A multivariate student- <i>t</i> process model for dependent tail-weighted degradation data
Ancha Xu, Guanqi Fang, Liangliang Zhuang, Cheng Gu
Abstract
Traditionally, Gaussian assumption, implied by the Wiener process, is widely admitted for modeling degradation processes. However, when degradation data exhibit heavy tails, this assumption is not suitable. To overcome this limitation, this article proposes a novel class of tail-weighted multivariate degradation model, which is built upon Student-t process. The model is able to account for both between-unit variability and process dependency, while allows adjusting the tail heaviness through tuning the parameter of the degree of freedom. For reliability assessment, we derive the system reliability function and present an efficient Monte Carlo method for its evaluation. Further, we introduce an expectation-maximization algorithm for parameter estimation and design a bootstrap method for interval estimation. Comprehensive simulation studies are conducted to validate the effectiveness of the inference method. Finally, the proposed methodology is applied to analyze two real-world degradation datasets.