Common stochastic effects induced multivariate degradation process with temporal dependency in degradation characteristic and unit dimensions

Degradation modelling plays a vital role in reliability engineering. Existing degradation models mainly focus on degradation data with a single degradation characteristic (DC) and assume that test units are mutually independent. However, in certain degradation tests, interest lies in multiple statistically dependent DCs, and the test units may be interdependent due to sharing certain unobservable effects. This article proposes a novel multivariate degradation model that considers dependency in both DC and unit dimensions. Temporal dependency in the DC dimension is modelled based on sharing Brownian noises, and the number of underlying Brownian noises is determined using factor analysis. Temporal dependency in the unit dimension is also considered and incorporated into the model by sharing temporal volatility to all units. Statistical inferences corresponding to the proposed model, including an expectation–maximisation algorithm for point estimation, a parametric bootstrap approach for interval estimation, a hypothesis test approach for testing significance of temporal dependency in unit dimension, a goodness-of-fit test for model validation, and the reliability function under a series failure structure are developed. Performance and applicability of the proposed model are demonstrated by a simulation study and a case study. Supplementary materials for this article are available online.