The McDonald’s Inverse Weibull Distribution

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Saman Hanif Shahbaz

2016-12-01

Full Text Available We have proposed a new Inverse Weibull distribution by using the generalized Beta distribution of McDonald (1984. Basic properties of the proposed distribution has been studied. Parameter estimation has been discussed alongside an illustrative example.

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...

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.

Modifications of the Weibull distribution: A review

International Nuclear Information System (INIS)

Almalki, Saad J.; Nadarajah, Saralees

2014-01-01

It is well known that the Weibull distribution is the most popular and the most widely used distribution in reliability and in analysis of lifetime data. Unfortunately, its hazard function cannot exhibit non-monotonic shapes like the bathtub shape or the unimodal shape. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. This paper gives an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution. - Highlights: • A comprehensive review of known discrete modifications and generalizations of the Weibull distribution. • A comprehensive review of known continuous modifications and generalizations of the Weibull distribution. • Over 110 references on modifications/generalizations of the Weibull distribution. • More than 55% of the cited references appeared in the last 5 years

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

On alternative q-Weibull and q-extreme value distributions: Properties and applications

Science.gov (United States)

Zhang, Fode; Ng, Hon Keung Tony; Shi, Yimin

2018-01-01

Tsallis statistics and Tsallis distributions have been attracting a significant amount of research work in recent years. Importantly, the Tsallis statistics, q-distributions have been applied in different disciplines. Yet, a relationship between some existing q-Weibull distributions and q-extreme value distributions that is parallel to the well-established relationship between the conventional Weibull and extreme value distributions through a logarithmic transformation has not be established. In this paper, we proposed an alternative q-Weibull distribution that leads to a q-extreme value distribution via the q-logarithm transformation. Some important properties of the proposed q-Weibull and q-extreme value distributions are studied. Maximum likelihood and least squares estimation methods are used to estimate the parameters of q-Weibull distribution and their performances are investigated through a Monte Carlo simulation study. The methodologies and the usefulness of the proposed distributions are illustrated by fitting the 2014 traffic fatalities data from The National Highway Traffic Safety Administration.

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.

Analysis of the upper-truncated Weibull distribution for wind speed

International Nuclear Information System (INIS)

Kantar, Yeliz Mert; Usta, Ilhan

2015-01-01

Highlights: • Upper-truncated Weibull distribution is proposed to model wind speed. • Upper-truncated Weibull distribution nests Weibull distribution as special case. • Maximum likelihood is the best method for upper-truncated Weibull distribution. • Fitting accuracy of upper-truncated Weibull is analyzed on wind speed data. - Abstract: Accurately modeling wind speed is critical in estimating the wind energy potential of a certain region. In order to model wind speed data smoothly, several statistical distributions have been studied. Truncated distributions are defined as a conditional distribution that results from restricting the domain of statistical distribution and they also cover base distribution. This paper proposes, for the first time, the use of upper-truncated Weibull distribution, in modeling wind speed data and also in estimating wind power density. In addition, a comparison is made between upper-truncated Weibull distribution and well known Weibull distribution using wind speed data measured in various regions of Turkey. The obtained results indicate that upper-truncated Weibull distribution shows better performance than Weibull distribution in estimating wind speed distribution and wind power. Therefore, upper-truncated Weibull distribution can be an alternative for use in the assessment of wind energy potential

Transmuted New Generalized Inverse Weibull Distribution

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Muhammad Shuaib Khan

2017-06-01

Full Text Available This paper introduces the transmuted new generalized inverse Weibull distribution by using the quadratic rank transmutation map (QRTM scheme studied by Shaw et al. (2007. The proposed model contains the twenty three lifetime distributions as special sub-models. Some mathematical properties of the new distribution are formulated, such as quantile function, Rényi entropy, mean deviations, moments, moment generating function and order statistics. The method of maximum likelihood is used for estimating the model parameters. We illustrate the flexibility and potential usefulness of the new distribution by using reliability data.

Using the Weibull distribution reliability, modeling and inference

CERN Document Server

McCool, John I

2012-01-01

Understand and utilize the latest developments in Weibull inferential methods While the Weibull distribution is widely used in science and engineering, most engineers do not have the necessary statistical training to implement the methodology effectively. Using the Weibull Distribution: Reliability, Modeling, and Inference fills a gap in the current literature on the topic, introducing a self-contained presentation of the probabilistic basis for the methodology while providing powerful techniques for extracting information from data. The author explains the use of the Weibull distribution

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.

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.

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...

A Weibull distribution accrual failure detector for cloud computing.

Science.gov (United States)

Liu, Jiaxi; Wu, Zhibo; Wu, Jin; Dong, Jian; Zhao, Yao; Wen, Dongxin

2017-01-01

Failure detectors are used to build high availability distributed systems as the fundamental component. To meet the requirement of a complicated large-scale distributed system, accrual failure detectors that can adapt to multiple applications have been studied extensively. However, several implementations of accrual failure detectors do not adapt well to the cloud service environment. To solve this problem, a new accrual failure detector based on Weibull Distribution, called the Weibull Distribution Failure Detector, has been proposed specifically for cloud computing. It can adapt to the dynamic and unexpected network conditions in cloud computing. The performance of the Weibull Distribution Failure Detector is evaluated and compared based on public classical experiment data and cloud computing experiment data. The results show that the Weibull Distribution Failure Detector has better performance in terms of speed and accuracy in unstable scenarios, especially in cloud computing.

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.

A MULTIVARIATE WEIBULL DISTRIBUTION

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Cheng Lee

2010-07-01

Full Text Available A multivariate survival function of Weibull Distribution is developed by expanding the theorem by Lu and Bhattacharyya. From the survival function, the probability density function, the cumulative probability function, the determinant of the Jacobian Matrix, and the general moment are derived.

Comparison of estimation methods for fitting weibull distribution to ...

African Journals Online (AJOL)

Comparison of estimation methods for fitting weibull distribution to the natural stand of Oluwa Forest Reserve, Ondo State, Nigeria. ... Journal of Research in Forestry, Wildlife and Environment ... The result revealed that maximum likelihood method was more accurate in fitting the Weibull distribution to the natural stand.

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

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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.

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.

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.

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.

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

Evaluation of burst probability for tubes by Weibull distributions

International Nuclear Information System (INIS)

Kao, S.

1975-10-01

The investigations of candidate distributions that best describe the burst pressure failure probability characteristics of nuclear power steam generator tubes has been continued. To date it has been found that the Weibull distribution provides an acceptable fit for the available data from both the statistical and physical viewpoints. The reasons for the acceptability of the Weibull distribution are stated together with the results of tests for the suitability of fit. In exploring the acceptability of the Weibull distribution for the fitting, a graphical method to be called the ''density-gram'' is employed instead of the usual histogram. With this method a more sensible graphical observation on the empirical density may be made for cases where the available data is very limited. Based on these methods estimates of failure pressure are made for the left-tail probabilities

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

Single versus mixture Weibull distributions for nonparametric satellite reliability

International Nuclear Information System (INIS)

Castet, Jean-Francois; Saleh, Joseph H.

2010-01-01

Long recognized as a critical design attribute for space systems, satellite reliability has not yet received the proper attention as limited on-orbit failure data and statistical analyses can be found in the technical literature. To fill this gap, we recently conducted a nonparametric analysis of satellite reliability for 1584 Earth-orbiting satellites launched between January 1990 and October 2008. In this paper, we provide an advanced parametric fit, based on mixture of Weibull distributions, and compare it with the single Weibull distribution model obtained with the Maximum Likelihood Estimation (MLE) method. We demonstrate that both parametric fits are good approximations of the nonparametric satellite reliability, but that the mixture Weibull distribution provides significant accuracy in capturing all the failure trends in the failure data, as evidenced by the analysis of the residuals and their quasi-normal dispersion.

A Study on The Mixture of Exponentiated-Weibull Distribution

Directory of Open Access Journals (Sweden)

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.

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 ...

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....

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.

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.

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

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

Directory of Open Access Journals (Sweden)

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

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

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

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

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

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.

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.

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.

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

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

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)

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.

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.

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...

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

Directory of Open Access Journals (Sweden)

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.

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

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)

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.

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.

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)

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.

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.

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.

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

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.

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 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.

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)

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

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)

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 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.

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.

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)

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

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

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

Directory of Open Access Journals (Sweden)

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.

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.

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.

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

Directory of Open Access Journals (Sweden)

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 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.

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.

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

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

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.

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

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

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.

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.

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

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

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

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

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

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...

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.

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...

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 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%).

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.

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.

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

Directory of Open Access Journals (Sweden)

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

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)

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.

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.

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.

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

Weibull-Based Design Methodology for Rotating Structures in Aircraft Engines

Directory of Open Access Journals (Sweden)

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.

SEMI-COMPETING RISKS ON A TRIVARIATE WEIBULL SURVIVAL MODEL

Directory of Open Access Journals (Sweden)

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

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

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.

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.

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.

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...

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.

Estimation of the reliability function for two-parameter exponentiated Rayleigh or Burr type X distribution

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Anupam Pathak

2014-11-01

Full Text Available Abstract: Problem Statement: The two-parameter exponentiated Rayleigh distribution has been widely used especially in the modelling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The uniformly minimum variance unbiased and maximum likelihood estimation methods are the way to estimate the parameters of the distribution. In this study we explore and compare the performance of the uniformly minimum variance unbiased and maximum likelihood estimators of the reliability function R(t=P(X>t and P=P(X>Y for the two-parameter exponentiated Rayleigh distribution. Approach: A new technique of obtaining these parametric functions is introduced in which major role is played by the powers of the parameter(s and the functional forms of the parametric functions to be estimated are not needed.  We explore the performance of these estimators numerically under varying conditions. Through the simulation study a comparison are made on the performance of these estimators with respect to the Biasness, Mean Square Error (MSE, 95% confidence length and corresponding coverage percentage. Conclusion: Based on the results of simulation study the UMVUES of R(t and ‘P’ for the two-parameter exponentiated Rayleigh distribution found to be superior than MLES of R(t and ‘P’.

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...

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.

Comparison of Two Methods Used to Model Shape Parameters of Pareto Distributions

Science.gov (United States)

Liu, C.; Charpentier, R.R.; Su, J.

2011-01-01

Two methods are compared for estimating the shape parameters of Pareto field-size (or pool-size) distributions for petroleum resource assessment. Both methods assume mature exploration in which most of the larger fields have been discovered. Both methods use the sizes of larger discovered fields to estimate the numbers and sizes of smaller fields: (1) the tail-truncated method uses a plot of field size versus size rank, and (2) the log-geometric method uses data binned in field-size classes and the ratios of adjacent bin counts. Simulation experiments were conducted using discovered oil and gas pool-size distributions from four petroleum systems in Alberta, Canada and using Pareto distributions generated by Monte Carlo simulation. The estimates of the shape parameters of the Pareto distributions, calculated by both the tail-truncated and log-geometric methods, generally stabilize where discovered pool numbers are greater than 100. However, with fewer than 100 discoveries, these estimates can vary greatly with each new discovery. The estimated shape parameters of the tail-truncated method are more stable and larger than those of the log-geometric method where the number of discovered pools is more than 100. Both methods, however, tend to underestimate the shape parameter. Monte Carlo simulation was also used to create sequences of discovered pool sizes by sampling from a Pareto distribution with a discovery process model using a defined exploration efficiency (in order to show how biased the sampling was in favor of larger fields being discovered first). A higher (more biased) exploration efficiency gives better estimates of the Pareto shape parameters. ?? 2011 International Association for Mathematical Geosciences.

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.

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.

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.

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

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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.

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.

SYVAC3 parameter distribution package

Energy Technology Data Exchange (ETDEWEB)

Andres, T; Skeet, A

1995-01-01

SYVAC3 (Systems Variability Analysis Code, generation 3) is a computer program that implements a method called systems variability analysis to analyze the behaviour of a system in the presence of uncertainty. This method is based on simulating the system many times to determine the variation in behaviour it can exhibit. SYVAC3 specializes in systems representing the transport of contaminants, and has several features to simplify the modelling of such systems. It provides a general tool for estimating environmental impacts from the dispersal of contaminants. This report describes a software object type (a generalization of a data type) called Parameter Distribution. This object type is used in SYVAC3, and can also be used independently. Parameter Distribution has the following subtypes: beta distribution; binomial distribution; constant distribution; lognormal distribution; loguniform distribution; normal distribution; piecewise uniform distribution; Triangular distribution; and uniform distribution. Some of these distributions can be altered by correlating two parameter distribution objects. This report provides complete specifications for parameter distributions, and also explains how to use them. It should meet the needs of casual users, reviewers, and programmers who wish to add their own subtypes. (author). 30 refs., 75 tabs., 56 figs.

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.

Recovering Parameters of Johnson's SB Distribution

Science.gov (United States)

Bernard R. Parresol

2003-01-01

A new parameter recovery model for Johnson's SB distribution is developed. This latest alternative approach permits recovery of the range and both shape parameters. Previous models recovered only the two shape parameters. Also, a simple procedure for estimating the distribution minimum from sample values is presented. The new methodology...

