Bivariate and two-phase degradation modeling and reliability analysis with random effects

Abstract

The paper aims at predicting the remaining useful life of highly reliable and long-life products with multiple and multi-stage characteristics in the degradation process. Considering the unit-to-unit variability among the product units, a new bivariate and two-phase Wiener process model with random effects is established. Schwarz Information Criterion is used to identify the change points of the degradation model, and the analytical expressions of life and remaining useful life are given by the concept of first hitting time. Furthermore, the appropriate Copula function is selected to describe the correlation between the two quality characteristics based on Akaike Information Criterion. A bivariate degradation model is established and the unknown parameters of the model are estimated by Markov Chain Monte Carlo method. Finally, the applicability and effectiveness of the proposed method are verified by the comparative analysis of turbine engine.