Inverse Gaussian processes with correlated random effects for multivariate degradation modeling

Many engineering products have more than one failure mode and the evolution of each mode can be monitored by measuring a performance characteristic (PC). It is found that the underlying multi-dimensional degradation often occurs with inherent process stochasticity and heterogeneity across units, as well as dependency among PCs. To accommodate these features, in this paper, we propose a novel multivariate degradation model based on the inverse Gaussian process. The model incorporates random effects that are subject to a multivariate normal distribution to capture both the unit-wise variability and the PC-wise dependence. Built upon this structure, we obtain some mathematically tractable properties such as the joint and conditional distribution functions, which subsequently facilitate the future degradation prediction and lifetime estimation. An expectation-maximization algorithm is developed to infer the model parameters along with the validation tools for model checking. In addition, two simulation studies are performed to assess the performance of the inference method and to evaluate the effect of model misspecification. Finally, the application of the proposed methodology is demonstrated by two illustrative examples.