Estimating the parameters of 3-p Weibull distribution through differential evolution

•The Weibull distribution is used lifetime distributions in reliability engineering.•The estimation of the parameters of this distribution is essential.•Maximum likelihood (ML) estimation is a common method for parameter estimation.•The working principle of ML estimation based on maximizing the like...

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Published inApplied mathematics and computation Vol. 251; pp. 211 - 224
Main Authors Örkcü, H. Hasan, Aksoy, Ertugˇrul, Dogˇan, Mustafa İsa
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2015
Subjects
Algorithms
Convergence
Differential evolution algorithm
Estimates
Estimation accuracy
Evolution
Mathematical analysis
Mathematical models
Maximum likelihood estimation
Mutation schemes
Operators
Parameter estimation
Weibull distribution
Maximum likelihood estimation
Differential evolution algorithm
Mutation schemes
Weibull distribution
Estimation accuracy
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Abstract •The Weibull distribution is used lifetime distributions in reliability engineering.•The estimation of the parameters of this distribution is essential.•Maximum likelihood (ML) estimation is a common method for parameter estimation.•The working principle of ML estimation based on maximizing the likelihood function.•We used differential evolution algorithm as parameter estimation tool in 3-p Weibull. The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering and the estimation of the parameters of this distribution is essential in the most real applications. Maximum likelihood (ML) estimation is a common method, which is usually used to elaborate on the parameter estimation. The working principle of ML estimation method based on maximizing the established likelihood function and maximizing this function formed for the parameter estimation of a three-parameter (3-p) Weibull distribution is a quite challenging problem. In this paper, this problem have been briefly discussed and an effective approach based on the differential evolution (DE) algorithm operators is proposed in order to enhance the estimation accuracy with less system resources. Three explanatory numerical examples are given to show that DE approach which requires significantly less CPU time and exhibits a rapid convergence to the maximum value of the likelihood function in less iterations, provides accurate estimates and is satisfactory for the parameter estimation of the 3-p Weibull distribution.
AbstractList •The Weibull distribution is used lifetime distributions in reliability engineering.•The estimation of the parameters of this distribution is essential.•Maximum likelihood (ML) estimation is a common method for parameter estimation.•The working principle of ML estimation based on maximizing the likelihood function.•We used differential evolution algorithm as parameter estimation tool in 3-p Weibull. The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering and the estimation of the parameters of this distribution is essential in the most real applications. Maximum likelihood (ML) estimation is a common method, which is usually used to elaborate on the parameter estimation. The working principle of ML estimation method based on maximizing the established likelihood function and maximizing this function formed for the parameter estimation of a three-parameter (3-p) Weibull distribution is a quite challenging problem. In this paper, this problem have been briefly discussed and an effective approach based on the differential evolution (DE) algorithm operators is proposed in order to enhance the estimation accuracy with less system resources. Three explanatory numerical examples are given to show that DE approach which requires significantly less CPU time and exhibits a rapid convergence to the maximum value of the likelihood function in less iterations, provides accurate estimates and is satisfactory for the parameter estimation of the 3-p Weibull distribution.
The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering and the estimation of the parameters of this distribution is essential in the most real applications. Maximum likelihood (ML) estimation is a common method, which is usually used to elaborate on the parameter estimation. The working principle of ML estimation method based on maximizing the established likelihood function and maximizing this function formed for the parameter estimation of a three-parameter (3-p) Weibull distribution is a quite challenging problem. In this paper, this problem have been briefly discussed and an effective approach based on the differential evolution (DE) algorithm operators is proposed in order to enhance the estimation accuracy with less system resources. Three explanatory numerical examples are given to show that DE approach which requires significantly less CPU time and exhibits a rapid convergence to the maximum value of the likelihood function in less iterations, provides accurate estimates and is satisfactory for the parameter estimation of the 3-p Weibull distribution.
Author Örkcü, H. Hasan
Dogˇan, Mustafa İsa
Aksoy, Ertugˇrul
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Differential evolution algorithm
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Weibull distribution
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Snippet •The Weibull distribution is used lifetime distributions in reliability engineering.•The estimation of the parameters of this distribution is...
The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering and the estimation of the parameters of this...
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SubjectTerms Algorithms
Convergence
Differential evolution algorithm
Estimates
Estimation accuracy
Evolution
Mathematical analysis
Mathematical models
Maximum likelihood estimation
Mutation schemes
Operators
Parameter estimation
Weibull distribution
Title Estimating the parameters of 3-p Weibull distribution through differential evolution
URI https://dx.doi.org/10.1016/j.amc.2014.10.127
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