applied to twelve journals in the field of applied economy, where the basic source of information comes from ISI. The censored age is due to the fact that the citations of 10 or more years appear accumulated in the ISI database. After the model has been fitted, we have built a two-dimensional analysis combining the impact factor, that picks up the short term citations, with the percentile 90, that measures the durability or validity period of the scientific articles.

Exploramos la aplicación del modelo Weibull a la antigüedad de las citas en los artículos científicos, cuando dicha antigüedad está censurada a la derecha. Se ha aplicado el modelo Weibull a doce revistas del ámbito de economía aplicada, usando la información proveniente del ISI. La censura es debida a que las citas de 10 o más años de antigüedad aparecen agregadas en la base de datos del ISI. Una vez ajustado el modelo, hemos realizado un análisis bidimensional combinando el factor de impacto, que recoge las citas a corto plazo, con el percentil 90, que mide la durabilidad o periodo de vigencia de los artículos científicos.

The impact of vessel size on vulnerability curves: data and models for within-species variability in saplings of aspen, Populus tremuloides Michx.

Science.gov (United States)

Cai, Jing; Tyree, Melvin T

2010-07-01

The objective of this study was to quantify the relationship between vulnerability to cavitation and vessel diameter within a species. We measured vulnerability curves (VCs: percentage loss hydraulic conductivity versus tension) in aspen stems and measured vessel-size distributions. Measurements were done on seed-grown, 4-month-old aspen (Populus tremuloides Michx) grown in a greenhouse. VCs of stem segments were measured using a centrifuge technique and by a staining technique that allowed a VC to be constructed based on vessel diameter size-classes (D). Vessel-based VCs were also fitted to Weibull cumulative distribution functions (CDF), which provided best-fit values of Weibull CDF constants (c and b) and P(50) = the tension causing 50% loss of hydraulic conductivity. We show that P(50) = 6.166D(-0.3134) (R(2) = 0.995) and that b and 1/c are both linear functions of D with R(2) > 0.95. The results are discussed in terms of models of VCs based on vessel D size-classes and in terms of concepts such as the 'pit area hypothesis' and vessel pathway redundancy.

A simple linear regression method for quantitative trait loci linkage analysis with censored observations.

Science.gov (United States)

Anderson, Carl A; McRae, Allan F; Visscher, Peter M

2006-07-01

Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.

Establishment of a center of excellence for applied mathematical and statistical research

Science.gov (United States)

Woodward, W. A.; Gray, H. L.

1983-01-01

The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.

Inferring the temperature dependence of Beremin cleavage model parameters from the Master Curve

International Nuclear Information System (INIS)

Cao Yupeng; Hui Hu; Wang Guozhen; Xuan Fuzhen

2011-01-01

Research highlights: → Temperature dependence of Beremin model parameters is inferred by Master Curve approach. → Weibull modulus decreases while Weibull stress scale parameter increases with increasing the temperature. → Estimation of Weibull stress parameters in terms of small amounts of specimens leads to a considerable uncertainty. - Abstract: The temperature dependence of Beremin model parameters in the ductile-to-brittle transition region was addressed by employing the Master Curve. Monte Carlo simulation was performed to produce a large number of 1T fracture toughness data randomly drawn from the scatter band at a temperature of interest and thus to determine Beremin model parameters. In terms of the experimental data of a C-Mn steel (the 16MnR steel in China), results revealed that the Weibull modulus, m, decreases with temperature over the lower transition range and remains a constant in the lower-to-mid transition region. The Weibull scale parameter, σ u , increases with temperature over the temperature range of investigated. A small sample may lead to a considerable uncertainty in estimates of the Weibull stress parameters. However, no significant difference was observed for the average of Weibull stress parameters from different sample sizes.

A physical probabilistic model to predict failure rates in buried PVC pipelines

International Nuclear Information System (INIS)

Davis, P.; Burn, S.; Moglia, M.; Gould, S.

2007-01-01

For older water pipeline materials such as cast iron and asbestos cement, future pipe failure rates can be extrapolated from large volumes of existing historical failure data held by water utilities. However, for newer pipeline materials such as polyvinyl chloride (PVC), only limited failure data exists and confident forecasts of future pipe failures cannot be made from historical data alone. To solve this problem, this paper presents a physical probabilistic model, which has been developed to estimate failure rates in buried PVC pipelines as they age. The model assumes that under in-service operating conditions, crack initiation can occur from inherent defects located in the pipe wall. Linear elastic fracture mechanics theory is used to predict the time to brittle fracture for pipes with internal defects subjected to combined internal pressure and soil deflection loading together with through-wall residual stress. To include uncertainty in the failure process, inherent defect size is treated as a stochastic variable, and modelled with an appropriate probability distribution. Microscopic examination of fracture surfaces from field failures in Australian PVC pipes suggests that the 2-parameter Weibull distribution can be applied. Monte Carlo simulation is then used to estimate lifetime probability distributions for pipes with internal defects, subjected to typical operating conditions. As with inherent defect size, the 2-parameter Weibull distribution is shown to be appropriate to model uncertainty in predicted pipe lifetime. The Weibull hazard function for pipe lifetime is then used to estimate the expected failure rate (per pipe length/per year) as a function of pipe age. To validate the model, predicted failure rates are compared to aggregated failure data from 17 UK water utilities obtained from the United Kingdom Water Industry Research (UKWIR) National Mains Failure Database. In the absence of actual operating pressure data in the UKWIR database, typical

Residence times and alluvial architecture of a sediment superslug in response to different flow regimes

Science.gov (United States)

Moody, John A.

2017-01-01

A superslug was deposited in a basin in the Colorado Front Range Mountains as a consequence of an extreme flood following a wildfire disturbance in 1996. The subsequent evolution of this superslug was measured by repeat topographic surveys (31 surveys from 1996 through 2014) of 18 cross sections approximately uniformly spaced over 1500 m immediately above the basin outlet. These surveys allowed the identification within the superslug of chronostratigraphic units deposited and eroded by different geomorphic processes in response to different flow regimes.Over the time period of the study, the superslug went through aggradation, incision, and stabilization phases that were controlled by a shift in geomorphic processes from generally short-duration, episodic, large-magnitude floods that deposited new chronostratigraphic units to long-duration processes that eroded units. These phases were not contemporaneous at each channel cross section, which resulted in a complex response that preserved different chronostratigraphic units at each channel cross section having, in general, two dominant types of alluvial architecture—laminar and fragmented. Age and transit-time distributions for these two alluvial architectures evolved with time since the extreme flood. Because of the complex shape of the distributions they were best modeled by two-parameter Weibull functions. The Weibull scale parameter approximated the median age of the distributions, and the Weibull shape parameter generally had a linear relation that increased with time since the extreme flood. Additional results indicated that deposition of new chronostratigraphic units can be represented by a power-law frequency distribution, and that the erosion of units decreases with depth of burial to a limiting depth. These relations can be used to model other situations with different flow regimes where vertical aggradation and incision are dominant processes, to predict the residence time of possible contaminated

Sadhana | Indian Academy of Sciences

Indian Academy of Sciences (India)

In this study, we have discussed the development of an inventory model when the deterioration rate of the item follows Weibull two parameter distributions under the effect of selling price and time dependent demand, since, not only the selling price, but also the time is a crucial factor to enhance the demand in the market as ...

Study for increasing micro-drill reliability by vibrating drilling

International Nuclear Information System (INIS)

Yang Zhaojun; Li Wei; Chen Yanhong; Wang Lijiang

1998-01-01

A study for increasing micro-drill reliability by vibrating drilling is described. Under the experimental conditions of this study it is observed, from reliability testing and the fitting of a life-distribution function, that the lives of micro-drills under ordinary drilling follow the log-normal distribution and the lives of micro-drills under vibrating drilling follow the Weibull distribution. Calculations for reliability analysis show that vibrating drilling can increase the lives of micro-drills and correspondingly reduce the scatter of drill lives. Therefore, vibrating drilling increases the reliability of micro-drills

Empirical Estimates in Economic and Financial Optimization Problems

Czech Academy of Sciences Publication Activity Database

Houda, Michal; Kaňková, Vlasta

2012-01-01

Roč. 19, č. 29 (2012), s. 50-69 ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/11/0150; GA ČR GAP402/10/0956 Institutional research plan: CEZ:AV0Z10750506 Keywords : stochastic programming * empirical estimates * moment generating functions * stability * Wasserstein metric * L1-norm * Lipschitz property * consistence * convergence rate * normal distribution * Pareto distribution * Weibull distribution * distribution tails * simulation Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2012/E/houda-empirical estimates in economic and financial optimization problems.pdf

How Many Model Evaluations Are Required To Predict The AEP Of A Wind Power Plant?