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...

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.

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.

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.

ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS

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muhammad zahid rashid

2011-04-01

Full Text Available The exponential distribution is commonly used to model the behavior of units that have a constant failure rate. The two-parameter exponential distribution provides a simple but nevertheless useful model for the analysis of lifetimes, especially when investigating reliability of technical equipment.This paper is concerned with estimation of parameters of the two parameter (location and scale exponential distribution. We used the least squares method (LSM, relative least squares method (RELS, ridge regression method (RR,  moment estimators (ME, modified moment estimators (MME, maximum likelihood estimators (MLE and modified maximum likelihood estimators (MMLE. We used the mean square error MSE, and total deviation TD, as measurement for the comparison between these methods. We determined the best method for estimation using different values for the parameters and different sample sizes

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.

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

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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.

Stand diameter distribution modelling and prediction based on Richards function.

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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.

Distribution characteristics of interfacial parameter in downward gas-liquid two-phase flow in vertical circular tube

International Nuclear Information System (INIS)

Liu Guoqiang; Yan Changqi; Tian Daogui; Sun Licheng

2014-01-01

Experimental study was performed on distribution characteristics of interfacial parameters of downward gas-liquid flow in a vertical circular tube with the measurement by a two-sensor optical fiber probe. The test section is a circular pipe with the inner diameter of 50 mm and the length of 2000 mm. The superficial velocities of the gas and the liquid phases cover the ranges of 0.004-0.077 m/s and 0.43-0.71 m/s, respectively. The results show that the distributions of the interfacial parameters in downward bubbly flows are quite different from those in upward bubbly flows. For the case of upward flow, the parameters present the 'wall-peak' or 'core-peak' distributions, but for the case of downward flow, they show 'wall-peak' or 'wide-peak' distributions. The average value of void fraction in vertical downward flow is about 119.6%-145.0% larger than that in upward flow, and the interfacial area concentration is about 18.8%-82.5% larger than that in upward flow. The distribution of interfacial parameters shows an obvious tendency of uniformity. (authors)

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.

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.

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)

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

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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.

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.

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.

Failure probability under parameter uncertainty.

Science.gov (United States)

Gerrard, R; Tsanakas, A

2011-05-01

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls. However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. We show that parameter uncertainty increases the probability (understood as expected frequency) of failures. For a large class of loss distributions, arising from increasing transformations of location-scale families (including the log-normal, Weibull, and Pareto distributions), the article shows that failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (1) by reducing the nominal required failure probability, depending on the size of the available data set, and (2) by modifying of the distribution itself that is used to calculate the risk control. Approach (1) corresponds to a frequentist/regulatory view of probability, while approach (2) is consistent with a Bayesian/personalistic view. We furthermore show that the two approaches are consistent in achieving the required failure probability. Finally, we briefly discuss the effects of data pooling and its systemic risk implications. © 2010 Society for Risk Analysis.

The reliability assessment of the electromagnetic valve of high-speed electric multiple units braking system based on two-parameter exponential distribution

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Jianwei Yang

2016-06-01

Full Text Available In order to solve the reliability assessment of braking system component of high-speed electric multiple units, this article, based on two-parameter exponential distribution, provides the maximum likelihood estimation and Bayes estimation under a type-I life test. First of all, we evaluate the failure probability value according to the classical estimation method and then obtain the maximum likelihood estimation of parameters of two-parameter exponential distribution by performing and using the modified likelihood function. On the other hand, based on Bayesian theory, this article also selects the beta and gamma distributions as the prior distribution, combines with the modified maximum likelihood function, and innovatively applies a Markov chain Monte Carlo algorithm to parameters assessment based on Bayes estimation method for two-parameter exponential distribution, so that two reliability mathematical models of the electromagnetic valve are obtained. Finally, through type-I life test, the failure rates according to maximum likelihood estimation and Bayes estimation method based on Markov chain Monte Carlo algorithm are, respectively, 2.650 × 10−5 and 3.037 × 10−5. Compared with the failure rate of a electromagnetic valve 3.005 × 10−5, it proves that the Bayes method can use a Markov chain Monte Carlo algorithm to estimate reliability for two-parameter exponential distribution and Bayes estimation is more closer to the value of electromagnetic valve. So, by fully integrating multi-source, Bayes estimation method can preferably modify and precisely estimate the parameters, which can provide a certain theoretical basis for the safety operation of high-speed electric multiple units.

Recurrent frequency-size distribution of characteristic events

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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.

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

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.  

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.

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

A Comparative Study of Distribution System Parameter Estimation Methods

Energy Technology Data Exchange (ETDEWEB)

Sun, Yannan; Williams, Tess L.; Gourisetti, Sri Nikhil Gup

2016-07-17

In this paper, we compare two parameter estimation methods for distribution systems: residual sensitivity analysis and state-vector augmentation with a Kalman filter. These two methods were originally proposed for transmission systems, and are still the most commonly used methods for parameter estimation. Distribution systems have much lower measurement redundancy than transmission systems. Therefore, estimating parameters is much more difficult. To increase the robustness of parameter estimation, the two methods are applied with combined measurement snapshots (measurement sets taken at different points in time), so that the redundancy for computing the parameter values is increased. The advantages and disadvantages of both methods are discussed. The results of this paper show that state-vector augmentation is a better approach for parameter estimation in distribution systems. Simulation studies are done on a modified version of IEEE 13-Node Test Feeder with varying levels of measurement noise and non-zero error in the other system model parameters.

Separating the contributions of variability and parameter uncertainty in probability distributions

International Nuclear Information System (INIS)

Sankararaman, S.; Mahadevan, S.

2013-01-01

This paper proposes a computational methodology to quantify the individual contributions of variability and distribution parameter uncertainty to the overall uncertainty in a random variable. Even if the distribution type is assumed to be known, sparse or imprecise data leads to uncertainty about the distribution parameters. If uncertain distribution parameters are represented using probability distributions, then the random variable can be represented using a family of probability distributions. The family of distributions concept has been used to obtain qualitative, graphical inference of the contributions of natural variability and distribution parameter uncertainty. The proposed methodology provides quantitative estimates of the contributions of the two types of uncertainty. Using variance-based global sensitivity analysis, the contributions of variability and distribution parameter uncertainty to the overall uncertainty are computed. The proposed method is developed at two different levels; first, at the level of a variable whose distribution parameters are uncertain, and second, at the level of a model output whose inputs have uncertain distribution parameters

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.

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)

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

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....

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

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.

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

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.

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.

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.

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.

Experimental and computational correlation of fracture parameters KIc, JIc, and GIc for unimodular and bimodular graphite components

Science.gov (United States)

Bhushan, Awani; Panda, S. K.

2018-05-01

The influence of bimodularity (different stress ∼ strain behaviour in tension and compression) on fracture behaviour of graphite specimens has been studied with fracture toughness (KIc), critical J-integral (JIc) and critical strain energy release rate (GIc) as the characterizing parameter. Bimodularity index (ratio of tensile Young's modulus to compression Young's modulus) of graphite specimens has been obtained from the normalized test data of tensile and compression experimentation. Single edge notch bend (SENB) testing of pre-cracked specimens from the same lot have been carried out as per ASTM standard D7779-11 to determine the peak load and critical fracture parameters KIc, GIc and JIc using digital image correlation technology of crack opening displacements. Weibull weakest link theory has been used to evaluate the mean peak load, Weibull modulus and goodness of fit employing two parameter least square method (LIN2), biased (MLE2-B) and unbiased (MLE2-U) maximum likelihood estimator. The stress dependent elasticity problem of three-dimensional crack progression behaviour for the bimodular graphite components has been solved as an iterative finite element procedure. The crack characterizing parameters critical stress intensity factor and critical strain energy release rate have been estimated with the help of Weibull distribution plot between peak loads versus cumulative probability of failure. Experimental and Computational fracture parameters have been compared qualitatively to describe the significance of bimodularity. The bimodular influence on fracture behaviour of SENB graphite has been reflected on the experimental evaluation of GIc values only, which has been found to be different from the calculated JIc values. Numerical evaluation of bimodular 3D J-integral value is found to be close to the GIc value whereas the unimodular 3D J-value is nearer to the JIc value. The significant difference between the unimodular JIc and bimodular GIc indicates that

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.

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 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.

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.

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

Directory of Open Access Journals (Sweden)

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

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)

The Power of Heterogeneity: Parameter Relationships from Distributions

Science.gov (United States)

Röding, Magnus; Bradley, Siobhan J.; Williamson, Nathan H.; Dewi, Melissa R.; Nann, Thomas; Nydén, Magnus

2016-01-01

Complex scientific data is becoming the norm, many disciplines are growing immensely data-rich, and higher-dimensional measurements are performed to resolve complex relationships between parameters. Inherently multi-dimensional measurements can directly provide information on both the distributions of individual parameters and the relationships between them, such as in nuclear magnetic resonance and optical spectroscopy. However, when data originates from different measurements and comes in different forms, resolving parameter relationships is a matter of data analysis rather than experiment. We present a method for resolving relationships between parameters that are distributed individually and also correlated. In two case studies, we model the relationships between diameter and luminescence properties of quantum dots and the relationship between molecular weight and diffusion coefficient for polymers. Although it is expected that resolving complicated correlated relationships require inherently multi-dimensional measurements, our method constitutes a useful contribution to the modelling of quantitative relationships between correlated parameters and measurements. We emphasise the general applicability of the method in fields where heterogeneity and complex distributions of parameters are obstacles to scientific insight. PMID:27182701

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.

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.

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%.

Effects of Initial Values and Convergence Criterion in the Two-Parameter Logistic Model When Estimating the Latent Distribution in BILOG-MG 3.

Directory of Open Access Journals (Sweden)

Ingo W Nader

Full Text Available Parameters of the two-parameter logistic model are generally estimated via the expectation-maximization algorithm, which improves initial values for all parameters iteratively until convergence is reached. Effects of initial values are rarely discussed in item response theory (IRT, but initial values were recently found to affect item parameters when estimating the latent distribution with full non-parametric maximum likelihood. However, this method is rarely used in practice. Hence, the present study investigated effects of initial values on item parameter bias and on recovery of item characteristic curves in BILOG-MG 3, a widely used IRT software package. Results showed notable effects of initial values on item parameters. For tighter convergence criteria, effects of initial values decreased, but item parameter bias increased, and the recovery of the latent distribution worsened. For practical application, it is advised to use the BILOG default convergence criterion with appropriate initial values when estimating the latent distribution from data.

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

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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.

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...

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.

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

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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

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

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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.

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

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.

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

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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

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

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.

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.

Optimization of VPSC Model Parameters for Two-Phase Titanium Alloys: Flow Stress Vs Orientation Distribution Function Metrics

Science.gov (United States)

Miller, V. M.; Semiatin, S. L.; Szczepanski, C.; Pilchak, A. L.

2018-06-01

The ability to predict the evolution of crystallographic texture during hot work of titanium alloys in the α + β temperature regime is greatly significant to numerous engineering disciplines; however, research efforts are complicated by the rapid changes in phase volume fractions and flow stresses with temperature in addition to topological considerations. The viscoplastic self-consistent (VPSC) polycrystal plasticity model is employed to simulate deformation in the two phase field. Newly developed parameter selection schemes utilizing automated optimization based on two different error metrics are considered. In the first optimization scheme, which is commonly used in the literature, the VPSC parameters are selected based on the quality of fit between experiment and simulated flow curves at six hot-working temperatures. Under the second newly developed scheme, parameters are selected to minimize the difference between the simulated and experimentally measured α textures after accounting for the β → α transformation upon cooling. It is demonstrated that both methods result in good qualitative matches for the experimental α phase texture, but texture-based optimization results in a substantially better quantitative orientation distribution function match.

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

Distribution of age at menopause in two Danish samples

DEFF Research Database (Denmark)

Boldsen, J L; Jeune, B

1990-01-01

We analyzed the distribution of reported age at natural menopause in two random samples of Danish women (n = 176 and n = 150) to determine the shape of the distribution and to disclose any possible trends in the distribution parameters. It was necessary to correct the frequencies of the reported...... ages for the effect of differing ages at reporting. The corrected distribution of age at menopause differs from the normal distribution in the same way in both samples. Both distributions could be described by a mixture of two normal distributions. It appears that most of the parameters of the normal...... distribution mixtures remain unchanged over a 50-year time lag. The position of the distribution, that is, the mean age at menopause, however, increases slightly but significantly....

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 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

On the distribution of plasma parameters in RF glow discharge

International Nuclear Information System (INIS)

Ning Cheng; Liu Zuli; Liu Donghui; Han Caiyuan.

1993-01-01

A self-consistent numerical model based on the two-fluid equations for describing the transport of charged particles in the RF glow discharge is presented. For a plasma generator filled with low-pressure air and parallel-plate electrodes, the model is numerical solved. The space-time distribution of parameters and the spatial distribution of some time-averaged parameters in plasma, which show the physical picture of the RF glow discharge, are obtained

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 ...

