Parameter estimation for load‐sharing system subject to Wiener degradation process using the expectation‐maximization algorithm

• Published in: Quality and reliability engineering international Vol. 35; no. 4; pp. 1010 - 1024
• Main Authors: Xu, Jianyu, Liu, Bin, Zhao, Xiujie
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.06.2019
• Subjects: Algorithms; Component reliability; continuous degradation; Degradation; EM algorithm; Estimating techniques; Failure rates; load‐sharing system; Maximization; Maximum likelihood estimators; Optimization; Parameter estimation; Reliability analysis; Wiener degradation
• DOI: 10.1002/qre.2442
• ISSN: 0748-8017

In practice, many systems exhibit load‐sharing behavior, where the surviving components share the total load imposed on the system. Different from general systems, the components of load‐sharing systems are interdependent in nature, in such a way that when one component fails, the system load has to be shared by the remaining components, which increases the failure rate or degradation rate of the remaining components. Because of the load‐sharing mechanism among components, parameter estimation and reliability assessment are usually complicated for load‐sharing systems. Although load‐sharing systems with components subject to sudden failures have been intensely studied in literatures with detailed estimation and analysis approaches, those with components subject to degradation are rarely investigated. In this paper, we propose the parameter estimation method for load‐sharing systems subject to continuous degradation with a constant load. Likelihood function based on the degradation data of components is established as a first step. The maximum likelihood estimators for unknown parameters are deduced and obtained via expectation‐maximization (EM) algorithm considering the nonclosed form of the likelihood function. Numerical examples are used to illustrate the effectiveness of the proposed method.