International Nuclear Information System (INIS)

Murcia, J P; Réthoré, P E; Natarajan, A; Sørensen, J D

2015-01-01

Wind farm flow models have advanced considerably with the use of large eddy simulations (LES) and Reynolds averaged Navier-Stokes (RANS) computations. The main limitation of these techniques is their high computational time requirements; which makes their use for wind farm annual energy production (AEP) predictions expensive. The objective of the present paper is to minimize the number of model evaluations required to capture the wind power plant's AEP using stationary wind farm flow models. Polynomial chaos techniques are proposed based on arbitrary Weibull distributed wind speed and Von Misses distributed wind direction. The correlation between wind direction and wind speed are captured by defining Weibull-parameters as functions of wind direction. In order to evaluate the accuracy of these methods the expectation and variance of the wind farm power distributions are compared against the traditional binning method with trapezoidal and Simpson's integration rules.The wind farm flow model used in this study is the semi-empirical wake model developed by Larsen [1]. Three test cases are studied: a single turbine, a simple and a real offshore wind power plant. A reduced number of model evaluations for a general wind power plant is proposed based on the convergence of the present method for each case. (paper)

An analysis of confidence limit calculations used in AAPM Task Group No. 119

International Nuclear Information System (INIS)

Knill, Cory; Snyder, Michael

2011-01-01

Purpose: The report issued by AAPM Task Group No. 119 outlined a procedure for evaluating the effectiveness of IMRT commissioning. The procedure involves measuring gamma pass-rate indices for IMRT plans of standard phantoms and determining if the results fall within a confidence limit set by assuming normally distributed data. As stated in the TG report, the assumption of normally distributed gamma pass rates is a convenient approximation for commissioning purposes, but may not accurately describe the data. Here the authors attempt to better describe gamma pass-rate data by fitting it to different distributions. The authors then calculate updated confidence limits using those distributions and compare them to those derived using TG No. 119 method. Methods: Gamma pass-rate data from 111 head and neck patients are fitted using the TG No. 119 normal distribution, a truncated normal distribution, and a Weibull distribution. Confidence limits to 95% are calculated for each and compared. A more general analysis of the expected differences between the TG No. 119 method of determining confidence limits and a more time-consuming curve fitting method is performed. Results: The TG No. 119 standard normal distribution does not fit the measured data. However, due to the small range of measured data points, the inaccuracy of the fit has only a small effect on the final value of the confidence limits. The confidence limits for the 111 patient plans are within 0.1% of each other for all distributions. The maximum expected difference in confidence limits, calculated using TG No. 119's approximation and a truncated distribution, is 1.2%. Conclusions: A three-parameter Weibull probability distribution more accurately fits the clinical gamma index pass-rate data than the normal distribution adopted by TG No. 119. However, the sensitivity of the confidence limit on distribution fit is low outside of exceptional circumstances.

The effects of surface finish and grain size on the strength of sintered silicon carbide

Science.gov (United States)

You, Y. H.; Kim, Y. W.; Lee, J. G.; Kim, C. H.

1985-01-01

The effects of surface treatment and microstructure, especially abnormal grain growth, on the strength of sintered SiC were studied. The surfaces of sintered SiC were treated with 400, 800 and 1200 grit diamond wheels. Grain growth was induced by increasing the sintering times at 2050 C. The beta to alpha transformation occurred during the sintering of beta-phase starting materials and was often accompanied by abnormal grain growth. The overall strength distributions were established using Weibull statistics. The strength of the sintered SiC is limited by extrinsic surface flaws in normal-sintered specimens. The finer the surface finish and grain size, the higher the strength. But the strength of abnormal sintering specimens is limited by the abnormally grown large tabular grains. The Weibull modulus increases with decreasing grain size and decreasing grit size for grinding.

Electromigration driven failures on miniature silver fuses at the Large Hadron Collider

CERN Document Server

Trikoupis, Nikolaos; Perez Fontenla, Ana Teresa

2017-01-01

Spurious faults were observed on the miniature silver fuses of electronic cards used for the cryogenics instrumentation in the LHC (Large Hadron Collider) accelerator at CERN. By applying analytical tools and techniques such as Scanning Electron Microscopy, spectrometry and Weibull reliability calculations and by the knowledge of operating temperatures and operational time of each unit, the origin of the problem has now been understood and can be attributed to electromigration. The selected fuse was operated at moderate temperature and load conditions and was considered as a “lifetime” component. However, it turned out to have a smaller than expected MTTF with failures following a Weibull distribution of $\\beta = 3.91$ and $\\eta = 2323$. The literature describes extensively the effects of electromigration, but there are only limited references referring to the impact of this phenomenon on miniature silver fuses for electronic circuits.

Does artificial aging affect mechanical properties of CAD/CAM composite materials.

Science.gov (United States)

Egilmez, Ferhan; Ergun, Gulfem; Cekic-Nagas, Isil; Vallittu, Pekka K; Lassila, Lippo V J

2018-01-01

The purpose of this study was to determine the flexural strength and Weibull characteristics of different CAD/CAM materials after different in vitro aging conditions. The specimens were randomly assigned to one of the six in vitro aging conditions: (1) water storage (37°C, 3 weeks), (2) boiling water (24h), (3) hydrochloric acid exposure (pH: 1.2, 24h), (4) autoclave treatment (134°C, 200kPa, 12h), (5) thermal cycling (5000 times, 5-55°C), (6) cyclic loading (100N, 50,000 cycles). No treatment was applied to the specimens in control group. Three-point bending test was used for the calculation of flexural strength. The reliability of the strength was assessed by Weibull distribution. Surface roughness and topography was examined by coherence scanning interferometry. Evaluated parameters were compared using the Kruskall-Wallis or Mann-Whitney U test. Water storage, autoclave treatment and thermal cycling significantly decreased the flexural strength of all materials (p0.05). Weibull moduli of Cerasmart™ and Lava™ Ultimate were similar with control. Vita Enamic ® exhibited similar Weibull moduli in all aging groups except the HCl treated group (p>0.05). R a values of Cerasmart™ and Lava™ Ultimate were in the range of 0.053-0.088μm in the aged groups. However R a results of Vita Enamic ® were larger than 0.2μm. Flexural strength of newly developed restorative CAD/CAM materials was significantly decreased by artificial aging. Cyclic loading or HCl exposure does not affect to the flexural strength and structural reliability of Cerasmart™ and Lava™ Ultimate. Copyright © 2017 Japan Prosthodontic Society. Published by Elsevier Ltd. All rights reserved.

Wind energy potential on Malaysian Resort Islands: a case study of Tioman, Redang and Perhentian Island

International Nuclear Information System (INIS)

Kamaruzzaman Sopian

2000-01-01

Wind data collected at three east coast islands of Peninsular Malaysia namely Tioman, Redang and Perhentian Island were analyzed for the wind energy potential. The results were presented as Weibull distribution and preliminary analysis indicate that the site at Redang Island have the greatest potential with a mean power density of 85.1 w/m 2 at 10 meters above sea level. (Author)

Aspects of modern fracture statistics

International Nuclear Information System (INIS)

Tradinik, W.; Pabst, R.F.; Kromp, K.

1981-01-01

This contribution begins with introductory general remarks about fracture statistics. Then the fundamentals of the distribution of fracture probability are described. In the following part the application of the Weibull Statistics is justified. In the fourth chapter the microstructure of the material is considered in connection with calculations made in order to determine the fracture probability or risk of fracture. (RW) [de

Design prediction for long term stress rupture service of composite pressure vessels

Science.gov (United States)

Robinson, Ernest Y.

1992-01-01

Extensive stress rupture studies on glass composites and Kevlar composites were conducted by the Lawrence Radiation Laboratory beginning in the late 1960's and extending to about 8 years in some cases. Some of the data from these studies published over the years were incomplete or were tainted by spurious failures, such as grip slippage. Updated data sets were defined for both fiberglass and Kevlar composite stand test specimens. These updated data are analyzed in this report by a convenient form of the bivariate Weibull distribution, to establish a consistent set of design prediction charts that may be used as a conservative basis for predicting the stress rupture life of composite pressure vessels. The updated glass composite data exhibit an invariant Weibull modulus with lifetime. The data are analyzed in terms of homologous service load (referenced to the observed median strength). The equations relating life, homologous load, and probability are given, and corresponding design prediction charts are presented. A similar approach is taken for Kevlar composites, where the updated stand data do show a turndown tendency at long life accompanied by a corresponding change (increase) of the Weibull modulus. The turndown characteristic is not present in stress rupture test data of Kevlar pressure vessels. A modification of the stress rupture equations is presented to incorporate a latent, but limited, strength drop, and design prediction charts are presented that incorporate such behavior. The methods presented utilize Cartesian plots of the probability distributions (which are a more natural display for the design engineer), based on median normalized data that are independent of statistical parameters and are readily defined for any set of test data.

