A Multivariate Stochastic Degradation Model for Dependent Performance Characteristics

Abstract

Simultaneous degradation of multiple dependent performance characteristics (PCs) is a common phenomenon for industrial products. The associated degradation modeling is of practical importance yet challenging. The dependence of the PCs can usually be attributed to two sources, one being the overall system health status and the other the common operating environments. Based on the observation, this study proposes a parsimonious multivariate Wiener process model whose number of parameters increases linearly with the dimension. We introduce a common stochastic time scale shared by all the PCs to model the dependence from the dynamic operating environment. Conditional on the time scale, the degradation of each PC is modeled as the sum of two independent Wiener processes, where one represents the common effects shared by all the PCs, and the other represents degradation caused by randomness unique to this PC. An EM algorithm is developed for model parameter estimation, and extensive simulations are implemented to validate the proposed model and the algorithms. For efficient reliability evaluation under a multivariate degradation model, including the proposed one, a bridge sampling-based algorithm is further developed. The applicability and the advantages of the proposed methods are demonstrated using a multivariate degradation dataset of a coating material. Supplementary materials for this article are available online.

Keywords:

• Inverse Gaussian process
• Multiple dependent degradation
• Stochastic time scale
• Wiener process

Supplementary Materials

Technical Materials: The supplementary file provides technical details of the Propositions, the adaptive sampling algorithm, additional simulation results in Section 5 and details about the EM algorithm (PDF file).

Source Codes: The Matlab codes for the EM algorithm are provided. The coating material dataset used in this study is also included (ZIP file).

Acknowledgments

The authors would like to thank the editor, an associate editor, and three referees for their constructive comments that have led to a substantial improvement on an earlier version of the article.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Zhai was supported by the National Natural Science Foundation of China (71901138, 72271154). Ye was supported by the National Natural Science Foundation of China (72071138) and Singapore MOE AcRF Tier 1 grant (R-266-000-145-114).