Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects

Abstract

In this paper, a reliability modeling approach for products with two performance characteristics related to two degradation processes is developed. The joint modeling of such processes is performed by using a copula function in order to consider the dependence structure between degradation processes. The proposed approach considers that different random effects affect the stochastic behavior of each performance characteristic. For such approach, different bivariate models with marginal gamma processes with heterogeneous random effects as marginal distributions are considered. As the random effects may differ between performance characteristics, different modifications of the structure of the parameters of the gamma process are proposed. Such that the random effects affect both the drift and diffusion, just the drift, and just the diffusion of the marginal gamma processes. The statistical inference of the joint bivariate models is performed via Bayesian approach. The obtained results show that a bivariate model with heterogeneous random effects has a slight better performance among the proposed models. Which implies that the bivariate heterogeneous random effects gamma process models may provide a better approach to model multivariate degradation data, and thus a better reliability assessment of the product under study.