Calling patterns in human communication dynamics.

Science.gov (United States)

Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Podobnik, Boris; Zhou, Wei-Xing; Stanley, H Eugene

2013-01-29

Modern technologies not only provide a variety of communication modes (e.g., texting, cell phone conversation, and online instant messaging), but also detailed electronic traces of these communications between individuals. These electronic traces indicate that the interactions occur in temporal bursts. Here, we study intercall duration of communications of the 100,000 most active cell phone users of a Chinese mobile phone operator. We confirm that the intercall durations follow a power-law distribution with an exponential cutoff at the population level but find differences when focusing on individual users. We apply statistical tests at the individual level and find that the intercall durations follow a power-law distribution for only 3,460 individuals (3.46%). The intercall durations for the majority (73.34%) follow a Weibull distribution. We quantify individual users using three measures: out-degree, percentage of outgoing calls, and communication diversity. We find that the cell phone users with a power-law duration distribution fall into three anomalous clusters: robot-based callers, telecom fraud, and telephone sales. This information is of interest to both academics and practitioners, mobile telecom operators in particular. In contrast, the individual users with a Weibull duration distribution form the fourth cluster of ordinary cell phone users. We also discover more information about the calling patterns of these four clusters (e.g., the probability that a user will call the c(r)-th most contact and the probability distribution of burst sizes). Our findings may enable a more detailed analysis of the huge body of data contained in the logs of massive users.

Brittle-fracture statistics for the determination of the strength of fuel particle coatings

International Nuclear Information System (INIS)

Bongartz, K.; Schuster, H.

1976-04-01

Two influences on characteristic strength values of brittle materials were investigated: the specimen number which is limited in the laboratory by practical reasons, and the procedure for fitting the Weibull formalism to experimental results. The study was performed with respect to the evaluation of the strength of coatings of HTR-fuel particles. Strength values following Weibull statistics were produced artificially to simulate experimental results. The applicability of four different methods was studied to get best fits of the Weibull parameters to these values. The relation of the scatter of strength values and Weibull parameter to the specimen number is determined. (orig./GSCH) [de

Reliability modeling of an engineered barrier system

International Nuclear Information System (INIS)

Ananda, M.M.A.; Singh, A.K.; Flueck, J.A.

1993-01-01

The Weibull distribution is widely used in reliability literature as a distribution of time to failure, as it allows for both increasing failure rate (IFR) and decreasing failure rate (DFR) models. It has also been used to develop models for an engineered barrier system (EBS), which is known to be one of the key components in a deep geological repository for high level radioactive waste (HLW). The EBS failure time can more realistically be modelled by an IFR distribution, since the failure rate for the EBS is not expected to decrease with time. In this paper, we use an IFR distribution to develop a reliability model for the EBS

Reliability modeling of an engineered barrier system

International Nuclear Information System (INIS)

Ananda, M.M.A.; Singh, A.K.; Flueck, J.A.

1993-01-01

The Weibull distribution is widely used in reliability literature as a distribution of time to failure, as it allows for both increasing failure rate (IFR) and decreasing failure rate (DFR) models. It has also been used to develop models for an engineered barrier system (EBS), which is known to be one of the key components in a deep geological repository for high level radioactive waste (HLW). The EBS failure time can more realistically be modelled by an IFR distribution, since the failure rate for the EBS is not expected to decrease with time. In this paper, an IFR distribution is used to develop a reliability model for the EBS

Universal behaviour in the stock market: Time dynamics of the electronic orderbook

Science.gov (United States)

Kızılersü, Ayşe; Kreer, Markus; Thomas, Anthony W.; Feindt, Michael

2016-07-01

A consequence of the digital revolution is that share trading at the stock exchange takes place via electronic order books which are accessed by traders and investors via the internet. Our empirical findings of the London Stock Exchange demonstrate that once ultra-high frequency manipulation on time scales less than around ten milliseconds is excluded, all relevant changes in the order book happen with time differences that are randomly distributed and well described by a left-truncated Weibull distribution with universal shape parameter (independent of time and same for all stocks). The universal shape parameter corresponds to maximum entropy of the distribution.

Contribution to optimization of preventive replacement

International Nuclear Information System (INIS)

Legat, V.; Zaludova, A.H.; Cervenka, V.; Jurca, V.

1996-01-01

The paper presents a method for determining the optimal interval for preventive maintenance/replacement using either an age-based or diagnostic-based renewal strategy. For the case of a finite-time horizon, for which the computations are complicated, a simple formula is proposed for modifying the commonly used inifinite-time solution so that it gives a good approximation to the exact finite-time solution. Examples demonstrate that the method is sufficiently accurate and simple in practice for typical engineering components with Weibull life distributions and for a reasonable range of the cost factor (ratio of unit corrective to unit preventive maintenance costs). This paper investigates the problem of the accuracy of the results compared to the exact, finite-time solution for a selected matrix of time-to failure Weibull shape parameters and cost factors commonly occurring in technical practice. Applications offer substantial benefits to both manufacturer and user of technical equipment

Estimating the mean and standard deviation of environmental data with below detection limit observations: Considering highly skewed data and model misspecification.

Science.gov (United States)

Shoari, Niloofar; Dubé, Jean-Sébastien; Chenouri, Shoja'eddin

2015-11-01

In environmental studies, concentration measurements frequently fall below detection limits of measuring instruments, resulting in left-censored data. Some studies employ parametric methods such as the maximum likelihood estimator (MLE), robust regression on order statistic (rROS), and gamma regression on order statistic (GROS), while others suggest a non-parametric approach, the Kaplan-Meier method (KM). Using examples of real data from a soil characterization study in Montreal, we highlight the need for additional investigations that aim at unifying the existing literature. A number of studies have examined this issue; however, those considering data skewness and model misspecification are rare. These aspects are investigated in this paper through simulations. Among other findings, results show that for low skewed data, the performance of different statistical methods is comparable, regardless of the censoring percentage and sample size. For highly skewed data, the performance of the MLE method under lognormal and Weibull distributions is questionable; particularly, when the sample size is small or censoring percentage is high. In such conditions, MLE under gamma distribution, rROS, GROS, and KM are less sensitive to skewness. Related to model misspecification, MLE based on lognormal and Weibull distributions provides poor estimates when the true distribution of data is misspecified. However, the methods of rROS, GROS, and MLE under gamma distribution are generally robust to model misspecifications regardless of skewness, sample size, and censoring percentage. Since the characteristics of environmental data (e.g., type of distribution and skewness) are unknown a priori, we suggest using MLE based on gamma distribution, rROS and GROS. Copyright © 2015 Elsevier Ltd. All rights reserved.

Imperfect Preventive Maintenance Model Study Based On Reliability Limitation

Directory of Open Access Journals (Sweden)

Zhou Qian

2016-01-01

Full Text Available Effective maintenance is crucial for equipment performance in industry. Imperfect maintenance conform to actual failure process. Taking the dynamic preventive maintenance cost into account, the preventive maintenance model was constructed by using age reduction factor. The model regards the minimization of repair cost rate as final target. It use allowed smallest reliability as the replacement condition. Equipment life was assumed to follow two parameters Weibull distribution since it was one of the most commonly adopted distributions to fit cumulative failure problems. Eventually the example verifies the rationality and benefits of the model.

Evaluation of the resistance to cyclic fatigue among ProTaper Next, ProTaper Universal, and Vortex Blue rotary instruments.

Science.gov (United States)

Nguyen, Harrison H; Fong, Hanson; Paranjpe, Avina; Flake, Natasha M; Johnson, James D; Peters, Ove A

2014-08-01

The purpose of this study was to compare the fracture resistance to cyclic fatigue of ProTaper Next (PTN; Dentsply Tulsa Dental Specialties, Tulsa, OK), ProTaper Universal (PTU, Dentsply Tulsa Dental Specialties), and Vortex Blue (VB, Dentsply Tulsa Dental Specialties) rotary instruments. Twenty instruments each of PTN X1-X5, PTU S1-F5, and VB 20/04-50/04 were rotated until fracture in a simulated canal of 90° and a 5-mm radius using a custom-made testing platform. The number of cycles to fracture (NCF) was calculated. Weibull analysis was used to predict the maximum number of cycles when 99% of the instrument samples survive. VB 20/04-30/04 had significantly higher NCF than PTU S1-F5 and PTN X1-X5. VB 35/04-45/04 had significantly higher NCF than PTU S2-F5 and PTN X2-X5. PTN X1 had higher NCF than PTU S1-F5. PTN X2 had higher NCF than PTU F2-F5. The Weibull distribution predicted the highest number of cycles at which 99% of instruments survive to be 766 cycles for VB 25/04 and the lowest to be 50 cycles for PTU F2. Under the limitations of this study, VB 20/04-45/04 were more resistant to cyclic fatigue than PTN X2-X5 and PTU S2-F5. PTN X1 and X2 were more resistant to cyclic fatigue than PTU F2-F5. The Weibull distribution appears to be a feasible and potentially clinically relevant model to predict resistance to cyclic fatigue. Copyright © 2014 American Association of Endodontists. All rights reserved.