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.

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...

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

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

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)

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 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.

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-parameter

A hybrid optimization approach to the estimation of distributed parameters in two-dimensional confined aquifers

Science.gov (United States)

Heidari, M.; Ranjithan, S.R.

1998-01-01

In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is experimentally demonstrated that only one piece of prior information of the least sensitive parameter is sufficient to arrive at the global or near-global optimum solution. For hydraulic head data with measurement errors, the error in the estimation of parameters increases as the standard deviation of the errors increases. Results from our experiments show that, in general, the accuracy of the estimated parameters depends on the level of noise in the hydraulic head data and the initial values used in the truncated-Newton search technique.In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is

Measurements of local two-phase flow parameters in a boiling flow channel

International Nuclear Information System (INIS)

Yun, Byong Jo; Park, Goon-CherI; Chung, Moon Ki; Song, Chul Hwa

1998-01-01

Local two-phase flow parameters were measured lo investigate the internal flow structures of steam-water boiling flow in an annulus channel. Two kinds of measuring methods for local two-phase flow parameters were investigated. These are a two-conductivity probe for local vapor parameters and a Pitot cube for local liquid parameters. Using these probes, the local distribution of phasic velocities, interfacial area concentration (IAC) and void fraction is measured. In this study, the maximum local void fraction in subcooled boiling condition is observed around the heating rod and the local void fraction is smoothly decreased from the surface of a heating rod to the channel center without any wall void peaking, which was observed in air-water experiments. The distributions of local IAC and bubble frequency coincide with those of local void fraction for a given area-averaged void fraction. (author)

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

Directory of Open Access Journals (Sweden)

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.

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

Directory of Open Access Journals (Sweden)

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.

An empirical multivariate log-normal distribution representing uncertainty of biokinetic parameters for 137Cs

International Nuclear Information System (INIS)

Miller, G.; Martz, H.; Bertelli, L.; Melo, D.

2008-01-01

A simplified biokinetic model for 137 Cs has six parameters representing transfer of material to and from various compartments. Using a Bayesian analysis, the joint probability distribution of these six parameters is determined empirically for two cases with quite a lot of bioassay data. The distribution is found to be a multivariate log-normal. Correlations between different parameters are obtained. The method utilises a fairly large number of pre-determined forward biokinetic calculations, whose results are stored in interpolation tables. Four different methods to sample the multidimensional parameter space with a limited number of samples are investigated: random, stratified, Latin Hypercube sampling with a uniform distribution of parameters and importance sampling using a lognormal distribution that approximates the posterior distribution. The importance sampling method gives much smaller sampling uncertainty. No sampling method-dependent differences are perceptible for the uniform distribution methods. (authors)

Wind Resource Assessment in Abadan Airport in Iran

Directory of Open Access Journals (Sweden)

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

Statistical distributions applications and parameter estimates

CERN Document Server

Thomopoulos, Nick T

2017-01-01

This book gives a description of the group of statistical distributions that have ample application to studies in statistics and probability.  Understanding statistical distributions is fundamental for researchers in almost all disciplines.  The informed researcher will select the statistical distribution that best fits the data in the study at hand.  Some of the distributions are well known to the general researcher and are in use in a wide variety of ways.  Other useful distributions are less understood and are not in common use.  The book describes when and how to apply each of the distributions in research studies, with a goal to identify the distribution that best applies to the study.  The distributions are for continuous, discrete, and bivariate random variables.  In most studies, the parameter values are not known a priori, and sample data is needed to estimate parameter values.  In other scenarios, no sample data is available, and the researcher seeks some insight that allows the estimate of ...

An investigation on effect of geometrical parameters on spray cone angle and droplet size distribution of a two-fluid atomizer

Energy Technology Data Exchange (ETDEWEB)

Shafaee, Maziar; Banitabaei, Sayed Abdolhossein; Esfahanian, Vahid; Ashjaee, Mehdi [Tehran University, Tehran (Iran, Islamic Republic of)

2011-12-15

A visual study is conducted to determine the effect of geometrical parameters of a two-fluid atomizer on its spray cone angle. The liquid (water) jets exit from six peripheral inclined orifices and are introduced to a high speed gas (air) stream in the gravitational direction. Using a high speed imaging system, the spray cone angle has been determined in constant operational conditions, i.e., Reynolds and Weber numbers for different nozzle geometries. Also, the droplet sizes (Sauter mean diameter) and their distributions have been determined using Malvern Master Sizer x. The investigated geometrical parameters are the liquid jet diameter, liquid port angle and the length of the gas-liquid mixing chamber. The results show that among these parameters, the liquid jet diameter has a significant effect on spray cone angle. In addition, an empirical correlation has been obtained to predict the spray cone angle of the present two-fluid atomizer in terms of nozzle geometries.

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

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.

Parameter Estimation of Nonlinear Models in Forestry.

OpenAIRE

Fekedulegn, Desta; Mac Siúrtáin, Máirtín Pádraig; Colbert, Jim J.

1999-01-01

Partial derivatives of the negative exponential, monomolecular, Mitcherlich, Gompertz, logistic, Chapman-Richards, von Bertalanffy, Weibull and the Richard’s nonlinear growth models are presented. The application of these partial derivatives in estimating the model parameters is illustrated. The parameters are estimated using the Marquardt iterative method of nonlinear regression relating top height to age of Norway spruce (Picea abies L.) from the Bowmont Norway Spruce Thinnin...

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Directory of Open Access Journals (Sweden)

Chi Zhang

2015-05-01

Full Text Available To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP distributions by incorporating a multiplicative factor (or dependency parameter λ, named as Type I and Type II bivariate ZIGP distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit either positively or negatively correlated and either over- or under-dispersed count data, comparing to the existing models that can only fit positively correlated count data with over-dispersion. The two marginal distributions of Type I bivariate ZIGP share a common parameter of zero inflation while the two marginal distributions of Type II bivariate ZIGP have their own parameters of zero inflation, resulting in a much wider range of applications. The important distributional properties are explored and some useful statistical inference methods including maximum likelihood estimations of parameters, standard errors estimation, bootstrap confidence intervals and related testing hypotheses are developed for the two distributions. A real data are thoroughly analyzed by using the proposed distributions and statistical methods. Several simulation studies are conducted to evaluate the performance of the proposed methods.

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.

Parameter estimation of the zero inflated negative binomial beta exponential distribution

Science.gov (United States)

Sirichantra, Chutima; Bodhisuwan, Winai

2017-11-01

The zero inflated negative binomial-beta exponential (ZINB-BE) distribution is developed, it is an alternative distribution for the excessive zero counts with overdispersion. The ZINB-BE distribution is a mixture of two distributions which are Bernoulli and negative binomial-beta exponential distributions. In this work, some characteristics of the proposed distribution are presented, such as, mean and variance. The maximum likelihood estimation is applied to parameter estimation of the proposed distribution. Finally some results of Monte Carlo simulation study, it seems to have high-efficiency when the sample size is large.

Errors in determination of irregularity factor for distributed parameters in a reactor core

International Nuclear Information System (INIS)

Vlasov, V.A.; Zajtsev, M.P.; Il'ina, L.I.; Postnikov, V.V.

1988-01-01

Two types errors (measurement error and error of regulation of reactor core distributed parameters), offen met during high-power density reactor operation, are analyzed. Consideration is given to errors in determination of irregularity factor for radial power distribution for a hot channel under conditions of its minimization and for the conditions when the regulation of relative power distribution is absent. The first regime is investigated by the method of statistic experiment using the program of neutron-physical calculation optimization taking as an example a large channel water cooled graphite moderated reactor. It is concluded that it is necessary, to take into account the complex interaction of measurement error with the error of parameter profiling over the core both for conditions of continuous manual or automatic parameter regulation (optimization) and for the conditions without regulation namely at a priore equalized distribution. When evaluating the error of distributed parameter control

Five and four-parameter lifetime distributions for bathtub-shaped failure rate using Perks mortality equation

International Nuclear Information System (INIS)

Zeng, Hongtao; Lan, Tian; Chen, Qiming

2016-01-01

Two lifetime distributions derived from Perks' mortality rate function, one with 4 parameters and the other with 5 parameters, for the modeling of bathtub-shaped failure rates are proposed in this paper. The Perks' mortality/failure rate functions have historically been used for human life modeling in life insurance industry. Although this distribution is no longer used in insurance industry, considering many nice and some unique features of this function, it is necessary to revisit it and introduce it to the reliability community. The parameters of the distributions can control the scale, shape, and location of the PDF. The 4-parameter distribution can be used to model the bathtub failure rate. This model is applied to three previously published groups of lifetime data. This study shows they fit very well. The 5-parameter version can potentially model constant hazard rates of the later life of some devices in addition to the good features of 4-parameter version. Both the 4 and 5-parameter versions have closed form PDF and CDF. The truncated distributions of both versions stay within the original distribution family with simple parameter transformation. This nice feature is normally considered to be only possessed by the simple exponential distribution - Highlights: • Two new distributions are proposed to model bathtub shaped hazard rate. • Derive the close-form PDF, CDF and feature of scalability and truncatability. • Perks4 is verified to be good to model common bathtub shapes through comparison. • Perks5 has the potential to model the stabilization of hazard rate at later life.

Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

Science.gov (United States)

Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.

2018-05-01

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

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)

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.

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....

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.

Two-parameter fracture mechanics: Theory and applications

International Nuclear Information System (INIS)

O'Dowd, N.P.; Shih, C.F.

1993-02-01

A family of self-similar fields provides the two parameters required to characterize the full range of high- and low-triaxiality crack tip states. The two parameters, J and Q, have distinct roles: J sets the size scale of the process zone over which large stresses and strains develop, while Q scales the near-tip stress distribution relative to a high triaxiality reference stress state. An immediate consequence of the theory is this: it is the toughness values over a range of crack tip constraint that fully characterize the material's fracture resistance. It is shown that Q provides a common scale for interpreting cleavage fracture and ductile tearing data thus allowing both failure modes to be incorporated in a single toughness locus. The evolution of Q, as plasticity progresses from small scale yielding to fully yielded conditions, has been quantified for several crack geometries and for a wide range of material strain hardening properties. An indicator of the robustness of the J-Q fields is introduced; Q as a field parameter and as a pointwise measure of stress level is discussed

Effects of two-temperature parameter and thermal nonlocal parameter on transient responses of a half-space subjected to ramp-type heating

Science.gov (United States)

Xue, Zhang-Na; Yu, Ya-Jun; Tian, Xiao-Geng

2017-07-01

Based upon the coupled thermoelasticity and Green and Lindsay theory, the new governing equations of two-temperature thermoelastic theory with thermal nonlocal parameter is formulated. To more realistically model thermal loading of a half-space surface, a linear temperature ramping function is adopted. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Specific attention is paid to study the effect of thermal nonlocal parameter, ramping time, and two-temperature parameter on the distributions of temperature, displacement and stress distribution.

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.

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

Micromachined two dimensional resistor arrays for determination of gas parameters

NARCIS (Netherlands)

van Baar, J.J.J.; Verwey, Willem B.; Dijkstra, Mindert; Dijkstra, Marcel; Wiegerink, Remco J.; Lammerink, Theodorus S.J.; Krijnen, Gijsbertus J.M.; Elwenspoek, Michael Curt

A resistive sensor array is presented for two dimensional temperature distribution measurements in a micromachined flow channel. This allows simultaneous measurement of flow velocity and fluid parameters, like thermal conductivity, diffusion coefficient and viscosity. More general advantages of

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

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

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

Directory of Open Access Journals (Sweden)

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.

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

PARAMETER ESTIMATION OF THE HYBRID CENSORED LOMAX DISTRIBUTION

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Samir Kamel Ashour

2010-12-01

Full Text Available Survival analysis is used in various fields for analyzing data involving the duration between two events. It is also known as event history analysis, lifetime data analysis, reliability analysis or time to event analysis. One of the difficulties which arise in this area is the presence of censored data. The lifetime of an individual is censored when it cannot be exactly measured but partial information is available. Different circumstances can produce different types of censoring. The two most common censoring schemes used in life testing experiments are Type-I and Type-II censoring schemes. Hybrid censoring scheme is mixture of Type-I and Type-II censoring scheme. In this paper we consider the estimation of parameters of Lomax distribution based on hybrid censored data. The parameters are estimated by the maximum likelihood and Bayesian methods. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals.

