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

• Published in: Applied mathematics and computation Vol. 251; pp. 211 - 224
• Main Authors: Örkcü, H. Hasan, Aksoy, Ertugˇrul, Dogˇan, Mustafa İsa
• Format: Journal Article
• Language: English
• 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
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2014.10.127

•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.