Historical floods in flood frequency analysis: Is this game worth the candle?

Science.gov (United States)

Strupczewski, Witold G.; Kochanek, Krzysztof; Bogdanowicz, Ewa

2017-11-01

In flood frequency analysis (FFA) the profit from inclusion of historical information on the largest historical pre-instrumental floods depends primarily on reliability of the information, i.e. the accuracy of magnitude and return period of floods. This study is focused on possible theoretical maximum gain in accuracy of estimates of upper quantiles, that can be obtained by incorporating the largest historical floods of known return periods into the FFA. We assumed a simple case: N years of systematic records of annual maximum flows and either one largest (XM1) or two largest (XM1 and XM2) flood peak flows in a historical M-year long period. The problem is explored by Monte Carlo simulations with the maximum likelihood (ML) method. Both correct and false distributional assumptions are considered. In the first case the two-parameter extreme value models (Gumbel, log-Gumbel, Weibull) with various coefficients of variation serve as parent distributions. In the case of unknown parent distribution, the Weibull distribution was assumed as estimating model and the truncated Gumbel as parent distribution. The return periods of XM1 and XM2 are determined from the parent distribution. The results are then compared with the case, when return periods of XM1 and XM2 are defined by their plotting positions. The results are presented in terms of bias, root mean square error and the probability of overestimation of the quantile with 100-year return period. The results of the research indicate that the maximal profit of inclusion of pre-instrumental foods in the FFA may prove smaller than the cost of reconstruction of historical hydrological information.

Análisis cinético y estadístico de la precipitación en una aleación de Cu-0,49Co-0,44Ti, mediante microcalorimetría y medidas de microdureza

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Donoso, E.

2009-12-01

Full Text Available Starting with a solid solution of Cu-0,49Co-0,44Ti tempered from 1173 K, the kinetics of precipitation of atoms of cobalt and titanium was studied by means of differential scanning calorimetry (DSC. The analysis of the calorimetric curves show the presence of an exothermal reaction that is attributed to the formation of particles of CoTi in the copper matrix. The energy of activation of the reaction was estimated by means of a modified method of Kissinger. The kinetic parameters were estimated with the use of the formalism of Johnson-Mehl-Avrami. On the other hand, a statistical analysis of the process of precipitation was performed by measuring the microhardness Vickers, employing a Weibull probability distribution function. Using minimum square method the Weibull parameters were estimated. The goodness of fit was analyzed by using the Chi square test with a condidence level of 95 percent. Increasing the aging time, for the sam annealing temperature, theWeibull modulus increase too, which may be attributed to precipitation of CoTi phase.

Mediante calorimetría diferencial de barrido (DSC se estudió la cinética de precipitación de átomos de cobalto y titanio a partir de una solución sólida de Cu-0,49Co-0,44Ti, templada desde 1.173 K. El análisis de las curvas calorimétricas muestran la presencia de una reacción exotérmica la cual se atribuye a la formación de partículas de CoTi en la matriz de cobre. La energía de activación de la reacción fue estimada a partir del método de Kissinger modificado. Los parámetros cinéticos fueron calculados mediante el formalismo de Johnson- Mehl-Avrami. Por otra parte, se efectuó un análisis estadístico del proceso de precipitación, mediante medidas de microdureza Vickers, empleando una función de distribución de probabilidad deWeibull. Se estimaron los parámetros deWeibull mediante el método de mínimos cuadrados. La bondad de ajuste se analizó considerando el test de chi

Comparison of susceptibility to pitting corrosion of AA2024-T4, AA7075-T651 and AA7475-T761 aluminium alloys in neutral chloride solutions using electrochemical noise analysis

International Nuclear Information System (INIS)

Na, Kyung-Hwan; Pyun, Su-Il

2008-01-01

The susceptibility to pitting corrosion of AA2024-T4, AA7075-T651 and AA7475-T761 aluminium alloys was investigated in aqueous neutral chloride solution for the purpose of comparison using electrochemical noise measurement. The experimentally measured electrochemical noises were analysed based upon the combined stochastic theory and shot-noise theory using the Weibull distribution function. From the occurrence of two linear regions on one Weibull probability plot, it was suggested that there existed two stochastic processes of uniform corrosion and pitting corrosion; pitting corrosion was distinguished from uniform corrosion in terms of the frequency of events in the stochastic analysis. Accordingly, the present analysis method allowed us to investigate pitting corrosion independently. The susceptibility to pitting corrosion was appropriately evaluated by determining pit embryo formation rate in the stochastic analysis. The susceptibility was decreased in the following order: AA2024-T4 (the naturally aged condition), AA7475-T761 (the overaged condition) and AA7075-T651 (the near-peak-aged condition)

A note on inventory model for ameliorating items with time dependent second order demand rate

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Gobinda Chandra Panda

2013-03-01

Full Text Available Background: This paper is concerned with the development of ameliorating inventory models. The ameliorating inventory is the inventory of goods whose utility increases over the time by ameliorating activation. Material and Methods: This study is performed according to two areas: one is an economic order quantity (EOQ model for the items whose utility is ameliorating in accordance with Weibull distribution, and the other is a partial selling quantity (PSQ model developed for selling the surplus inventory accumulated by ameliorating activation with linear demand. The aim of this paper was to develop a mathematical model for inventory type concerned in the paper. Numerical examples were presented show the effect of ameliorating rate on inventory polices.  Results and Conclusions:  The inventory model for items with Weibull ameliorating is developed. For the case of small ameliorating rate (less than linear demand rate, EOQ model is developed, and for the case where ameliorating rate is greater than linear demand rate, PSQ model is developed.  .  

The effect of surface corrosion damage on the fatigue life of 6061-T6 aluminum alloy extrusions

Energy Technology Data Exchange (ETDEWEB)

Weber, Matthew; Eason, Paul D.; Özdeş, Hüseyin; Tiryakioğlu, Murat, E-mail: m.tiryakioglu@unf.edu

2017-04-06

An investigation was performed where 6061-T6 extrusions were exposed to a 3.5% NaCl solution at pH 2 for 2 days and 24 days to create distinct surface flaws. The effect of these flaws on the rotating beam fatigue life was then investigated and analyzed by using Wöhler curves, Weibull statistics and scanning electron microscopy (SEM). It was determined that corrosion damage reduced the fatigue life significantly and specimens corroded for both 2-days and 24-days exhibited similar fatigue lives. Statistical analyses showed that fatigue life of all three datasets followed the 3-parameter Weibull distribution and the difference between the fatigue lives of two corroded datasets was statistically insignificant. Analysis of fracture surfaces showed that sizes of pits that led to fatigue crack initiation were very different in the two corroded datasets. Implications of the similarity in fatigue lives despite disparity in surface condition are discussed in detail in the paper.

Modeling high-intensity pulsed electric field inactivation of a lipase from Pseudomonas fluorescens.

Science.gov (United States)

Soliva-Fortuny, R; Bendicho-Porta, S; Martín-Belloso, O

2006-11-01

The inactivation kinetics of a lipase from Pseudomonas fluorescens (EC 3.1.1.3.) were studied in a simulated skim milk ultrafiltrate treated with high-intensity pulsed electric fields. Samples were subjected to electric field intensities ranging from 16.4 to 27.4 kV/cm for up to 314.5 micros, thus achieving a maximum inactivation of 62.1%. The suitability of describing experimental data using mechanistic first-order kinetics and an empirical model based on the Weibull distribution function is discussed. In addition, different mathematical expressions relating the residual activity values to field strength and treatment time are supplied. A first-order fractional conversion model predicted residual activity with good accuracy (A(f) = 1.018). A mechanistic insight of the model kinetics was that experimental values were the consequence of different structural organizations of the enzyme, with uneven resistance to the pulsed electric field treatments. The Weibull model was also useful in predicting the energy density necessary to achieve lipase inactivation.