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)

Experimental study on two-phase flow parameters of subcooled boiling in inclined annulus

International Nuclear Information System (INIS)

Lee, Tae Ho; Kim, Moon Oh; Park, Goon Cherl

1999-01-01

Local two-phase flow parameters of subcooled flow boiling in inclined annulus were measured to investigate the effect of inclination on the internal flow structure. Two-conductivity probe technique was applied to measured local gas phasic parameters, including void by fraction, vapor bubble frequency, chord length, vapor bubble velocity and interfacial area concentration. Local liquid velocity was measured by Pitot tube. Experiments were conducted for three angles of inclination: 0 o (vertical), 30 o , 60 o . The system pressure was maintained at atmospheric pressure. The range of average void fraction was up to 10 percent and the average liquid superficial velocities were less than 1.3 m/sec. The results of experiments showed that the distributions of two-phase flow parameters were influenced by the angle of channel inclination. Especially, the void fraction and chord length distributions were strongly affected by the increase of inclination angle, and flow pattern transition to slug flow was observed depending on the flow conditions. The profiles of vapor velocity, liquid velocity and interfacial area concentration were found to be affected by the non-symmetric bubble size distribution in inclined channel. Using the measured distributions of local phasic parameters, an analysis for predicting average void fraction was performed based on the drift flux model and flowing volumetric concentration. And it was demonstrated that the average void fraction can be more appropriately presented in terms of flowing volumetric concentration. (Author). 18 refs., 2 tabs., 18 figs

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

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)

Application of extreme value distribution function in the determination of standard meteorological parameters for nuclear power plants

International Nuclear Information System (INIS)

Jiang Haimei; Liu Xinjian; Qiu Lin; Li Fengju

2014-01-01

Based on the meteorological data from weather stations around several domestic nuclear power plants, the statistical results of extreme minimum temperatures, minimum. central pressures of tropical cyclones and some other parameters are calculated using extreme value I distribution function (EV- I), generalized extreme value distribution function (GEV) and generalized Pareto distribution function (GP), respectively. The influence of different distribution functions and parameter solution methods on the statistical results of extreme values is investigated. Results indicate that generalized extreme value function has better applicability than the other two distribution functions in the determination of standard meteorological parameters for nuclear power plants. (authors)

Solliton-like order parameter distributions in the critical region

Directory of Open Access Journals (Sweden)

A.V.Babich

2006-01-01

Full Text Available Some exact one-component order parameter distributions for the Michelson thermodynamic potential are obtained. The phase transition of second kind in Ginzburg-Landau type model is investigated. The exact partial distribution of the order parameter in the form of Jakobi elliptic function is obtained. The energy of this distribution is lower at some temperature interval than for the best known models.

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.

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

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.

Ensemble distribution for immiscible two-phase flow in porous media.

Science.gov (United States)

Savani, Isha; Bedeaux, Dick; Kjelstrup, Signe; Vassvik, Morten; Sinha, Santanu; Hansen, Alex

2017-02-01

We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In particular, we find an expression for the overall mobility of the system from the ensemble distribution. The entropy production at the scale of the porous medium is shown to give the expected product of the average flow and its driving force, obtained from a black-box description. We test numerically some of the central theoretical results.

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

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.

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.

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.

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

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.

A Study of Transmission Control Method for Distributed Parameters Measurement in Large Factories and Storehouses

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Shujing Su

2015-01-01

Full Text Available For the characteristics of parameters dispersion in large factories, storehouses, and other applications, a distributed parameter measurement system is designed that is based on the ring network. The structure of the system and the circuit design of the master-slave node are described briefly. The basic protocol architecture about transmission communication is introduced, and then this paper comes up with two kinds of distributed transmission control methods. Finally, the reliability, extendibility, and control characteristic of these two methods are tested through a series of experiments. Moreover, the measurement results are compared and discussed.

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.

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

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

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

function more suitable for wind distribution is the density function of Weibull, which can be determined by numerical methods and linear regression. The objective of this study is to characterize analytically and geometrically all methodological procedures necessary to carry out a full characterization of the wind regime of a region and its applications in Botucatu-SP to determine the energy potential for implementation of wind turbines. Thus it was possible to make statements of theorems related to how to characterize the wind regime, establishing a concise analytical methodology for defining the wind parameters of any region to be studied. For the development of this research, it was used a CAMPBELL anemometer.

Investigating the Impact of Item Parameter Drift for Item Response Theory Models with Mixture Distributions

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Yoon Soo ePark

2016-02-01

Full Text Available This study investigates the impact of item parameter drift (IPD on parameter and ability estimation when the underlying measurement model fits a mixture distribution, thereby violating the item invariance property of unidimensional item response theory (IRT models. An empirical study was conducted to demonstrate the occurrence of both IPD and an underlying mixture distribution using real-world data. Twenty-one trended anchor items from the 1999, 2003, and 2007 administrations of Trends in International Mathematics and Science Study (TIMSS were analyzed using unidimensional and mixture IRT models. TIMSS treats trended anchor items as invariant over testing administrations and uses pre-calibrated item parameters based on unidimensional IRT. However, empirical results showed evidence of two latent subgroups with IPD. Results showed changes in the distribution of examinee ability between latent classes over the three administrations. A simulation study was conducted to examine the impact of IPD on the estimation of ability and item parameters, when data have underlying mixture distributions. Simulations used data generated from a mixture IRT model and estimated using unidimensional IRT. Results showed that data reflecting IPD using mixture IRT model led to IPD in the unidimensional IRT model. Changes in the distribution of examinee ability also affected item parameters. Moreover, drift with respect to item discrimination and distribution of examinee ability affected estimates of examinee ability. These findings demonstrate the need to caution and evaluate IPD using a mixture IRT framework to understand its effect on item parameters and examinee ability.

Investigating the Impact of Item Parameter Drift for Item Response Theory Models with Mixture Distributions.

Science.gov (United States)

Park, Yoon Soo; Lee, Young-Sun; Xing, Kuan

2016-01-01

This study investigates the impact of item parameter drift (IPD) on parameter and ability estimation when the underlying measurement model fits a mixture distribution, thereby violating the item invariance property of unidimensional item response theory (IRT) models. An empirical study was conducted to demonstrate the occurrence of both IPD and an underlying mixture distribution using real-world data. Twenty-one trended anchor items from the 1999, 2003, and 2007 administrations of Trends in International Mathematics and Science Study (TIMSS) were analyzed using unidimensional and mixture IRT models. TIMSS treats trended anchor items as invariant over testing administrations and uses pre-calibrated item parameters based on unidimensional IRT. However, empirical results showed evidence of two latent subgroups with IPD. Results also showed changes in the distribution of examinee ability between latent classes over the three administrations. A simulation study was conducted to examine the impact of IPD on the estimation of ability and item parameters, when data have underlying mixture distributions. Simulations used data generated from a mixture IRT model and estimated using unidimensional IRT. Results showed that data reflecting IPD using mixture IRT model led to IPD in the unidimensional IRT model. Changes in the distribution of examinee ability also affected item parameters. Moreover, drift with respect to item discrimination and distribution of examinee ability affected estimates of examinee ability. These findings demonstrate the need to caution and evaluate IPD using a mixture IRT framework to understand its effects on item parameters and examinee ability.

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 ...

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

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.

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.

Reservoir theory, groundwater transit time distributions, and lumped parameter models

International Nuclear Information System (INIS)

Etcheverry, D.; Perrochet, P.

1999-01-01

The relation between groundwater residence times and transit times is given by the reservoir theory. It allows to calculate theoretical transit time distributions in a deterministic way, analytically, or on numerical models. Two analytical solutions validates the piston flow and the exponential model for simple conceptual flow systems. A numerical solution of a hypothetical regional groundwater flow shows that lumped parameter models could be applied in some cases to large-scale, heterogeneous aquifers. (author)

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

Control of complex dynamics and chaos in distributed parameter systems

Energy Technology Data Exchange (ETDEWEB)

Chakravarti, S.; Marek, M.; Ray, W.H. [Univ. of Wisconsin, Madison, WI (United States)

1995-12-31

This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in the complex quasi-periodic or chaotic spatiotemporal patterns.

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

Modified distribution parameter for churn-turbulent flows in large diameter channels

Energy Technology Data Exchange (ETDEWEB)

Schlegel, J.P., E-mail: jschlege@purdue.edu; Macke, C.J.; Hibiki, T.; Ishii, M.

2013-10-15

Highlights: • Void fraction data collected in pipe sizes up to 0.304 m using impedance void meters. • Flow conditions extend to transition between churn-turbulent and annular flow. • Flow regime identification results agree with previous studies. • A new model for the distribution parameter in churn-turbulent flow is proposed. -- Abstract: Two phase flows in large diameter channels are important in a wide range of industrial applications, but especially in analysis of nuclear reactor safety for the prediction of BWR behavior and safety analysis in PWRs. To remedy an inability of current drift-flux models to accurately predict the void fraction in churn-turbulent flows in large diameter pipes, extensive experiments have been performed in pipes with diameters of 0.152 m, 0.203 m and 0.304 m to collect area-averaged void fraction data using electrical impedance void meters. The standard deviation and skewness of the impedance meter signal have been used to characterize the flow regime and confirm previous flow regime transition results. By treating churn-turbulent flow as a transition between cap-bubbly dispersed flow and annular separated flow and using a linear ramp, the distribution parameter has been modified for churn-turbulent flow. The modified distribution parameter has been evaluated through comparison of the void fraction predicted by the drift-flux model and the measured void fraction.

Modified distribution parameter for churn-turbulent flows in large diameter channels

International Nuclear Information System (INIS)

Schlegel, J.P.; Macke, C.J.; Hibiki, T.; Ishii, M.

2013-01-01

Highlights: • Void fraction data collected in pipe sizes up to 0.304 m using impedance void meters. • Flow conditions extend to transition between churn-turbulent and annular flow. • Flow regime identification results agree with previous studies. • A new model for the distribution parameter in churn-turbulent flow is proposed. -- Abstract: Two phase flows in large diameter channels are important in a wide range of industrial applications, but especially in analysis of nuclear reactor safety for the prediction of BWR behavior and safety analysis in PWRs. To remedy an inability of current drift-flux models to accurately predict the void fraction in churn-turbulent flows in large diameter pipes, extensive experiments have been performed in pipes with diameters of 0.152 m, 0.203 m and 0.304 m to collect area-averaged void fraction data using electrical impedance void meters. The standard deviation and skewness of the impedance meter signal have been used to characterize the flow regime and confirm previous flow regime transition results. By treating churn-turbulent flow as a transition between cap-bubbly dispersed flow and annular separated flow and using a linear ramp, the distribution parameter has been modified for churn-turbulent flow. The modified distribution parameter has been evaluated through comparison of the void fraction predicted by the drift-flux model and the measured void fraction

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.   

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

Full Two-Body Problem Mass Parameter Observability Explored Through Doubly Synchronous Systems

Science.gov (United States)

Davis, Alex Benjamin; Scheeres, Daniel

2018-04-01

The full two-body problem (F2BP) is often used to model binary asteroid systems, representing the bodies as two finite mass distributions whose dynamics are influenced by their mutual gravity potential. The emergent behavior of the F2BP is highly coupled translational and rotational mutual motion of the mass distributions. For these systems the doubly synchronous equilibrium occurs when both bodies are tidally-locked and in a circular co-orbit. Stable oscillations about this equilibrium can be shown, for the nonplanar system, to be combinations of seven fundamental frequencies of the system and the mutual orbit rate. The fundamental frequencies arise as the linear periods of center manifolds identified about the equilibrium which are heavily influenced by each body’s mass parameters. We leverage these eight dynamical constraints to investigate the observability of binary asteroid mass parameters via dynamical observations. This is accomplished by proving the nonsingularity of the relationship between the frequencies and mass parameters for doubly synchronous systems. Thus we can invert the relationship to show that given observations of the frequencies, we can solve for the mass parameters of a target system. In so doing we are able to predict the estimation covariance of the mass parameters based on observation quality and define necessary observation accuracies for desired mass parameter certainties. We apply these tools to 617 Patroclus, a doubly synchronous Trojan binary and flyby target of the LUCY mission, as well as the Pluto and Charon system in order to predict mutual behaviors of these doubly synchronous systems and to provide observational requirements for these systems’ mass parameters

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

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

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

A distributed approach for parameters estimation in System Biology models

International Nuclear Information System (INIS)

Mosca, E.; Merelli, I.; Alfieri, R.; Milanesi, L.

2009-01-01

Due to the lack of experimental measurements, biological variability and experimental errors, the value of many parameters of the systems biology mathematical models is yet unknown or uncertain. A possible computational solution is the parameter estimation, that is the identification of the parameter values that determine the best model fitting respect to experimental data. We have developed an environment to distribute each run of the parameter estimation algorithm on a different computational resource. The key feature of the implementation is a relational database that allows the user to swap the candidate solutions among the working nodes during the computations. The comparison of the distributed implementation with the parallel one showed that the presented approach enables a faster and better parameter estimation of systems biology models.

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.

A two-population sporadic meteoroid bulk density distribution and its implications for environment models

Science.gov (United States)

Moorhead, Althea V.; Blaauw, Rhiannon C.; Moser, Danielle E.; Campbell-Brown, Margaret D.; Brown, Peter G.; Cooke, William J.

