Reliability Analysis for Mixture Weibull Distribution with Progressively Censored Data Based on Stochastic Expectation-maximization Method

Abstract

The mixture Weibull distribution is widely used in modeling lifetimes in reliability engineering. Due to the real-time maintenance and the replacement during operating environments, the field failure data are often progressively censored. The classical parameter estimation methods are not available for the lifetime data affected by both multiple failure modes and progressively censoring. This paper proposes an improved stochastic expectation-maximization (SEM) method based on the whale optimization algorithm (WOA). The method consists of two steps. The S-step aims to generate progressively censored data corresponding to each failure data by current parameters estimates. The M-step aims to maximize the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q$</tex> function formed by the expanded data to obtain new parameters estimates. The WOA is used to optimize the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q$</tex> function for optimal parameters estimates instead of the complex analytical process of maximization. A numerical example and a real-world dataset are carried out. The results demonstrate the accuracy and applicability of the proposed method in parameter estimations and data fitting.