On Modeling Bivariate Wiener Degradation Process

Abstract

Modern products are usually designed with high reliability and have complex structures, and degradation analysis of the complex systems with two or multiple performance characteristics is still a challenge. In this paper, we propose a new bivariate degradation model based on the Wiener process. There are three main merits of the proposed model: it can describe the common factor affecting the degradation of the two performance characteristics and unit-to-unit variation simultaneously, the reliability functions of the system and the remaining useful life of the system have analytic forms, and the model parameters and the missing values can be estimated by the Bayesian method and data augmentation. The simulation study and data analysis show that the Bayesian method and the proposed model have satisfactory performance.