Generalized Linear Mixed Models for Reliability Analysis of Multi-Copy Repairable Systems

The power law process (PLP) is usually applied to failure data from a single repairable system. When a system has a number of copies for analysis, the usual approach is to assume homogeneity among all system copies, and then to pool data from these copies. In the real world, however, it may be more reasonable to assume heterogeneity among the system copies. Therefore, this paper proposes a new generalized linear mixed model (GLMM), called PLP-GLMM, to analyse failure data from multi-copy repairable systems. In the PLP-GLMM, the underlying model for each system copy is assumed to be a PLP at Stage 1, and parameters vary among copies at Stage 2. The PLP-GLMM can make inferences about both the population, and each system copy when accounting for copy-to-copy variance. A modified Anderson-Darling test is adapted to the goodness-of-fit test of the PLP-GLMM. A numerical application is given to show the effectiveness of the model