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

Jianyu Xu*, Bin Liu, Xiujie Zhao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1010-1024
Number of pages15
JournalQuality and Reliability Engineering International
Issue number4
Publication statusPublished - Jun 2019
Externally publishedYes


  • EM algorithm
  • Wiener degradation
  • continuous degradation
  • load-sharing system

Cite this