Multivariate degradation modeling and reliability evaluation using gamma processes with hierarchical random effects

Degradation data analysis provides an effective way to perform reliability evaluation for highly reliable products. In engineering practice, multiple performance characteristics are usually monitored simultaneously to reflect products' health status comprehensively, resulting in the multivariate degradation data. Analyzing such data for reliability modeling and evaluation is of great interest but challenging. In this paper, by means of hierarchical random effects, a novel multivariate gamma degradation model is proposed. The developed model takes the temporal randomness of degradation processes, the non-linearity of degradation, the unit-to-unit heterogeneity and the dependence among marginal degradation processes into consideration simultaneously. Then, the reliability function is derived analytically. Subsequently, unknown model parameters are estimated by integrating the expectation maximization algorithm and the variational inference technique, where the latter is employed to derive tractable conditional distributions of latent variables. Meanwhile, a procedure that provides plausible guesses of parameters is developed to initialize this estimation method. Further, approximate confidence intervals are constructed for uncertainty quantification. Finally, the proposed model and methods are illustrated and verified by simulation and case studies.