Creep test observation of viscoelastic failure of edible fats

Energy Technology Data Exchange (ETDEWEB)

Vithanage, C R; Grimson, M J; Wills, P R [Department of Physics, University of Auckland, Private Bag 92019 (New Zealand); Smith, B G, E-mail: cvit002@aucklanduni.ac.nz [Food Science Programmes, Department of Chemistry, University of Auckland, Private Bag 92019 (New Zealand)

2011-03-01

A rheological creep test was used to investigate the viscoelastic failure of five edible fats. Butter, spreadable blend and spread were selected as edible fats because they belong to three different groups according to the Codex Alimentarius. Creep curves were analysed according to the Burger model. Results were fitted to a Weibull distribution representing the strain-dependent lifetime of putative fibres in the material. The Weibull shape and scale (lifetime) parameters were estimated for each substance. A comparison of the rheometric measurements of edible fats demonstrated a clear difference between the three different groups. Taken together the results indicate that butter has a lower threshold for mechanical failure than spreadable blend and spread. The observed behaviour of edible fats can be interpreted using a model in which there are two types of bonds between fat crystals; primary bonds that are strong and break irreversibly, and secondary bonds, which are weaker but break and reform reversibly.

Statistical inferences for bearings life using sudden death test

Directory of Open Access Journals (Sweden)

Morariu Cristin-Olimpiu

2017-01-01

Full Text Available In this paper we propose a calculus method for reliability indicators estimation and a complete statistical inferences for three parameters Weibull distribution of bearings life. Using experimental values regarding the durability of bearings tested on stands by the sudden death tests involves a series of particularities of the estimation using maximum likelihood method and statistical inference accomplishment. The paper detailing these features and also provides an example calculation.

Influence of microscopic inhomogeneity on macroscopic transport current of Ag/Bi2223 tapes

International Nuclear Information System (INIS)

Ogawa, Kazuhiro; Osamura, Kozo

2004-01-01

In Ag/Bi2223 tapes, inhomogeneities such as spatially distributed weak links or non-superconducting oxides are inevitably introduced because of the complicated manufacturing process and thermodynamic instability. In order to clarify the effect of the difference in such microscopic inhomogeneites on the macroscopic current transport properties, we carried out a numerical analysis. By changing volume fraction (V f ) of the Bi2223 phase and the shape of local distribution of critical current at each weak link, it is revealed that I-V characteristics are largely affected by the breadth of local distributions with different dependence on V f of Bi2223 and calculated results can be analyzed by Weibull distribution function with some parameters including the information of two-dimensional distribution

Planning an Availability Demonstration Test with Consideration of Confidence Level

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Frank Müller

2017-08-01

Full Text Available The full service life of a technical product or system is usually not completed after an initial failure. With appropriate measures, the system can be returned to a functional state. Availability is an important parameter for evaluating such repairable systems: Failure and repair behaviors are required to determine this availability. These data are usually given as mean value distributions with a certain confidence level. Consequently, the availability value also needs to be expressed with a confidence level. This paper first highlights the bootstrap Monte Carlo simulation (BMCS for availability demonstration and inference with confidence intervals based on limited failure and repair data. The BMCS enables point-, steady-state and average availability to be determined with a confidence level based on the pure samples or mean value distributions in combination with the corresponding sample size of failure and repair behavior. Furthermore, the method enables individual sample sizes to be used. A sample calculation of a system with Weibull-distributed failure behavior and a sample of repair times is presented. Based on the BMCS, an extended, new procedure is introduced: the “inverse bootstrap Monte Carlo simulation” (IBMCS to be used for availability demonstration tests with consideration of confidence levels. The IBMCS provides a test plan comprising the required number of failures and repair actions that must be observed to demonstrate a certain availability value. The concept can be applied to each type of availability and can also be applied to the pure samples or distribution functions of failure and repair behavior. It does not require special types of distribution. In other words, for example, a Weibull, a lognormal or an exponential distribution can all be considered as distribution functions of failure and repair behavior. After presenting the IBMCS, a sample calculation will be carried out and the potential of the BMCS and the IBMCS

Reliability analysis of mining equipment: A case study of a crushing plant at Jajarm Bauxite Mine in Iran

International Nuclear Information System (INIS)

Barabady, Javad; Kumar, Uday

2008-01-01

The performance of mining machines depends on the reliability of the equipment used, the operating environment, the maintenance efficiency, the operation process, the technical expertise of the miners, etc. As the size and complexity of mining equipments continue to increase, the implications of equipment failure become ever more critical. Therefore, reliability analysis is required to identify the bottlenecks in the system and to find the components or subsystems with low reliability for a given designed performance. It is important to select a suitable method for data collection as well as for reliability analysis. This paper presents a case study describing reliability and availability analysis of the crushing plant number 3 at Jajarm Bauxite Mine in Iran. In this study, the crushing plant number 3 is divided into six subsystems. The parameters of some probability distributions, such as Weibull, Exponential, and Lognormal distributions have been estimated by using ReliaSoft's Weibull++6 software. The results of the analysis show that the conveyer subsystem and secondary screen subsystem are critical from a reliability point of view, and the secondary crusher subsystem and conveyer subsystem are critical from an availability point of view. The study also shows that the reliability analysis is very useful for deciding maintenance intervals

Valuing carbon assets for high-tech with application to the wind energy industry

International Nuclear Information System (INIS)

Han, Liyan; Liu, Yang; Lin, Qiang; Huang, Gubo

2015-01-01

In contrast to the traditional methods for high-tech evaluation, we introduce a new, more active idea for considering the carbon asset effect, in addition to the economic and technological considerations for strategic significance. The method proposed in this paper considers a reduced amount of carbon emissions, less than that of the current industry baseline, to be an asset that is beneficial to a firm that adopts a new technology. The measured carbon asset values vary across different technologies, in different industries and over time. The new method is applied to the valuing of wind energy technology and uses the Weibull distribution to estimate the wind energy capacity and a concrete sensitivity analysis. These applications support the validity of the new method and show that the impact of the fluctuations of carbon sinks on the values of carbon assets is significantly greater than that of volatility in the production output. The paper also presents some policy recommendations based on the results. - Highlights: • Carbon asset dimension for high-tech evaluation. • Valuing wind energy technology by Weibull distribution. • Greater impact of the carbon sink price on the carbon asset value than that of production output. • The environmental risk could be measured based on the carbon asset assessment.

Inactivation kinetics of Escherichia coli O157:H7, Salmonella enterica Serovar Typhimurium, and Listeria monocytogenes in ready-to-eat sliced ham by near-infrared heating at different radiation intensities.

Science.gov (United States)

Ha, Jae-Won; Kang, Dong-Hyun

2014-07-01

The aim of this study was to investigate the inactivation kinetics of Salmonella enterica serovar Typhimurium, Escherichia coli O157:H7, and Listeria monocytogenes on ready-to-eat sliced ham by near-infrared (NIR) heating as a function of the processing parameter, radiation intensity. Precooked ham slices inoculated with the three pathogens were treated at different NIR intensities (ca. 100, 150, and 200 μW/cm(2)/nm). An increase in the applied radiation intensity resulted in a gradual increase of inactivation of all pathogens. The survival curves of the three pathogens exhibited both shoulder and tailing behavior at all light intensities. Among nonlinear models, the Weibull distribution and log-logistic model were used to describe the experimental data, and the statistical results (mean square error and R(2) values) indicated the suitability of the model for prediction. The log-logistic model more accurately described survival curves of the three pathogens than did the Weibull distribution at all radiation intensities. The output of this study and the proposed kinetics model would be beneficial to the deli meat industry for selecting the optimum processing conditions of NIR heating to meet the target pathogen inactivation on ready-to-eat sliced ham.

High alkali-resistant basalt fiber for reinforcing concrete

International Nuclear Information System (INIS)

Lipatov, Ya.V.; Gutnikov, S.I.; Manylov, M.S.; Zhukovskaya, E.S.; Lazoryak, B.I.

2015-01-01

Highlights: • Doping of basalt fiber with ZrSiO 4 increased its alkali resistance. • Alkali treatment results in formation of protective surface layer on fibers. • Morphology and chemical composition of surface layer were investigated. • Mechanical properties of fibers were analyzed by a Weibull distribution. • Zirconia doped basalt fibers demonstrate high performance in concrete. - Abstract: Basalt glasses and fibers with zirconia content in the range from 0 to 7 wt% were obtained using ZrSiO 4 as a zirconium source. Weight loss and tensile strength loss of fibers after refluxing in alkali solution were determined. Basalt fiber with 5.7 wt% ZrO 2 had the best alkali resistance properties. Alkali treatment results in formation of protective surface layer on fibers. Morphology and chemical composition of surface layer were investigated. It was shown that alkali resistance of zirconia doped basalt fibers is caused by insoluble compounds of Zr 4+ , Fe 3+ and Mg 2+ in corrosion layer. Mechanical properties of initial and leached fibers were evaluated by a Weibull distribution. The properties of basalt fibers with ZrSiO 4 were compared with AR-glass fibers. The performance of concrete with obtained fibers was investigated

Statistical analysis of absorptive laser damage in dielectric thin films

International Nuclear Information System (INIS)

Budgor, A.B.; Luria-Budgor, K.F.

