A hybrid variable neighbourhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution

Abbasi, B, Niaki, S, Khalife, M and Faize, Y 2011, 'A hybrid variable neighbourhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution', Expert Systems with Applications, vol. 38, pp. 700-708.


Document type: Journal Article
Collection: Journal Articles

Title A hybrid variable neighbourhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution
Author(s) Abbasi, B
Niaki, S
Khalife, M
Faize, Y
Year 2011
Journal name Expert Systems with Applications
Volume number 38
Start page 700
End page 708
Total pages 9
Publisher Pergamon
Abstract The Weibull distribution plays an important role in failure distribution modeling of reliability research. While there are three parameters in the general form of this distribution, for simplicity, one of its parameters is usually omitted and as a result, the others are estimated easily. However, due to its more flexibility, when the general form of the Weibull distribution is of interest, the estimation procedure is not an easy task anymore. For example, in the maximum likelihood estimation method, the likelihood function that is formed for a three-parameter Weibull distribution is very hard to maximize. In this paper, a new hybrid methodology based on a variable neighborhood search and a simulated annealing approach is proposed to maximize the likelihood function of a three-parameter Weibull distribution. The performance of the proposed methodology in terms of both the estimation accuracy and the required CPU time is then evaluated and compared to the ones of an existing current method through a wide range of numerical examples in which a sensitivity analysis is performed on the sample size. The results of the comparison study show that while the proposed method provides accurate estimates as well as those of the existing method, it requires significantly less CPU time.
Subject Operations Research
Applied Statistics
Keyword(s) Weibull probability distribution
variable neighborhood search
simulated annealing
parameter estimation
maximum likelihood estimation
DOI - identifier 10.1016/j.eswa.2010.07.022
Copyright notice © 2010 Elsevier Ltd. All rights reserved.
ISSN 0957-4174
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