2017-12-01

The bulk density of a meteoroid affects its dynamics in space, its ablation in the atmosphere, and the damage it does to spacecraft and lunar or planetary surfaces. Meteoroid bulk densities are also notoriously difficult to measure, and we are typically forced to assume a density or attempt to measure it via a proxy. In this paper, we construct a density distribution for sporadic meteoroids based on existing density measurements. We considered two possible proxies for density: the KB parameter introduced by Ceplecha and Tisserand parameter, TJ. Although KB is frequently cited as a proxy for meteoroid material properties, we find that it is poorly correlated with ablation-model-derived densities. We therefore follow the example of Kikwaya et al. in associating density with the Tisserand parameter. We fit two density distributions to meteoroids originating from Halley-type comets (TJ 2); the resulting two-population density distribution is the most detailed sporadic meteoroid density distribution justified by the available data. Finally, we discuss the implications for meteoroid environment models and spacecraft risk assessments. We find that correcting for density increases the fraction of meteoroid-induced spacecraft damage produced by the helion/antihelion source.

Boundary feedback stabilization of distributed parameter systems

DEFF Research Database (Denmark)

Pedersen, Michael

1988-01-01

The author introduces the method of pseudo-differential stabilization. He notes that the theory of pseudo-differential boundary operators is a fruitful approach to problems arising in control and stabilization theory of distributed-parameter systems. The basic pseudo-differential calculus can...

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)

Mathematical Model to estimate the wind power using four-parameter Burr distribution

Science.gov (United States)

Liu, Sanming; Wang, Zhijie; Pan, Zhaoxu

2018-03-01

When the real probability of wind speed in the same position needs to be described, the four-parameter Burr distribution is more suitable than other distributions. This paper introduces its important properties and characteristics. Also, the application of the four-parameter Burr distribution in wind speed prediction is discussed, and the expression of probability distribution of output power of wind turbine is deduced.

Estimation of the shape parameter of a generalized Pareto distribution based on a transformation to Pareto distributed variables

OpenAIRE

van Zyl, J. Martin

2012-01-01

Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance of the estimation of the shape parameter of generalized Pareto distributed using transformed observations, based on the probability weighted method is tested. It was found to improve the performance of the probability weighted estimator and performs good wit...

Multivariate phase type distributions - Applications and parameter estimation

DEFF Research Database (Denmark)

Meisch, David

The best known univariate probability distribution is the normal distribution. It is used throughout the literature in a broad field of applications. In cases where it is not sensible to use the normal distribution alternative distributions are at hand and well understood, many of these belonging...... and statistical inference, is the multivariate normal distribution. Unfortunately only little is known about the general class of multivariate phase type distribution. Considering the results concerning parameter estimation and inference theory of univariate phase type distributions, the class of multivariate...... projects and depend on reliable cost estimates. The Successive Principle is a group analysis method primarily used for analyzing medium to large projects in relation to cost or duration. We believe that the mathematical modeling used in the Successive Principle can be improved. We suggested a novel...

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.

Spatio-temporal modeling of nonlinear distributed parameter systems

CERN Document Server

Li, Han-Xiong

2011-01-01

The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein s

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

Science.gov (United States)

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

Distribution Development for STORM Ingestion Input Parameters

Energy Technology Data Exchange (ETDEWEB)

Fulton, John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-07-01

The Sandia-developed Transport of Radioactive Materials (STORM) code suite is used as part of the Radioisotope Power System Launch Safety (RPSLS) program to perform statistical modeling of the consequences due to release of radioactive material given a launch accident. As part of this modeling, STORM samples input parameters from probability distributions with some parameters treated as constants. This report described the work done to convert four of these constant inputs (Consumption Rate, Average Crop Yield, Cropland to Landuse Database Ratio, and Crop Uptake Factor) to sampled values. Consumption rate changed from a constant value of 557.68 kg / yr to a normal distribution with a mean of 102.96 kg / yr and a standard deviation of 2.65 kg / yr. Meanwhile, Average Crop Yield changed from a constant value of 3.783 kg edible / m ² to a normal distribution with a mean of 3.23 kg edible / m ² and a standard deviation of 0.442 kg edible / m ² . The Cropland to Landuse Database ratio changed from a constant value of 0.0996 (9.96%) to a normal distribution with a mean value of 0.0312 (3.12%) and a standard deviation of 0.00292 (0.29%). Finally the crop uptake factor changed from a constant value of 6.37e^-4 (Bq crop /kg)/(Bq soil /kg) to a lognormal distribution with a geometric mean value of 3.38e^-4 (Bq crop /kg)/(Bq soil /kg) and a standard deviation value of 3.33 (Bq crop /kg)/(Bq soil /kg)

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

Modified Moment, Maximum Likelihood and Percentile Estimators for the Parameters of the Power Function Distribution

Directory of Open Access Journals (Sweden)

Azam Zaka

2014-10-01

Full Text Available This paper is concerned with the modifications of maximum likelihood, moments and percentile estimators of the two parameter Power function distribution. Sampling behavior of the estimators is indicated by Monte Carlo simulation. For some combinations of parameter values, some of the modified estimators appear better than the traditional maximum likelihood, moments and percentile estimators with respect to bias, mean square error and total deviation.

Constraining model parameters on remotely sensed evaporation: justification for distribution in ungauged basins?

Directory of Open Access Journals (Sweden)

H. C. Winsemius

2008-12-01

Full Text Available In this study, land surface related parameter distributions of a conceptual semi-distributed hydrological model are constrained by employing time series of satellite-based evaporation estimates during the dry season as explanatory information. The approach has been applied to the ungauged Luangwa river basin (150 000 (km² in Zambia. The information contained in these evaporation estimates imposes compliance of the model with the largest outgoing water balance term, evaporation, and a spatially and temporally realistic depletion of soil moisture within the dry season. The model results in turn provide a better understanding of the information density of remotely sensed evaporation. Model parameters to which evaporation is sensitive, have been spatially distributed on the basis of dominant land cover characteristics. Consequently, their values were conditioned by means of Monte-Carlo sampling and evaluation on satellite evaporation estimates. The results show that behavioural parameter sets for model units with similar land cover are indeed clustered. The clustering reveals hydrologically meaningful signatures in the parameter response surface: wetland-dominated areas (also called dambos show optimal parameter ranges that reflect vegetation with a relatively small unsaturated zone (due to the shallow rooting depth of the vegetation which is easily moisture stressed. The forested areas and highlands show parameter ranges that indicate a much deeper root zone which is more drought resistent. Clustering was consequently used to formulate fuzzy membership functions that can be used to constrain parameter realizations in further calibration. Unrealistic parameter ranges, found for instance in the high unsaturated soil zone values in the highlands may indicate either overestimation of satellite-based evaporation or model structural deficiencies. We believe that in these areas, groundwater uptake into the root zone and lateral movement of

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

Directory of Open Access Journals (Sweden)

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.

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

Measurement of void fraction and bubble size distribution in two-phase flow system

International Nuclear Information System (INIS)

Huahun, G.

1987-01-01

The importance of study two phase flow parameter and microstructure has appeared increasingly, with the development of two-phase flow discipline. In the paper, the measurement methods of several important microstructure parameter in a two phase flow vertical channel have been studied. Using conductance probe the two phase flow pattern and the average void fraction have been measured previously by the authors. This paper concerns microstructure of the bubble size distribution and local void fraction. The authors studied the methods of measuring bubble velocity, size distribution and local void fraction using double conductance probes and a set of apparatus. Based on our experiments and Yoshihiro work, a formula of calculated local void fraction has been deduced by using the statistical characteristics of bubbles in two phase flow and the relation between calculated bubble size and voltage has been determined. Finally the authors checked by using photograph and fast valve, which is classical but reliable. The results are the same with what has been studied before

Regional probability distribution of the annual reference evapotranspiration and its effective parameters in Iran

Science.gov (United States)

Khanmohammadi, Neda; Rezaie, Hossein; Montaseri, Majid; Behmanesh, Javad

2017-10-01

The reference evapotranspiration (ET0) plays an important role in water management plans in arid or semi-arid countries such as Iran. For this reason, the regional analysis of this parameter is important. But, ET0 process is affected by several meteorological parameters such as wind speed, solar radiation, temperature and relative humidity. Therefore, the effect of distribution type of effective meteorological variables on ET0 distribution was analyzed. For this purpose, the regional probability distribution of the annual ET0 and its effective parameters were selected. Used data in this research was recorded data at 30 synoptic stations of Iran during 1960-2014. Using the probability plot correlation coefficient (PPCC) test and the L-moment method, five common distributions were compared and the best distribution was selected. The results of PPCC test and L-moment diagram indicated that the Pearson type III distribution was the best probability distribution for fitting annual ET0 and its four effective parameters. The results of RMSE showed that the ability of the PPCC test and L-moment method for regional analysis of reference evapotranspiration and its effective parameters was similar. The results also showed that the distribution type of the parameters which affected ET0 values can affect the distribution of reference evapotranspiration.

Adaptive distributed parameter and input estimation in linear parabolic PDEs

KAUST Repository

Mechhoud, Sarra

2016-01-01

In this paper, we discuss the on-line estimation of distributed source term, diffusion, and reaction coefficients of a linear parabolic partial differential equation using both distributed and interior-point measurements. First, new sufficient identifiability conditions of the input and the parameter simultaneous estimation are stated. Then, by means of Lyapunov-based design, an adaptive estimator is derived in the infinite-dimensional framework. It consists of a state observer and gradient-based parameter and input adaptation laws. The parameter convergence depends on the plant signal richness assumption, whereas the state convergence is established using a Lyapunov approach. The results of the paper are illustrated by simulation on tokamak plasma heat transport model using simulated data.

Reliability parameters of distribution networks components

Energy Technology Data Exchange (ETDEWEB)

Gono, R.; Kratky, M.; Rusek, S.; Kral, V. [Technical Univ. of Ostrava (Czech Republic)

2009-03-11

This paper presented a framework for the retrieval of parameters from various heterogenous power system databases. The framework was designed to transform the heterogenous outage data in a common relational scheme. The framework was used to retrieve outage data parameters from the Czech and Slovak republics in order to demonstrate the scalability of the framework. A reliability computation of the system was computed in 2 phases representing the retrieval of component reliability parameters and the reliability computation. Reliability rates were determined using component reliability and global reliability indices. Input data for the reliability was retrieved from data on equipment operating under similar conditions, while the probability of failure-free operations was evaluated by determining component status. Anomalies in distribution outage data were described as scheme, attribute, and term differences. Input types consisted of input relations; transformation programs; codebooks; and translation tables. The system was used to successfully retrieve data from 7 distributors in the Czech Republic and Slovak Republic between 2000-2007. The database included 301,555 records. Data were queried using SQL language. 29 refs., 2 tabs., 2 figs.

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.

Off-line tracking of series parameters in distribution systems using AMI data

Energy Technology Data Exchange (ETDEWEB)

Williams, Tess L.; Sun, Yannan; Schneider, Kevin

2016-05-01

Electric distribution systems have historically lacked measurement points, and equipment is often operated to its failure point, resulting in customer outages. The widespread deployment of sensors at the distribution level is enabling observability. This paper presents an off-line parameter value tracking procedure that takes advantage of the increasing number of measurement devices being deployed at the distribution level to estimate changes in series impedance parameter values over time. The tracking of parameter values enables non-diurnal and non-seasonal change to be flagged for investigation. The presented method uses an unbalanced Distribution System State Estimation (DSSE) and a measurement residual-based parameter estimation procedure. Measurement residuals from multiple measurement snapshots are combined in order to increase the effective local redundancy and improve the robustness of the calculations in the presence of measurement noise. Data from devices on the primary distribution system and from customer meters, via an AMI system, form the input data set. Results of simulations on the IEEE 13-Node Test Feeder are presented to illustrate the proposed approach applied to changes in series impedance parameters. A 5% change in series resistance elements can be detected in the presence of 2% measurement error when combining less than 1 day of measurement snapshots into a single estimate.

Determination of probability density functions for parameters in the Munson-Dawson model for creep behavior of salt

International Nuclear Information System (INIS)

Pfeifle, T.W.; Mellegard, K.D.; Munson, D.E.

1992-10-01

The modified Munson-Dawson (M-D) constitutive model that describes the creep behavior of salt will be used in performance assessment calculations to assess compliance of the Waste Isolation Pilot Plant (WIPP) facility with requirements governing the disposal of nuclear waste. One of these standards requires that the uncertainty of future states of the system, material model parameters, and data be addressed in the performance assessment models. This paper presents a method in which measurement uncertainty and the inherent variability of the material are characterized by treating the M-D model parameters as random variables. The random variables can be described by appropriate probability distribution functions which then can be used in Monte Carlo or structural reliability analyses. Estimates of three random variables in the M-D model were obtained by fitting a scalar form of the model to triaxial compression creep data generated from tests of WIPP salt. Candidate probability distribution functions for each of the variables were then fitted to the estimates and their relative goodness-of-fit tested using the Kolmogorov-Smirnov statistic. A sophisticated statistical software package obtained from BMDP Statistical Software, Inc. was used in the M-D model fitting. A separate software package, STATGRAPHICS, was used in fitting the candidate probability distribution functions to estimates of the variables. Skewed distributions, i.e., lognormal and Weibull, were found to be appropriate for the random variables analyzed

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.

