Reliability Analysis Based on a Bivariate Degradation Model Considering Random Initial State and Its Correlation With Degradation Rate

Dependent degradation processes of performance characteristics are ubiquitous in engineered systems. The initial state of each degradation process is usually random and relates to the degradation rate. Unfort unately, most existing Wiener-based bivariate degradation models fail to consider these two features, which may limit the accuracy of system reliability assessment. In order to surmount this limitation, in this article, we develop a new bivariate degradation model, which involves a generalized Wiener process-based marginal degradation model that considers the random initial state and the correlation between the initial state and the degradation rate and a corresponding degradation increment-based dependence structure (DS). The proposed bivariate degradation model and its reliability function are derived first. Then, a two-stage statistical inference is introduced using the maximum likelihood estimation method. Furthermore, a simulation study investigates the performance of the statistical inference and the misspecification effects of DSs and marginal degradation models. Finally, an illustrative example demonstrates the effectiveness of the proposed model.

I. Introduction

Engineered systems often have two or more performance characteristics (PCs) related to various output requirements. In practice, the systems are inevitably affected by environmental factors driving PCs degradation [1], and the systems will fail when any of their PCs exceeds the corresponding preset failure threshold [2]. Since the PCs of an engineered system originate from the same system composition operating under given profiles, their degradation generally follows dependent processes [3], [4]. Therefore, the system reliability analysis should be based on a multivariable degradation model made of two key factors: marginal degradation models to trace each PC degradation process and a dependence structure (DS) to describe the dependence among the degradation processes of the multiple PCs. This study focuses on systems with two PCs, as they are extensively used in practical engineering [4], [5], and their reliability analysis forms the foundation for the reliability assessment of systems with multiple PCs [6], [7].