Multivariate $t$ Degradation Processes for Dependent Multivariate Degradation Data

Abstract

Multiple performance characteristics (PCs) are common in modern products with complex structures and diverse functions. These PCs are usually dependent, with significant unit-specific variability among the multivariate degradation processes. Therefore, the associated degradation modeling for dependent multivariate degradation processes is important. This article proposes a novel multivariate $t$ degradation model for this purpose. Specifically, the dependence between multivariate degradation processes is captured by random drift parameters that follow a multivariate normal distribution, and the variation in diffusion parameters and variance–covariance is characterized by a gamma distribution. An expectation-maximization (EM) algorithm is employed for likelihood inference, and confidence intervals of the model parameters are constructed by normal approximation and bootstrap method. A theoretical exploration investigating the effects of model misspecification in multivariate degradation modeling is addressed. Monte Carlo simulation studies are performed to validate the effectiveness of the EM algorithm and the theoretical properties of the multivariate $t$ model. Finally, two illustrative examples are used to demonstrate the applicability and advantages of the proposed methods.