A Parameter Communication Optimization Strategy for Distributed Machine Learning in Sensors.

Science.gov (United States)

Zhang, Jilin; Tu, Hangdi; Ren, Yongjian; Wan, Jian; Zhou, Li; Li, Mingwei; Wang, Jue; Yu, Lifeng; Zhao, Chang; Zhang, Lei

2017-09-21

In order to utilize the distributed characteristic of sensors, distributed machine learning has become the mainstream approach, but the different computing capability of sensors and network delays greatly influence the accuracy and the convergence rate of the machine learning model. Our paper describes a reasonable parameter communication optimization strategy to balance the training overhead and the communication overhead. We extend the fault tolerance of iterative-convergent machine learning algorithms and propose the Dynamic Finite Fault Tolerance (DFFT). Based on the DFFT, we implement a parameter communication optimization strategy for distributed machine learning, named Dynamic Synchronous Parallel Strategy (DSP), which uses the performance monitoring model to dynamically adjust the parameter synchronization strategy between worker nodes and the Parameter Server (PS). This strategy makes full use of the computing power of each sensor, ensures the accuracy of the machine learning model, and avoids the situation that the model training is disturbed by any tasks unrelated to the sensors.

Angular anisotropy parameters for sequential two-photon double ionization of helium

International Nuclear Information System (INIS)

Ivanov, I A; Kheifets, A S

2009-01-01

We evaluate photoelectron angular anisotropy /3-parameters for the process of sequential two-photon double electron ionization of helium within the time-independent lowest order perturbation theory (LOPT). Our results indicate that for the photoelectron energies outside the interval (E slow , E fast ), where E slow = ω - IP He + and E fast ω - IP He , there is a considerable deviation from the dipole angular distribution thus indicating the effect of electron correlation.

Reliability Estimation of Parameters of Helical Wind Turbine with Vertical Axis

Directory of Open Access Journals (Sweden)

Adela-Eliza Dumitrascu

2015-01-01

Full Text Available Due to the prolonged use of wind turbines they must be characterized by high reliability. This can be achieved through a rigorous design, appropriate simulation and testing, and proper construction. The reliability prediction and analysis of these systems will lead to identifying the critical components, increasing the operating time, minimizing failure rate, and minimizing maintenance costs. To estimate the produced energy by the wind turbine, an evaluation approach based on the Monte Carlo simulation model is developed which enables us to estimate the probability of minimum and maximum parameters. In our simulation process we used triangular distributions. The analysis of simulation results has been focused on the interpretation of the relative frequency histograms and cumulative distribution curve (ogive diagram, which indicates the probability of obtaining the daily or annual energy output depending on wind speed. The experimental researches consist in estimation of the reliability and unreliability functions and hazard rate of the helical vertical axis wind turbine designed and patented to climatic conditions for Romanian regions. Also, the variation of power produced for different wind speeds, the Weibull distribution of wind probability, and the power generated were determined. The analysis of experimental results indicates that this type of wind turbine is efficient at low wind speed.

Reliability Estimation of Parameters of Helical Wind Turbine with Vertical Axis.

Science.gov (United States)

Dumitrascu, Adela-Eliza; Lepadatescu, Badea; Dumitrascu, Dorin-Ion; Nedelcu, Anisor; Ciobanu, Doina Valentina

2015-01-01

Due to the prolonged use of wind turbines they must be characterized by high reliability. This can be achieved through a rigorous design, appropriate simulation and testing, and proper construction. The reliability prediction and analysis of these systems will lead to identifying the critical components, increasing the operating time, minimizing failure rate, and minimizing maintenance costs. To estimate the produced energy by the wind turbine, an evaluation approach based on the Monte Carlo simulation model is developed which enables us to estimate the probability of minimum and maximum parameters. In our simulation process we used triangular distributions. The analysis of simulation results has been focused on the interpretation of the relative frequency histograms and cumulative distribution curve (ogive diagram), which indicates the probability of obtaining the daily or annual energy output depending on wind speed. The experimental researches consist in estimation of the reliability and unreliability functions and hazard rate of the helical vertical axis wind turbine designed and patented to climatic conditions for Romanian regions. Also, the variation of power produced for different wind speeds, the Weibull distribution of wind probability, and the power generated were determined. The analysis of experimental results indicates that this type of wind turbine is efficient at low wind speed.

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

Binomial Distribution Sample Confidence Intervals Estimation 1. Sampling and Medical Key Parameters Calculation

Directory of Open Access Journals (Sweden)

Tudor DRUGAN

2003-08-01

Full Text Available The aim of the paper was to present the usefulness of the binomial distribution in studying of the contingency tables and the problems of approximation to normality of binomial distribution (the limits, advantages, and disadvantages. The classification of the medical keys parameters reported in medical literature and expressing them using the contingency table units based on their mathematical expressions restrict the discussion of the confidence intervals from 34 parameters to 9 mathematical expressions. The problem of obtaining different information starting with the computed confidence interval for a specified method, information like confidence intervals boundaries, percentages of the experimental errors, the standard deviation of the experimental errors and the deviation relative to significance level was solves through implementation in PHP programming language of original algorithms. The cases of expression, which contain two binomial variables, were separately treated. An original method of computing the confidence interval for the case of two-variable expression was proposed and implemented. The graphical representation of the expression of two binomial variables for which the variation domain of one of the variable depend on the other variable was a real problem because the most of the software used interpolation in graphical representation and the surface maps were quadratic instead of triangular. Based on an original algorithm, a module was implements in PHP in order to represent graphically the triangular surface plots. All the implementation described above was uses in computing the confidence intervals and estimating their performance for binomial distributions sample sizes and variable.

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...

The complete information for phenomenal distributed parameter control of multicomponent chemical processes in gas, fluid and solid phase

International Nuclear Information System (INIS)

Niemiec, W.

1985-01-01

A constitutive mathematical model of distributed parameters of multicomponent chemical processes in gas, fluid and solid phase is utilized to the realization of phenomenal distributed parameter control of these processes. Original systems of partial differential constitutive state equations, in the following derivative forms /I/, /II/ and /III/ are solved in this paper from the point of view of information for phenomenal distributed parameter control of considered processes. Obtained in this way for multicomponent chemical processes in gas, fluid and solid phase: -dynamical working space-time characteristics/analytical solutions in working space-time of chemical reactors/, -dynamical phenomenal Green functions as working space-time transfer functions, -statical working space characteristics /analytical solutions in working space of chemical reactors/, -statical phenomenal Green functions as working space transfer functions, are applied, as information for realization of constitutive distributed parameter control of mass, energy and momentum aspects of above processes. Two cases are considered by existence of: A/sup o/ - initial conditions, B/sup o/ - initial and boundary conditions, for multicomponent chemical processes in gas, fluid and solid phase

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...

Ordering decision-making methods on spare parts for a new aircraft fleet based on a two-sample prediction

International Nuclear Information System (INIS)

Yongquan, Sun; Xi, Chen; He, Ren; Yingchao, Jin; Quanwu, Liu

2016-01-01

Ordering decision-making on spare parts is crucial in maximizing aircraft utilization and minimizing total operating cost. Extensive researches on spare parts inventory management and optimal allocation could be found based on the amount of historical operation data or condition-monitoring data. However, it is challengeable to make an ordering decision on spare parts under the case of establishment of a fleet by introducing new aircraft with little historical data. In this paper, spare parts supporting policy and ordering decision-making policy for new aircraft fleet are analyzed firstly. Then two-sample predictions for a Weibull distribution and a Weibull process are incorporated into forecast of the first failure time and failure number during certain time period using Bayesian and classical method respectively, according to which the ordering time and ordering quantity for spare parts are identified. Finally, a case study is presented to illustrate the methods of identifying the ordering time and ordering number of engine-driven pumps through forecasting the failure time and failure number, followed by a discussion on the impact of various fleet sizes on prediction results. This method has the potential to decide the ordering time and quantity of spare parts when a new aircraft fleet is established. - Highlights: • A modeling framework of ordering spare parts for a new fleet is proposed. • Models for ordering time and number are established based on two-sample prediction. • The computation of future failure time is simplified using Newtonian binomial law. • Comparison of the first failure time PDFs is used to identify process parameters. • Identification methods for spare parts are validated by Engine Driven Pump case study.

Hybrid artificial bee colony algorithm for parameter optimization of five-parameter bidirectional reflectance distribution function model.

Science.gov (United States)

Wang, Qianqian; Zhao, Jing; Gong, Yong; Hao, Qun; Peng, Zhong

2017-11-20

A hybrid artificial bee colony (ABC) algorithm inspired by the best-so-far solution and bacterial chemotaxis was introduced to optimize the parameters of the five-parameter bidirectional reflectance distribution function (BRDF) model. To verify the performance of the hybrid ABC algorithm, we measured BRDF of three kinds of samples and simulated the undetermined parameters of the five-parameter BRDF model using the hybrid ABC algorithm and the genetic algorithm, respectively. The experimental results demonstrate that the hybrid ABC algorithm outperforms the genetic algorithm in convergence speed, accuracy, and time efficiency under the same conditions.

Assessing senescence patterns in populations of large mammals

Directory of Open Access Journals (Sweden)

Gaillard, J.-M.

2004-06-01

Full Text Available Theoretical models such as those of Gompertz and Weibull are commonly used to study senescence in survival for humans and laboratory or captive animals. For wild populations of vertebrates, senescence in survival has more commonly been assessed by fitting simple linear or quadratic relationships between survival and age. By using appropriate constraints on survival parameters in Capture-Mark-Recapture (CMR models, we propose a first analysis of the suitability of the Gompertz and the two-parameter Weibull models for describing aging-related mortality in free-ranging populations of ungulates. We first show how to handle the Gompertz and the two-parameter Weibull models in the context of CMR analyses. Then we perform a comparative analysis of senescence patterns in both sexes of two ungulate species highly contrasted according to the intensity of sexual selection. Our analyses provide support to the Gompertz model for describing senescence patterns in ungulates. Evolutionary implications of our results are discussed

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

Distribution of two-phase flow thermal and hydraulic parameters over the cross-section of channels with a rod bundle

International Nuclear Information System (INIS)

Mironov, Yu.V.; Shpanskij, S.V.

1975-01-01

The paper describes PUCHOK-2, a program for thermohydraulic calculation of a channel with a bundle of smooth fuel elements. The pro.gram takes into consideration the non-uniformity of flow parameter distributions over the channel cross-section. The channel cross-section was divided into elementary cells, within which changes in flow parameters (mass velocity, heat- and steam content) were disregarded. The bundle was considered to be a system of parallel interconnected channels. Accounting for equal pressure drops in all the cells, the above model led to a system of non-linear algebraic equations. The system of equations was solved by the method of successive approximations. Theoretical results were compared with experimental data

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)

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.

Estimation of modal parameters using bilinear joint time frequency distributions

Science.gov (United States)

Roshan-Ghias, A.; Shamsollahi, M. B.; Mobed, M.; Behzad, M.

2007-07-01

In this paper, a new method is proposed for modal parameter estimation using time-frequency representations. Smoothed Pseudo Wigner-Ville distribution which is a member of the Cohen's class distributions is used to decouple vibration modes completely in order to study each mode separately. This distribution reduces cross-terms which are troublesome in Wigner-Ville distribution and retains the resolution as well. The method was applied to highly damped systems, and results were superior to those obtained via other conventional methods.

Geometric effects of 90-degree vertical elbows on local two-phase flow parameters

International Nuclear Information System (INIS)

Yadav, M.; Worosz, T.; Kim, S.

2011-01-01

This study presents the geometric effects of 90-degree vertical elbows on the development of the local two-phase flow parameters. A multi-sensor conductivity probe is used to measure local two-phase flow parameters. It is found that immediately downstream of the vertical-upward elbow, the bubbles have a bimodal distribution along the horizontal radius of the pipe cross-section causing a dual-peak in the profiles of local void fraction and local interfacial area concentration. Immediately downstream of the vertical-downward elbow it is observed that the bubbles tend to migrate towards the inside of the elbow's curvature. The axial transport of void fraction and interfacial area concentration indicates that the elbows promote bubble disintegration. Preliminary predictions are obtained from group-one interfacial area transport equation (IATE) model for vertical-upward and vertical-downward two-phase flow. (author)

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...

DNN-state identification of 2D distributed parameter systems

Science.gov (United States)

Chairez, I.; Fuentes, R.; Poznyak, A.; Poznyak, T.; Escudero, M.; Viana, L.

2012-02-01

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs is proposed. The adaptive laws for weights ensure the 'practical stability' of the DNN-trajectories to the parabolic 2D-PDE states. To verify the qualitative behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.

