A new multivariate gamma process model for degradation analysis

Abstract

AbstractIn reliability engineering, it is frequently encountered that multiple performance characteristics (PCs) deteriorate simultaneously. The associated degradation processes are usually dependent and exhibit some heterogeneity from unit to unit, which makes the multivariate degradation modeling and reliability evaluation more challenging. To this end, we propose a new multivariate gamma process model. This model introduces a multivariate random vector, whose joint distribution is constructed by marginal gamma distributions and a copula function, to describe the unit‐to‐unit variability and the dependence among PCs. Meanwhile, it does not require all PCs to be inspected at the same time points in contrast to the traditional copula‐based degradation models. In addition, two reliability evaluation methods are developed. Model parameters are estimated by the stochastic expectation maximization algorithm, and a three‐step procedure is provided to initialize this algorithm. Subsequently, numerical simulations are implemented to verify the proposed methods. Finally, two examples are provided for illustration, and it is shown that the proposed model and methods scale well to the degradation data with different numbers of PCs. What is more, comparisons with several benchmark models are performed, and the superiority of the proposed model is well demonstrated.