Maximum likelihood estimates, from censored data, for mixed-Weibull distributions

Jiang, Suhua; Kececioglu, Dimitri

doi:10.1109/24.257791

Cited by 55 publications

(38 citation statements)

References 16 publications

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“…Abbas et al [54] statistically analyzed the wind speed data in Pakistan to determine the best fitting distribution of wind speed. For this purpose, two parameters Gamma, Weibull, Lognormal and Rayleigh distributions, and three parameters Burr and Frechet distributions were fitted to data and parameters for each distribution were estimated using the MLM [42,50,[55][56][57][58][59][60][61].…”

Section: Introductionmentioning

confidence: 99%

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

2014

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Abstract: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.

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Section: Introductionmentioning

confidence: 99%

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

2014

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“…Note that for both Q T and N f , there are inflection points in the probability plots which are indicative of Weibull mixtures [25][26][27].…”

Section: Discussionmentioning

confidence: 99%

On the Relationship between Structural Quality Index and Fatigue Life Distributions in Aluminum Aerospace Castings

Özdeş¹,

Tiryakioğlu²

2016

Metals

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Abstract:Tensile and fatigue testing results of D357 and B201 aluminum alloy aerospace castings reported in the literature have been reanalyzed. Yield strength-elongation bivariate data have been used as a measure of the structural quality of castings, and converted into quality index. These results as well as fatigue data have been analyzed by using Weibull statistics. A distinct relationship has been observed between expected fatigue life and quality index. Moreover, probability of survival in fatigue life was found to be directly linked to the proportions of the quality index distributions in two different regions, providing further evidence about the strong relationship between elongation, i.e., structural quality and fatigue performance.

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“…The detailed analysis of the model and parameter estimation can be referred to [9,10,[31][32][33]38]. From equation (61), it is derived that…”

Section: Mixed Weibull Distributionmentioning

confidence: 99%

“…It has been recognized for more than four decades that the mixed Weibull distribution is an appropriate distribution to use in modeling the lifetimes of units that have more than one failure cause [31]. Jiang and Kececioglu [9,32] 1. It is mathematically tractable and yields a bathtub shape for the failure rate function.…”

Section: Introductionmentioning

confidence: 99%

Choosing an optimal model for failure data analysis by graphical approach

Zhang

Dwight

2013

Reliability Engineering & System Safety

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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. © 2013 Elsevier Ltd. All rights reserved. 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.Keywords: Weibull models, Failure data analysis, Model selection, Parameter estimation, Weibull probability paper NOTATION...

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Maximum likelihood estimates, from censored data, for mixed-Weibull distributions

Cited by 55 publications

References 16 publications

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

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

On the Relationship between Structural Quality Index and Fatigue Life Distributions in Aluminum Aerospace Castings

Choosing an optimal model for failure data analysis by graphical approach

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