1978-01-01

The Weibull distribution arises as an example of the theory of extreme events. It is commonly used to fit statistical data arising in the failure analysis of electrical components and in DC breakdown of materials. This distribution is employed to analyze time-to-damage and intensity-to-damage statistics obtained when irradiating thin film coated samples of SiO 2 , ZrO 2 , and Al 2 O 3 with tightly focused laser beams. The data used is furnished by Milam. The fit to the data is excellent; and least squared correlation coefficients greater than 0.9 are often obtained

Robustness of power systems under a democratic-fiber-bundle-like model.

Science.gov (United States)

Yağan, Osman

2015-06-01

We consider a power system with N transmission lines whose initial loads (i.e., power flows) L(1),...,L(N) are independent and identically distributed with P(L)(x)=P[L≤x]. The capacity C(i) defines the maximum flow allowed on line i and is assumed to be given by C(i)=(1+α)L(i), with α>0. We study the robustness of this power system against random attacks (or failures) that target a p fraction of the lines, under a democratic fiber-bundle-like model. Namely, when a line fails, the load it was carrying is redistributed equally among the remaining lines. Our contributions are as follows. (i) We show analytically that the final breakdown of the system always takes place through a first-order transition at the critical attack size p(☆)=1-(E[L]/max(x)(P[L>x](αx+E[L|L>x])), where E[·] is the expectation operator; (ii) we derive conditions on the distribution P(L)(x) for which the first-order breakdown of the system occurs abruptly without any preceding diverging rate of failure; (iii) we provide a detailed analysis of the robustness of the system under three specific load distributions-uniform, Pareto, and Weibull-showing that with the minimum load L(min) and mean load E[L] fixed, Pareto distribution is the worst (in terms of robustness) among the three, whereas Weibull distribution is the best with shape parameter selected relatively large; (iv) we provide numerical results that confirm our mean-field analysis; and (v) we show that p(☆) is maximized when the load distribution is a Dirac delta function centered at E[L], i.e., when all lines carry the same load. This last finding is particularly surprising given that heterogeneity is known to lead to high robustness against random failures in many other systems.

Bridge element deterioration rates.

Science.gov (United States)

2008-10-01

This report describes the development of bridge element deterioration rates using the NYSDOT : bridge inspection database using Markov chains and Weibull-based approaches. It is observed : that Weibull-based approach is more reliable for developing b...

An extensive evaluation of wind resource using new methods and strategies for development and utilizing wind power in Mah-shahr station in Iran

International Nuclear Information System (INIS)

Nedaei, Mojtaba; Assareh, Ehsanolah; Biglari, Mojtaba

2014-01-01

Highlights: • In this research, results suggest that the Weibull distribution is the best function to model the wind data in Mah-shahr. • The compatibility of the wind data with three methods of estimating Weibull parameters was assessed. • An extreme analysis of wind in Mah-shahr was done to determine the maximum gust wind speeds over a 50-year return period. • An extensive economic evaluation of installing a wind park was performed on RETScreen® software. - Abstract: In this study, the 10-min period measured short-term wind speed data at 10 m and 40 m heights for Mah-shahr station in Iran was statistically analyzed to determine the potential of wind power generation. In addition in this paper different distribution functions are compared to each other in order to find the best distribution in Mah-shahr which is compatible with the wind data. It is found that the Weibull distribution is the best function to model the wind data in Mah-shahr. It should also be mentioned that the different methods for calculating Weibull parameters were used and compared to each other. Moreover an extreme analysis of wind data in Mah-shahr was carried out to determine the maximum gust wind speed over a 50-year return period (Ve50). Using the method of “periodic maxima” for analysis of extreme winds, it was revealed that the 50-year wind speed at 80 m in Mah-shahr which is 39.5 m/s is lower than usual values of Ve50 limits for different wind turbines. This means that the risk of extreme wind gusts in Mah-shahr might not be a problem for installation of wind turbines. From the primary evaluation of wind data in Mah-shahr it is found the studied site has an acceptable potential of wind power for electricity generation. Energy production of different wind turbines at different heights is determined. Then a simple economic evaluation carried out to determine whether studied site is suitable for development of commercial or small and residential wind turbines. It became clear

Preventative maintenance cycle of contact switches for nuclear power plants based on lifetime assessment and economic analysis

International Nuclear Information System (INIS)

Shi Jie

2010-01-01

An approach to determine the preventive maintenance cycle was proposed in consideration of the lifetime, optimal cost and economy. Two parameters Weibull distribution was used to calculate the lifetime of contact switch. The block replacement model and age replacement model were built with the objective of optimal cost, and the preventive replacement cycle was accounted. Eight proposals for preventive replacement cycle were given. Economy model was applied to assess those proposals and the optimal proposal was confirmed. (authors)

Statistical characterization of tensile strengths for a nuclear-type core graphite

International Nuclear Information System (INIS)

Kennedy, C.R.; Eatherly, W.P.

1986-09-01

A data set of tensile strengths comprising over 1200 experimental points has been analyzed statistically in conformance with the observed phenomenon of background and disparate flaws. The data are consistent with a bimodal normal distribution. If corrections are made for strength dependence on density, the background mode is Weibull. It is proposed the disparate mode can be represented by a combination of binomial and order statistics. The resultant bimodal model would show a strong dependence on stress volume

Randomized central limit theorems: A unified theory.

Science.gov (United States)

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Microstructural and reliability in grinding of silicon nitride

International Nuclear Information System (INIS)

Liu, C.-C.

2004-01-01

A sintered Si 3 N 4 matrix has been characterized by TEM. The film thickness distribution of Si 3 N 4 was measured by high resolution transmission electron microscopy (HREM). Surface grinding is performed on two table speeds of 0.08 and 0.25 m s -1 with different depth of cut. The ground surfaces were observed with scanning electron microscopy (SEM). The surface texture was found to have greater dependence on depth of cut and table speed. The surface roughness is improved after smaller depth of cut. The flexural strength of ground specimens were measured by four-point flexure tests. The effect of depth of cut during grinding on the flexural strength and reliability of silicon nitride is investigated. The large depth of cut of 30 μm/pass resulted in a further decreased in strength of 540 MPa and a Weibull modulus of 7.5. When the depth of cut of 5 μm/pass were subjected to the ground specimens, the average strength was increased to 670 MPa and Weibull modulus to 9.1

Calculation of thermal stresses in graphite fuel blocks

International Nuclear Information System (INIS)

Lejeail, Y.; Cabrillat, M.T.

2005-01-01

This paper presents a parametric study of temperature and thermal stress calculations inside a HTGR core graphite block, taking into account the effect of fluence on the thermal and mechanical properties, up to 4. 10 21 n/cm 2 . The Finite Element model, realized with Cast3M CEA code, includes the effects of irradiation creep, which tends to produce secondary stress relaxation. Then, the Weibull weakest link theory is recalled, evaluating the possible effects of volume, stress field distribution (loading factor), and multiaxiality for graphite-type materials, and giving the methodology to compare the stress to rupture for the structure to the one obtained from characterization, in the general case. The maximum of the Weibull stress in Finite Element calculations is compared to the value for tensile specimens. It is found that the maximum of the stress corresponds to the end of the irradiation cycle, after reactor shutdown, since both thermal conductivity and Young's modulus increase with time. However, this behaviour is partly counterbalanced by the increase of material strength with irradiation. (authors)

Characterization of structure and development of models to quantify wood potential of an unmanaged Araucaria angustifolia stand

Directory of Open Access Journals (Sweden)

Rafaella De Angeli Curto

2014-12-01

Full Text Available The objective of this study was to characterize of an unmanaged stand of Araucaria angustifolia and to development of models to quantify the wood potential, aiming to support the development of forest management plans in stands with similar conditions. The work was developed into a stand established in 1946, in National Forest of Açungui, in Campo Largo County, Paraná State, Brazil. There was only one thinning in the stand, between 1970 and 1980. From the frequency of individuals in each diametric class, it was observed the condition of stagnation and competition with cohort in the beginning of class distribution. With the application of the probability density function of Weibull-3P, Trorey model, and the 5th polynomial by diameter class, it was possible to confirm the stock estimative of timber volume of the stand. This analysis indicated that the stand presents average annual wood production smaller than the species potential. So it is recommended the thinning to promote growth of remnant trees. With the probability density function of Weibull-3p, that was selected, it is possible to project the diametric distribution of the stand, when analyzed complementarily with growth diameter information, if the stand remains unmanaged. Certainly, the optimum potential of timber production could have been manifested if the stand were managed during the cycle planed.

