Reliability Analysis of Repairable Systems With Dependent Component Failures Under Partially Perfect Repair

Abstract

Existing reliability models for repairable systems with a single component can be well applied for a range of repair actions from perfect repair to minimal repair. Establishing reliability models for multi-component repairable systems, however, is still a challenge problem when considering the dependency of component failures. This paper focuses on a special repair assumption, called partially perfect repair, for repairable systems with dependent component failures, where only the failed component is repaired to as good as new condition. A parametric reliability model is proposed to capture the statistical dependency among different component failures, in which the joint distribution of the latent component failure time is established using copula functions. The model parameters are estimated by using the maximum likelihood method, and the maximum likelihood function is calculated based on the conditional probability. Based on the proposed reliability model, statistical hypothesis testing procedures are developed to determine the dependency of component failures. The developed methods are illustrated with an application in a cylinder head assembling cell that consists of multiple stations.