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

Abstract

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.

KEYWORDS:

• Degradation data
• EM algorithm
• Hierarchical model
• Multivariate degradation
• Random effects
• Wiener process

Supplementary Materials

In the online supplementary materials of this article, we provide a PDF file containing technical details (the miscellaneous proofs and inference methods), additional numerical results of the simulation and case studies, a list of notations, and a description of data and codes. Additionally, we provide a zip file containing the R codes for reproducing Table 5 in this article.

Acknowledgments

We would like to thank the editor, associate editor, and referees for their constructive comments and suggestions that helped us considerably improve the article. We gratefully acknowledge Dr. Wendai Wang for providing data resources for this study.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

G. Fang was partially supported by National Natural Science Foundation of China (Grant No. 72201242), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ22G010003), and the Fundamental Research Funds for the Provincial Universities of Zhejiang (Grant No. XT202208). R. Pan was partially supported by National Science Foundation (Grant No. 2134409).