Design off-shore wind climate

Energy Technology Data Exchange (ETDEWEB)

Larsen, G C; Joergensen, H E [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)

1999-03-01

Specific recommendations of off-shore turbulence intensities, applicable for design purposes, are lacking in the present IEC-code. The present off-shore wind climate analysis presents the distribution of the turbulence standard deviation around the mean turbulence standard deviation, conditioned on the mean wind speed. Measured distributions, based on a huge amount of measuring data from two shallow water off-shore sites, are parameterized by fitting to a three parameter Weibull distribution. Combining a simple heuristic load model with the parameterized probability density functions of the turbulence standard deviations, an empirical off-shore design turbulence intensity is evaluated that in average yields the same fatigue damage as the distributed turbulence intensity. The proposed off-shore design turbulence intensity is, within the IEC code framework, applicable for extreme as well as for fatigue load determination. (au)

Probability density functions of photochemicals over a coastal area of Northern Italy

International Nuclear Information System (INIS)

Georgiadis, T.; Fortezza, F.; Alberti, L.; Strocchi, V.; Marani, A.; Dal Bo', G.

1998-01-01

The present paper surveys the findings of experimental studies and analyses of statistical probability density functions (PDFs) applied to air pollutant concentrations to provide an interpretation of the ground-level distributions of photochemical oxidants in the coastal area of Ravenna (Italy). The atmospheric-pollution data set was collected from the local environmental monitoring network for the period 1978-1989. Results suggest that the statistical distribution of surface ozone, once normalised over the solar radiation PDF for the whole measurement period, follows a log-normal law as found for other pollutants. Although the Weibull distribution also offers a good fit of the experimental data, the area's meteorological features seem to favour the former distribution once the statistical index estimates have been analysed. Local transport phenomena are discussed to explain the data tail trends

Cure modeling in real-time prediction: How much does it help?

Science.gov (United States)

Ying, Gui-Shuang; Zhang, Qiang; Lan, Yu; Li, Yimei; Heitjan, Daniel F

2017-08-01

Various parametric and nonparametric modeling approaches exist for real-time prediction in time-to-event clinical trials. Recently, Chen (2016 BMC Biomedical Research Methodology 16) proposed a prediction method based on parametric cure-mixture modeling, intending to cover those situations where it appears that a non-negligible fraction of subjects is cured. In this article we apply a Weibull cure-mixture model to create predictions, demonstrating the approach in RTOG 0129, a randomized trial in head-and-neck cancer. We compare the ultimate realized data in RTOG 0129 to interim predictions from a Weibull cure-mixture model, a standard Weibull model without a cure component, and a nonparametric model based on the Bayesian bootstrap. The standard Weibull model predicted that events would occur earlier than the Weibull cure-mixture model, but the difference was unremarkable until late in the trial when evidence for a cure became clear. Nonparametric predictions often gave undefined predictions or infinite prediction intervals, particularly at early stages of the trial. Simulations suggest that cure modeling can yield better-calibrated prediction intervals when there is a cured component, or the appearance of a cured component, but at a substantial cost in the average width of the intervals. Copyright © 2017 Elsevier Inc. All rights reserved.

A nonlinear model of gold production in Malaysia

Science.gov (United States)

Ramli, Norashikin; Muda, Nora; Umor, Mohd Rozi

2014-06-01

Malaysia is a country which is rich in natural resources and one of it is a gold. Gold has already become an important national commodity. This study is conducted to determine a model that can be well fitted with the gold production in Malaysia from the year 1995-2010. Five nonlinear models are presented in this study which are Logistic model, Gompertz, Richard, Weibull and Chapman-Richard model. These model are used to fit the cumulative gold production in Malaysia. The best model is then selected based on the model performance. The performance of the fitted model is measured by sum squares error, root mean squares error, coefficient of determination, mean relative error, mean absolute error and mean absolute percentage error. This study has found that a Weibull model is shown to have significantly outperform compare to the other models. To confirm that Weibull is the best model, the latest data are fitted to the model. Once again, Weibull model gives the lowest readings at all types of measurement error. We can concluded that the future gold production in Malaysia can be predicted according to the Weibull model and this could be important findings for Malaysia to plan their economic activities.

Some conclusions about the concrete strength of the bored piles of Angra 2 nuclear power plant

International Nuclear Information System (INIS)

Thomaz, E.C.S.; Joia, L.A.

1984-01-01

The concrete of the bored piles of Angra 2 was submitted to a deep control, so more than five thousand core samples were analyzed to verify the quality of the concrete. Based on these samples and using statistics regression theory some conclusions could be done. It was analyzed the dependence of the concrete strength upon the depth of the pile. Also based on these samples some probability distribution functions that could simulate the concrete strength were studied applying the Kolmogorov - Smirnov fitness test. Finally, a method for evaluating a confidence interval of one of the probability function (Weibull distribution) was developed adopting the Monte Carlo simulation technique. (Author) [pt

Production and mechanical properties of sintered carbides (hard steels WC-Co)

International Nuclear Information System (INIS)

Batalha, G.F.

1987-09-01

Densification and mechanical characteristics or WC-Co Cemented Carbides, were investigated by dilatometry, Hardness and bending tests, as a function of the two principal micro-structural parameters: the cobalt content and the particle size of carbide crystals. Vickers hardness of the studied compositions showed a linear variation with the increase of the cobalt content. By three point bending, the transverse rupture strenght increases with cobalt content, however, for larger grain size reaches a maximum, eventually reduced by brittle phases and incomplete dispersion. The results of brittle facture tests were statistically analised and fitted better to the 'Weakest Link Model' (Weibull distribution) than the 'Chain Model' (Gaussian distribution). (author) [pt

Failure analysis a practical guide for manufacturers of electronic components and systems

CERN Document Server

Bâzu, Marius

2011-01-01

Failure analysis is the preferred method to investigate product or process reliability and to ensure optimum performance of electrical components and systems. The physics-of-failure approach is the only internationally accepted solution for continuously improving the reliability of materials, devices and processes. The models have been developed from the physical and chemical phenomena that are responsible for degradation or failure of electronic components and materials and now replace popular distribution models for failure mechanisms such as Weibull or lognormal. Reliability engineers nee

Proceedings of the Conference on the Design of Experiments in Army Research Development and Testing (31st) Held at the Madison, Wisconsin on 23-25 October 1986

Science.gov (United States)

1986-06-01

indicates a ne ed for corrective action. If the scheme is applied to each of three employe es, the total sample is n = 6,000, about 12 percent of workload...x8 implies B. It should be noted that the calculations of xA and x8 yield wor st case va 1 ues if the null hypotheses are inequa 1 iti es. Each...parameter n is assumed to be independent of ~· Glaser (1984) employes a more general formulation with the Weibull distribution assuming that the

Hourly wind speed analysis in Sicily

Energy Technology Data Exchange (ETDEWEB)

Bivona, S.; Leone, C. [Palermo Univ., Dip di Fisica e Technologie Relative, Palermo (Italy); Burlon, R. [Palermo Univ., Dip. di Ingegnaria Nucleare, Palermo (Italy)

2003-07-01

The hourly average wind speed data recorded by CNMCA (Centro Nazionale di Meteorologia e Climatologia Aeronautica) have been used to study the statistical properties of the wind speed at nine locations on Sicily. By grouping the observations month by month, we show that the hourly average wind speed, with calms omitted, is represented by a Weibull function. The suitability of the distribution is judged by the discrepancies between the observed and calculated values of the monthly average wind speed and of the standard deviation. (Author)

An assessment on seasonal analysis of wind energy characteristics and wind turbine characteristics

International Nuclear Information System (INIS)

Akpinar, E. Kavak; Akpinar, S.

