A Class of Hierarchical Multivariate Wiener Processes for Modeling Dependent Degradation Data

In engineering practice, many products exhibit multiple and dependent degrading performance characteristics (PCs). It is common to observe that these PCs' initial measurements are nonconstant and sometimes correlated with the subsequent degradation rate, which typically varies from one unit to another. To accommodate the unit-wise heterogeneity, PC-wise dependency, and "initiation-growth" correlation, this article proposes a broad class of multi-dimensional degradation models under a framework of hierarchical multivariate Wiener processes. These models incorporate dual multi-normally distributed random effects concerning the initial values and degradation rates. To infer model parameters, expectation-maximization (EM) algorithms and several tools for model validation and selection are developed. Various simulation studies are carried out to assess the performance of the inference method and to compare different models. Two case studies are conducted to demonstrate the applicability of the proposed methodology. The online supplementary materials of this article contain derivations of EM estimators, additional numerical results, and R codes.