Multivariate reparameterized inverse Gaussian processes with common effects for degradation-based reliability prediction

In industry, many highly reliable products possess multiple performance characteristics (PCs) and they typically degrade simultaneously. When such PCs are governed by a common failure mechanism or influenced by a shared operating environmental condition, interdependence between these PCs arises. To model such dependence, this article proposes a novel multivariate reparameterized inverse Gaussian (rIG) process model. It utilizes an additive structure; that is, the degradation of each marginal PC is considered as the result of the sum of two independent rIG processes, with one capturing the shared common effects across all PCs and the other describing the intrinsic randomness specific to that PC. The model has some nice statistical properties, and the system lifetime distribution can be conveniently approximated. An expectation-maximization algorithm is proposed for estimating the model parameters, and a parametric bootstrap method is designed to derive the confidence intervals. Comprehensive numerical simulations are conducted to validate the performance of the inference method. Two case studies are thoroughly investigated to demonstrate the applicability of the proposed methodology. Supplementary materials for this article are available online.