2005-01-01

This paper presents seasonal variations of the wind characteristics and wind turbine characteristics in the regions around Elazig, namely Maden, Agin and Keban. Mean wind speed data in measured hourly time series format is statistically analyzed for the six year period 1998-2003. The probability density distributions are derived from the time series data and their distributional parameters are identified. Two probability density functions are fitted to the measured probability distributions on a seasonal basis. The wind energy characteristics of all the regions is studied based on the Weibull and Rayleigh distributions. Energy calculations and capacity factors for the wind turbine characteristics were determined for wind machines of different sizes between 300 and 2300 kW. It was found that Maden is the best region, among the regions analyzed, for wind characteristics and wind turbine characteristics

Comparison of Dose Response Models for Predicting Normal Tissue Complications from Cancer Radiotherapy: Application in Rat Spinal Cord

Energy Technology Data Exchange (ETDEWEB)

Adamus-Górka, Magdalena; Mavroidis, Panayiotis, E-mail: panayiotis.mavroidis@ki.se; Lind, Bengt K.; Brahme, Anders [Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, Stockholm S-17176 (Sweden)

2011-05-18

Seven different radiobiological dose-response models have been compared with regard to their ability to describe experimental data. The first four models, namely the critical volume, the relative seriality, the inverse tumor and the critical element models are mainly based on cell survival biology. The other three models: the Lyman (Gaussian distribution), the parallel architecture and the Weibull distribution models are semi-empirical and rather based on statistical distributions. The maximum likelihood estimation was used to fit the models to experimental data and the χ{sup 2}-distribution, AIC criterion and F-test were applied to compare the goodness-of-fit of the models. The comparison was performed using experimental data for rat spinal cord injury. Both the shape of the dose-response curve and the ability of handling the volume dependence were separately compared for each model. All the models were found to be acceptable in describing the present experimental dataset (p > 0.05). For the white matter necrosis dataset, the Weibull and Lyman models were clearly superior to the other models, whereas for the vascular damage case, the Relative Seriality model seems to have the best performance although the Critical volume, Inverse tumor, Critical element and Parallel architecture models gave similar results. Although the differences between many of the investigated models are rather small, they still may be of importance in indicating the advantages and limitations of each particular model. It appears that most of the models have favorable properties for describing dose-response data, which indicates that they may be suitable to be used in biologically optimized intensity modulated radiation therapy planning, provided a proper estimation of their radiobiological parameters had been performed for every tissue and clinical endpoint.

Comparison of Dose Response Models for Predicting Normal Tissue Complications from Cancer Radiotherapy: Application in Rat Spinal Cord

International Nuclear Information System (INIS)

Adamus-Górka, Magdalena; Mavroidis, Panayiotis; Lind, Bengt K.; Brahme, Anders

2011-01-01

Seven different radiobiological dose-response models have been compared with regard to their ability to describe experimental data. The first four models, namely the critical volume, the relative seriality, the inverse tumor and the critical element models are mainly based on cell survival biology. The other three models: the Lyman (Gaussian distribution), the parallel architecture and the Weibull distribution models are semi-empirical and rather based on statistical distributions. The maximum likelihood estimation was used to fit the models to experimental data and the χ 2 -distribution, AIC criterion and F-test were applied to compare the goodness-of-fit of the models. The comparison was performed using experimental data for rat spinal cord injury. Both the shape of the dose-response curve and the ability of handling the volume dependence were separately compared for each model. All the models were found to be acceptable in describing the present experimental dataset (p > 0.05). For the white matter necrosis dataset, the Weibull and Lyman models were clearly superior to the other models, whereas for the vascular damage case, the Relative Seriality model seems to have the best performance although the Critical volume, Inverse tumor, Critical element and Parallel architecture models gave similar results. Although the differences between many of the investigated models are rather small, they still may be of importance in indicating the advantages and limitations of each particular model. It appears that most of the models have favorable properties for describing dose-response data, which indicates that they may be suitable to be used in biologically optimized intensity modulated radiation therapy planning, provided a proper estimation of their radiobiological parameters had been performed for every tissue and clinical endpoint

Hyperchaotic Dynamics for Light Polarization in a Laser Diode

Science.gov (United States)

Bonatto, Cristian

2018-04-01

It is shown that a highly randomlike behavior of light polarization states in the output of a free-running laser diode, covering the whole Poincaré sphere, arises as a result from a fully deterministic nonlinear process, which is characterized by a hyperchaotic dynamics of two polarization modes nonlinearly coupled with a semiconductor medium, inside the optical cavity. A number of statistical distributions were found to describe the deterministic data of the low-dimensional nonlinear flow, such as lognormal distribution for the light intensity, Gaussian distributions for the electric field components and electron densities, Rice and Rayleigh distributions, and Weibull and negative exponential distributions, for the modulus and intensity of the orthogonal linear components of the electric field, respectively. The presented results could be relevant for the generation of single units of compact light source devices to be used in low-dimensional optical hyperchaos-based applications.

Flexural strength and the probability of failure of cold isostatic pressed zirconia core ceramics.

Science.gov (United States)

Siarampi, Eleni; Kontonasaki, Eleana; Papadopoulou, Lambrini; Kantiranis, Nikolaos; Zorba, Triantafillia; Paraskevopoulos, Konstantinos M; Koidis, Petros

2012-08-01

The flexural strength of zirconia core ceramics must predictably withstand the high stresses developed during oral function. The in-depth interpretation of strength parameters and the probability of failure during clinical performance could assist the clinician in selecting the optimum materials while planning treatment. The purpose of this study was to evaluate the flexural strength based on survival probability and Weibull statistical analysis of 2 zirconia cores for ceramic restorations. Twenty bar-shaped specimens were milled from 2 core ceramics, IPS e.max ZirCAD and Wieland ZENO Zr, and were loaded until fracture according to ISO 6872 (3-point bending test). An independent samples t test was used to assess significant differences of fracture strength (α=.05). Weibull statistical analysis of the flexural strength data provided 2 parameter estimates: Weibull modulus (m) and characteristic strength (σ(0)). The fractured surfaces of the specimens were evaluated by scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS). The investigation of the crystallographic state of the materials was performed with x-ray diffraction analysis (XRD) and Fourier transform infrared (FTIR) spectroscopy. Higher mean flexural strength (Plines zones). Both groups primarily sustained the tetragonal phase of zirconia and a negligible amount of the monoclinic phase. Although both zirconia ceramics presented similar fractographic and crystallographic properties, the higher flexural strength of WZ ceramics was associated with a lower m and more voids in their microstructure. These findings suggest a greater scattering of strength values and a flaw distribution that are expected to increase failure probability. Copyright © 2012 The Editorial Council of the Journal of Prosthetic Dentistry. Published by Mosby, Inc. All rights reserved.

Fire Regime in Marginal Jack Pine Populations at Their Southern Limit of Distribution, Riding Mountain National Park, Central Canada

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Jacques C. Tardif

2016-09-01

Full Text Available In central Canada, long fire history reconstructions are rare. In a context where both anthropogenic and climate influences on fire regime have changed, Parks Canada has a mandate to maintain ecological integrity. Here we present a fire history derived from fire-scarred jack pine (Pinus banksiana Lamb. trees growing at their southern distribution limit in Riding Mountain National Park (RMNP. In Lake Katherine Fire Management Unit (LKFMU, a subregion within the park, fire history was reconstructed from archival records, tree-ring records, and charcoal in lake sediment. From about 1450 to 1850 common era (CE the fire return intervals varied from 37 to 125 years, according to models. During the period 1864–1930 the study area burned frequently (Weibull Mean Fire Intervals between 2.66 and 5.62 years; this period coincided with the end of First Nations occupation and the start of European settlement. Major recruitment pulses were associated with the stand-replacing 1864 and 1894 fires. This period nevertheless corresponded to a reduction in charcoal accumulation. The current fire-free period in LKFMU (1930–today coincides with RMNP establishment, exclusion of First Nations land use and increased fire suppression. Charcoal accumulation further decreased during this period. In the absence of fire, jack pine exclusion in LKFMU is foreseeable and the use of prescribed burning is advocated to conserve this protected jack pine ecosystem, at the southern margins of its range, and in the face of potential climate change.

Local approach to brittle fracture under residual stress field. Assessment of pre-loading effect; Local approach no tekiyo ni yoru zanryu oryoku wo motsu buzai no zeisei hakai kyodo hyoka. Yokaju no eikyo no hyoka

Energy Technology Data Exchange (ETDEWEB)

Yamashita, Y.; Sakano, K.; Onozuka, M. [Ishikawajima-Harima Heavy Industries Co. Ltd., Tokyo (Japan); Minami, F. [Osaka University, Osaka (Japan)

2000-01-01

The effect of residual stresses on brittle fracture was investigated on the basis of the Local Approach. Compressive residual stress was introduced by pre-loading and the subsequent fracture test conducted with a 780 MPa class steel. Preloading apparently increased the critical load and critical CTOD at the onset of brittle fracture initiation. The Weibull stress criterion was used to evaluate the brittle fracture resistance of the pre-loaded specimen. The critical Weibull stress is a material property independent of test conditions with and without pre-loading. Using the Weibull stress criterion, the critical CTOD of the pre-loaded specimen can be predicted from test results of the specimen without pre-loading. (author)