Experimental investigation on local parameter measurement using optical probes in two-phase flow under rolling condition

International Nuclear Information System (INIS)

Tian Daogui; Sun Licheng; Yan Changqi; Liu Guoqiang

2013-01-01

In order to get more local interfacial information as well as to further comprehend the intrinsic mechanism of two-phase flow under rolling condition, a method was proposed to measure the local parameters by using optical probes under rolling condition in this paper. An experimental investigation of two-phase flow under rolling condition was conducted using the probe fabricated by the authors. It is verified that the probe method is feasible to measure the local parameters in two'-phase flow under rolling condition. The results show that the interfacial parameters distribution near wall region has a distinct periodicity due to the rolling motion. The averaged deviation of the void fraction measured by the probe from that obtained from measured pressure drop is about 8%. (authors)

Identification of systems with distributed parameters

International Nuclear Information System (INIS)

Moret, J.M.

1990-10-01

The problem of finding a model for the dynamical response of a system with distributed parameters based on measured data is addressed. First a mathematical formalism is developed in order to obtain the specific properties of such a system. Then a linear iterative identification algorithm is proposed that includes these properties, and that produces better results than usual non linear minimisation techniques. This algorithm is further improved by an original data decimation that allow to artificially increase the sampling period without losing between sample information. These algorithms are tested with real laboratory data

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.

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.

Ocular biometric parameters among 3-year-old Chinese children: testability, distribution and association with anthropometric parameters

Science.gov (United States)

Huang, Dan; Chen, Xuejuan; Gong, Qi; Yuan, Chaoqun; Ding, Hui; Bai, Jing; Zhu, Hui; Fu, Zhujun; Yu, Rongbin; Liu, Hu

2016-01-01

This survey was conducted to determine the testability, distribution and associations of ocular biometric parameters in Chinese preschool children. Ocular biometric examinations, including the axial length (AL) and corneal radius of curvature (CR), were conducted on 1,688 3-year-old subjects by using an IOLMaster in August 2015. Anthropometric parameters, including height and weight, were measured according to a standardized protocol, and body mass index (BMI) was calculated. The testability was 93.7% for the AL and 78.6% for the CR overall, and both measures improved with age. Girls performed slightly better in AL measurements (P = 0.08), and the difference in CR was statistically significant (P < 0.05). The AL distribution was normal in girls (P = 0.12), whereas it was not in boys (P < 0.05). For CR1, all subgroups presented normal distributions (P = 0.16 for boys; P = 0.20 for girls), but the distribution varied when the subgroups were combined (P < 0.05). CR2 presented a normal distribution (P = 0.11), whereas the AL/CR ratio was abnormal (P < 0.001). Boys exhibited a significantly longer AL, a greater CR and a greater AL/CR ratio than girls (all P < 0.001). PMID:27384307

Charge distributions in transverse coordinate space and in impact parameter space

Energy Technology Data Exchange (ETDEWEB)

Hwang, Dae Sung [Department of Physics, Sejong University, Seoul 143-747 (Korea, Republic of)], E-mail: dshwang@slac.stanford.edu; Kim, Dong Soo [Department of Physics, Kangnung National University, Kangnung 210-702 (Korea, Republic of); Kim, Jonghyun [Department of Physics, Sejong University, Seoul 143-747 (Korea, Republic of)

2008-11-27

We study the charge distributions of the valence quarks inside nucleon in the transverse coordinate space, which is conjugate to the transverse momentum space. We compare the results with the charge distributions in the impact parameter space.

Charge distributions in transverse coordinate space and in impact parameter space

OpenAIRE

Hwang, Dae Sung; Kim, Dong Soo; Kim, Jonghyun

2008-01-01

We study the charge distributions of the valence quarks inside nucleon in the transverse coordinate space, which is conjugate to the transverse momentum space. We compare the results with the charge distributions in the impact parameter space.

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.

Increasing parameter certainty and data utility through multi-objective calibration of a spatially distributed temperature and solute model

Directory of Open Access Journals (Sweden)

C. Bandaragoda

2011-05-01

Full Text Available To support the goal of distributed hydrologic and instream model predictions based on physical processes, we explore multi-dimensional parameterization determined by a broad set of observations. We present a systematic approach to using various data types at spatially distributed locations to decrease parameter bounds sampled within calibration algorithms that ultimately provide information regarding the extent of individual processes represented within the model structure. Through the use of a simulation matrix, parameter sets are first locally optimized by fitting the respective data at one or two locations and then the best results are selected to resolve which parameter sets perform best at all locations, or globally. This approach is illustrated using the Two-Zone Temperature and Solute (TZTS model for a case study in the Virgin River, Utah, USA, where temperature and solute tracer data were collected at multiple locations and zones within the river that represent the fate and transport of both heat and solute through the study reach. The result was a narrowed parameter space and increased parameter certainty which, based on our results, would not have been as successful if only single objective algorithms were used. We also found that the global optimum is best defined by multiple spatially distributed local optima, which supports the hypothesis that there is a discrete and narrowly bounded parameter range that represents the processes controlling the dominant hydrologic responses. Further, we illustrate that the optimization process itself can be used to determine which observed responses and locations are most useful for estimating the parameters that result in a global fit to guide future data collection efforts.

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.

Parameters of the Two-Phase Sand-Air Stream in the Blowing Process

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Danko J.

2012-12-01

Full Text Available Theoretical problems concerning the determination of work parameters of the two-phase sand-air stream in the cores making process by blowing methods as well as experimental methods of determination of the main and auxiliary parameters of this process decisive on the cores quality assessed by the value and distribution of their apparent density are presented in the paper. In addition the results of visualisations of the core-box filling with the sand-air stream, from the blowing chamber, obtained by the process filming by means of the quick-action camera are presented in the paper and compared with the results of simulation calculations with the application of the ProCast software.

Parameters of the Two-Phase Sand-Air Stream in the Blowing Process

Directory of Open Access Journals (Sweden)

J. Danko

2012-12-01

Full Text Available Theoretical problems concerning the determination of work parameters of the two-phase sand-air stream in the cores making process byblowing methods as well as experimental methods of determination of the main and auxiliary parameters of this process decisive on thecores quality assessed by the value and distribution of their apparent density are presented in the paper. In addition the results of visualisations of the core-box filling with the sand-air stream, from the blowing chamber, obtained by the process filming by means of the quick-action camera are presented in the paper and compared with the results of simulation calculations with the application of the ProCast software.

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.

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.

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

Excitation functions of parameters in Erlang distribution, Schwinger mechanism, and Tsallis statistics in RHIC BES program

International Nuclear Information System (INIS)

Gao, Li-Na; Liu, Fu-Hu; Lacey, Roy A.

2016-01-01

Experimental results of the transverse-momentum distributions of φ mesons and Ω hyperons produced in gold-gold (Au-Au) collisions with different centrality intervals, measured by the STAR Collaboration at different energies (7.7, 11.5, 19.6, 27, and 39 GeV) in the beam energy scan (BES) program at the relativistic heavy-ion collider (RHIC), are approximately described by the single Erlang distribution and the two-component Schwinger mechanism. Moreover, the STAR experimental transverse-momentum distributions of negatively charged particles, produced in Au-Au collisions at RHIC BES energies, are approximately described by the two-component Erlang distribution and the single Tsallis statistics. The excitation functions of free parameters are obtained from the fit to the experimental data. A weak softest point in the string tension in Ω hyperon spectra is observed at 7.7 GeV. (orig.)

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)

A Two-Stage Maximum Entropy Prior of Location Parameter with a Stochastic Multivariate Interval Constraint and Its Properties

Directory of Open Access Journals (Sweden)

Hea-Jung Kim

2016-05-01

Full Text Available This paper proposes a two-stage maximum entropy prior to elicit uncertainty regarding a multivariate interval constraint of the location parameter of a scale mixture of normal model. Using Shannon’s entropy, this study demonstrates how the prior, obtained by using two stages of a prior hierarchy, appropriately accounts for the information regarding the stochastic constraint and suggests an objective measure of the degree of belief in the stochastic constraint. The study also verifies that the proposed prior plays the role of bridging the gap between the canonical maximum entropy prior of the parameter with no interval constraint and that with a certain multivariate interval constraint. It is shown that the two-stage maximum entropy prior belongs to the family of rectangle screened normal distributions that is conjugate for samples from a normal distribution. Some properties of the prior density, useful for developing a Bayesian inference of the parameter with the stochastic constraint, are provided. We also propose a hierarchical constrained scale mixture of normal model (HCSMN, which uses the prior density to estimate the constrained location parameter of a scale mixture of normal model and demonstrates the scope of its applicability.

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.

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

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)

A micromechanical interpretation of the temperature dependence of Beremin model parameters for French RPV steel

International Nuclear Information System (INIS)

Mathieu, Jean-Philippe; Inal, Karim; Berveiller, Sophie; Diard, Olivier

2010-01-01

Local approach to brittle fracture for low-alloyed steels is discussed in this paper. A bibliographical introduction intends to highlight general trends and consensual points of the topic and evokes debatable aspects. French RPV steel 16MND5 (equ. ASTM A508 Cl.3), is then used as a model material to study the influence of temperature on brittle fracture. A micromechanical modelling of brittle fracture at the elementary volume scale already used in previous work is then recalled. It involves a multiscale modelling of microstructural plasticity which has been tuned on experimental inter-phase and inter-granular stresses heterogeneities measurements. Fracture probability of the elementary volume can then be computed using a randomly attributed defect size distribution based on realistic carbides repartition. This defect distribution is then deterministically correlated to stress heterogeneities simulated within the microstructure using a weakest-link hypothesis on the elementary volume, which results in a deterministic stress to fracture. Repeating the process allows to compute Weibull parameters on the elementary volume. This tool is then used to investigate the physical mechanisms that could explain the already experimentally observed temperature dependence of Beremin's parameter for 16MND5 steel. It is showed that, assuming that the hypothesis made in this work about cleavage micro-mechanisms are correct, effective equivalent surface energy (i.e. surface energy plus plastically dissipated energy when blunting the crack tip) for propagating a crack has to be temperature dependent to explain Beremin's parameters temperature evolution.

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

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

Science.gov (United States)

Peters, B. C., Jr.; Walker, H. F.

1975-01-01

New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.

Multiplicity distributions in impact parameter space

International Nuclear Information System (INIS)

Wakano, Masami

1976-01-01

A definition for the average multiplicity of pions as a function of momentum transfer and total energy in the high energy proton-proton collisions is proposed by using the n-pion production differential cross section with the given momentum transfer from a proton to other final products and the given energy of the latter. Contributions from nondiffractive and diffractive processes are formulated in a multi-Regge model. We define a relationship between impact parameter and momentum transfer in the sense of classical theory for inelastic processes and we obtain the average multiplicity of pions as a function of impact parameter and total energy from the corresponding quantity afore-mentioned. By comparing this quantity with the square root of the opaqueness at given impact parameter, we conclude that the overlap of localized constituents is important in determining the opaqueness at given impact parameter in a collision of two hadrons. (auth.)

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.

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

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.

From conservation laws to port-Hamiltonian representations of distributed-parameter systems

NARCIS (Netherlands)

Maschke, B.M.; van der Schaft, Arjan; Piztek, P.

Abstract: In this paper it is shown how the port-Hamiltonian formulation of distributed-parameter systems is closely related to the general thermodynamic framework of systems of conservation laws and closure equations. The situation turns out to be similar to the lumped-parameter case where the

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)

Effect of two-temperature electrons distribution on an electrostatic plasma sheath

International Nuclear Information System (INIS)

Ou, Jing; Xiang, Nong; Gan, Chunyun; Yang, Jinhong

2013-01-01

A magnetized collisionless plasma sheath containing two-temperature electrons is studied using a one-dimensional model in which the low-temperature electrons are described by Maxwellian distribution (MD) and high-temperature electrons are described by truncated Maxwellian distribution (TMD). Based on the ion wave approach, a modified sheath criterion including effect of TMD caused by high-temperature electrons energy above the sheath potential energy is established theoretically. The model is also used to investigate numerically the sheath structure and energy flux to the wall for plasmas parameters of an open divertor tokamak-like. Our results show that the profiles of the sheath potential, two-temperature electrons and ions densities, high-temperature electrons and ions velocities as well as the energy flux to the wall depend on the high-temperature electrons concentration, temperature, and velocity distribution function associated with sheath potential. In addition, the results obtained in the high-temperature electrons with TMD as well as with MD sheaths are compared for the different sheath potential

Weibull Wind-Speed Distribution Parameters Derived from a Combination of Wind-Lidar and Tall-Mast Measurements Over Land, Coastal and Marine Sites

DEFF Research Database (Denmark)

Gryning, Sven-Erik; Floors, Rogier Ralph; Peña, Alfredo

2016-01-01

Wind-speed observations from tall towers are used in combination with observations up to 600 m in altitude from a Doppler wind lidar to study the long-term conditions over suburban (Hamburg), rural coastal (Høvsøre) and marine (FINO3) sites. The variability in the wind field among the sites is ex...... of the vertical profile of the shape parameter fits well with observations over land, coastal regions and over the sea. An applied model for the dependence of the reversal height on the surface roughness is in good agreement with the observations over land....

