Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison

Abstract

Weibull distribution plays an important role in failure distribution modeling in reliability studies and the estimation of its parameters 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 maximizing likelihood function formed for the parameter estimation of a three-parameter (3-p) Weibull distribution is a quite difficult problem. Hence, the heuristic approaches must be used to discover good solutions. Particle swarm optimization (PSO) is a population based heuristic optimization technique developed from swarm intelligence. The performance of PSO greatly depends on its control parameters such as inertia weight and acceleration coefficients. Slightly different parameter settings may direct to very different performance. This paper gives a comprehensive investigation of different PSO variants (according to inertia weight procedures, acceleration coefficients, particle size, and search space) in the parameter estimation problem of 3-p Weibull distribution. Three explanatory numerical examples are given to show that PSO approach variants exhibit a rapid convergence to the maximum value of the likelihood function in less iteration, provides accurate estimates and PSO method is satisfactory for the parameter estimation of the 3-p Weibull distribution.