Global distribution of urban parameters derived from high-resolution global datasets for weather modelling

Science.gov (United States)

Kawano, N.; Varquez, A. C. G.; Dong, Y.; Kanda, M.

2016-12-01

Numerical model such as Weather Research and Forecasting model coupled with single-layer Urban Canopy Model (WRF-UCM) is one of the powerful tools to investigate urban heat island. Urban parameters such as average building height (Have), plain area index (λp) and frontal area index (λf), are necessary inputs for the model. In general, these parameters are uniformly assumed in WRF-UCM but this leads to unrealistic urban representation. Distributed urban parameters can also be incorporated into WRF-UCM to consider a detail urban effect. The problem is that distributed building information is not readily available for most megacities especially in developing countries. Furthermore, acquiring real building parameters often require huge amount of time and money. In this study, we investigated the potential of using globally available satellite-captured datasets for the estimation of the parameters, Have, λp, and λf. Global datasets comprised of high spatial resolution population dataset (LandScan by Oak Ridge National Laboratory), nighttime lights (NOAA), and vegetation fraction (NASA). True samples of Have, λp, and λf were acquired from actual building footprints from satellite images and 3D building database of Tokyo, New York, Paris, Melbourne, Istanbul, Jakarta and so on. Regression equations were then derived from the block-averaging of spatial pairs of real parameters and global datasets. Results show that two regression curves to estimate Have and λf from the combination of population and nightlight are necessary depending on the city's level of development. An index which can be used to decide which equation to use for a city is the Gross Domestic Product (GDP). On the other hand, λphas less dependence on GDP but indicated a negative relationship to vegetation fraction. Finally, a simplified but precise approximation of urban parameters through readily-available, high-resolution global datasets and our derived regressions can be utilized to estimate a

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 ...

Distribution and Parameter's Calculations of Television Cameras Inside a Nuclear Facility

International Nuclear Information System (INIS)

El-kafas, A.A.

2009-01-01

In this work, a distribution of television cameras and parameter's calculation inside and outside a nuclear facility is presented. Each of exterior and interior camera systems will be described and explained. The work shows the overall closed circuit television system. Fixed and moving cameras with various lens format and different angles of view are used. The calculations of width of images sensitive area and Lens focal length for the cameras will be introduced. The work shows the camera locations and distributions inside and outside the nuclear facility. The technical specifications and parameters for cameras selection are tabulated

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...

Reliability analysis for wind turbines with incomplete failure data collected from after the date of initial installation

International Nuclear Information System (INIS)

Guo Haitao; Watson, Simon; Tavner, Peter; Xiang Jiangping

2009-01-01

Reliability has an impact on wind energy project costs and benefits. Both life test data and field failure data can be used for reliability analysis. In wind energy industry, wind farm operators have greater interest in recording wind turbine operating data. However, field failure data may be tainted or incomplete, and therefore it needs a more general mathematical model and algorithms to solve the model. The aim of this paper is to provide a solution to this problem. A three-parameter Weibull failure rate function is discussed for wind turbines and the parameters are estimated by maximum likelihood and least squares. Two populations of German and Danish wind turbines are analyzed. The traditional Weibull failure rate function is also employed for comparison. Analysis shows that the three-parameter Weibull function can obtain more accuracy on reliability growth of wind turbines. This work will be helpful in the understanding of the reliability growth of wind energy systems as wind energy technologies evolving. The proposed three-parameter Weibull function is also applicable to the life test of the components that have been used for a period of time, not only in wind energy but also in other industries

SPOTting model parameters using a ready-made Python package

Science.gov (United States)

Houska, Tobias; Kraft, Philipp; Breuer, Lutz

2015-04-01

The selection and parameterization of reliable process descriptions in ecological modelling is driven by several uncertainties. The procedure is highly dependent on various criteria, like the used algorithm, the likelihood function selected and the definition of the prior parameter distributions. A wide variety of tools have been developed in the past decades to optimize parameters. Some of the tools are closed source. Due to this, the choice for a specific parameter estimation method is sometimes more dependent on its availability than the performance. A toolbox with a large set of methods can support users in deciding about the most suitable method. Further, it enables to test and compare different methods. We developed the SPOT (Statistical Parameter Optimization Tool), an open source python package containing a comprehensive set of modules, to analyze and optimize parameters of (environmental) models. SPOT comes along with a selected set of algorithms for parameter optimization and uncertainty analyses (Monte Carlo, MC; Latin Hypercube Sampling, LHS; Maximum Likelihood, MLE; Markov Chain Monte Carlo, MCMC; Scuffled Complex Evolution, SCE-UA; Differential Evolution Markov Chain, DE-MCZ), together with several likelihood functions (Bias, (log-) Nash-Sutcliff model efficiency, Correlation Coefficient, Coefficient of Determination, Covariance, (Decomposed-, Relative-, Root-) Mean Squared Error, Mean Absolute Error, Agreement Index) and prior distributions (Binomial, Chi-Square, Dirichlet, Exponential, Laplace, (log-, multivariate-) Normal, Pareto, Poisson, Cauchy, Uniform, Weibull) to sample from. The model-independent structure makes it suitable to analyze a wide range of applications. We apply all algorithms of the SPOT package in three different case studies. Firstly, we investigate the response of the Rosenbrock function, where the MLE algorithm shows its strengths. Secondly, we study the Griewank function, which has a challenging response surface for

Iterative methods for distributed parameter estimation in parabolic PDE

Energy Technology Data Exchange (ETDEWEB)

Vogel, C.R. [Montana State Univ., Bozeman, MT (United States); Wade, J.G. [Bowling Green State Univ., OH (United States)

1994-12-31

The goal of the work presented is the development of effective iterative techniques for large-scale inverse or parameter estimation problems. In this extended abstract, a detailed description of the mathematical framework in which the authors view these problem is presented, followed by an outline of the ideas and algorithms developed. Distributed parameter estimation problems often arise in mathematical modeling with partial differential equations. They can be viewed as inverse problems; the `forward problem` is that of using the fully specified model to predict the behavior of the system. The inverse or parameter estimation problem is: given the form of the model and some observed data from the system being modeled, determine the unknown parameters of the model. These problems are of great practical and mathematical interest, and the development of efficient computational algorithms is an active area of study.

Eliciting hyperparameters of prior distributions for the parameters of paired comparison models

Directory of Open Access Journals (Sweden)

Nasir Abbas

2013-02-01

Full Text Available Normal 0 false false false EN-US X-NONE AR-SA In the study of paired comparisons (PC, items may be ranked or issues may be prioritized through subjective assessment of certain judges. PC models are developed and then used to serve the purpose of ranking. The PC models may be studied through classical or Bayesian approach. Bayesian inference is a modern statistical technique used to draw conclusions about the population parameters. Its beauty lies in incorporating prior information about the parameters into the analysis in addition to current information (i.e. data. The prior and current information are formally combined to yield a posterior distribution about the population parameters, which is the work bench of the Bayesian statisticians. However, the problems the Bayesians face correspond to the selection and formal utilization of prior distribution. Once the type of prior distribution is decided to be used, the problem of estimating the parameters of the prior distribution (i.e. elicitation still persists. Different methods are devised to serve the purpose. In this study an attempt is made to use Minimum Chi-square (hence forth MCS for the elicitation purpose. Though it is a classical estimation technique, but is used here for the election purpose. The entire elicitation procedure is illustrated through a numerical data set.

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

Improving control and estimation for distributed parameter systems utilizing mobile actuator-sensor network.

Science.gov (United States)

Mu, Wenying; Cui, Baotong; Li, Wen; Jiang, Zhengxian

2014-07-01

This paper proposes a scheme for non-collocated moving actuating and sensing devices which is unitized for improving performance in distributed parameter systems. By Lyapunov stability theorem, each moving actuator/sensor agent velocity is obtained. To enhance state estimation of a spatially distributes process, two kinds of filters with consensus terms which penalize the disagreement of the estimates are considered. Both filters can result in the well-posedness of the collective dynamics of state errors and can converge to the plant state. Numerical simulations demonstrate that the effectiveness of such a moving actuator-sensor network in enhancing system performance and the consensus filters converge faster to the plant state when consensus terms are included. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Confidence limits for parameters of Poisson and binomial distributions

International Nuclear Information System (INIS)

Arnett, L.M.

1976-04-01

The confidence limits for the frequency in a Poisson process and for the proportion of successes in a binomial process were calculated and tabulated for the situations in which the observed values of the frequency or proportion and an a priori distribution of these parameters are available. Methods are used that produce limits with exactly the stated confidence levels. The confidence interval [a,b] is calculated so that Pr [a less than or equal to lambda less than or equal to b c,μ], where c is the observed value of the parameter, and μ is the a priori hypothesis of the distribution of this parameter. A Bayesian type analysis is used. The intervals calculated are narrower and appreciably different from results, known to be conservative, that are often used in problems of this type. Pearson and Hartley recognized the characteristics of their methods and contemplated that exact methods could someday be used. The calculation of the exact intervals requires involved numerical analyses readily implemented only on digital computers not available to Pearson and Hartley. A Monte Carlo experiment was conducted to verify a selected interval from those calculated. This numerical experiment confirmed the results of the analytical methods and the prediction of Pearson and Hartley that their published tables give conservative results

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.

Distributed parameter modeling and simulation for the evaporation system of a controlled circulation boiler based on 3-D combustion monitoring

International Nuclear Information System (INIS)

Chu Yuntao; Lou Chun; Cheng Qiang; Zhou Huaichun

2008-01-01

In this paper, a dynamic, distributed parameter model for the evaporation system of a controlled circulation boiler was developed. As an essential basis, the 3-D temperature distribution and the average emissivity of the particle phase inside its furnace can be got by a flame image processing technique from multiple, visible flame image detectors in a real-time combustion monitoring system. Then the transient, 2-D radiation flux can be obtained by solving a set of energy balance equations for the water wall elements, which serves as a distributed boundary condition for the dynamic, distributed parameter model proposed for the evaporation system. For large change of the boiler load, two important parameters, the correction factor of equivalent flame emissivity and the coefficient of the steam mass flow rate at the outlet of the drum, were determined using the operation data from a 300 MW boiler. The model was validated by comparing the simulation results for some main steam parameters of the system with those from measurements. Besides that, the transient distributions of the parameters, such as the steam quality and the mass velocity, were predicted by the model. This model can be used for on-line calculation or off-line prediction of the local abnormal phenomena occurring on the water walls, forming an important basis to effectively evaluate the security and the reliability of a power plant boiler

Some calculations of the failure statistics of coated fuel particles

International Nuclear Information System (INIS)

Martin, D.G.; Hobbs, J.E.

1977-03-01

Statistical variations of coated fuel particle parameters were considered in stress model calculations and the resulting particle failure fraction versus burn-up evaluated. Variations in the following parameters were considered simultaneously: kernel diameter and porosity, thickness of the buffer, seal, silicon carbide and inner and outer pyrocarbon layers, which were all assumed to be normally distributed, and the silicon carbide fracture stress which was assumed to follow a Weibull distribution. Two methods, based respectively on random sampling and convolution of the variations were employed and applied to particles manufactured by Dragon Project and RFL Springfields. Convolution calculations proved the more satisfactory. In the present calculations variations in the silicon carbide fracture stress caused the greatest spread in burn-up for a given change in failure fraction; kernel porosity is the next most important parameter. (author)

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...

Dielectric and electro-optical parameters of two ferroelectric liquid crystals: a comparative study

International Nuclear Information System (INIS)

Kumar Misra, Abhishek; Kumar Srivastava, Abhishek; Shukla, J P; Manohar, Rajiv

2008-01-01

Dielectric relaxation and an electro-optical study of two ferroelectric liquid crystals having different spontaneous polarizations (Felix 16/100 and Felix 17/000) showing SmC* and SmA phases have been performed in the temperature range 30-80 compfn C. The experimental data have been used to determine different relaxation parameters, viz. distribution parameter, relaxation frequency, dielectric strength and rotational viscosity. The Goldstone mode of dielectric permittivity has been well observed for both the samples under investigation. The activation energy of both the samples has also been determined by the best theoretical fitting of the Arrhenius plot. We have also evaluated the optical response time and anchoring energy coefficients from electro-optical measurement techniques for these samples.

A Note on Parameter Estimation in the Composite Weibull–Pareto Distribution

Directory of Open Access Journals (Sweden)

Enrique Calderín-Ojeda

2018-02-01

Full Text Available Composite models have received much attention in the recent actuarial literature to describe heavy-tailed insurance loss data. One of the models that presents a good performance to describe this kind of data is the composite Weibull–Pareto (CWL distribution. On this note, this distribution is revisited to carry out estimation of parameters via mle and mle2 optimization functions in R. The results are compared with those obtained in a previous paper by using the nlm function, in terms of analytical and graphical methods of model selection. In addition, the consistency of the parameter estimation is examined via a simulation study.

Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups

International Nuclear Information System (INIS)

Drozhzhinov, Yurii N; Zav'yalov, Boris I

2012-01-01