General Path Models for Degradation Data With Multiple Characteristics and Covariates

Abstract

Degradation data have been broadly used for assessing product and system reliability. Most existing work focuses on modeling and analysis of degradation data with a single characteristic. In some degradation tests, interest lies in measuring multiple characteristics of the product degradation process to understand different aspects of the reliability performance, resulting in degradation data with multiple characteristics. The literature on modeling such data is scarce. Motivated by the photodegradation process of polymeric material, we propose a multivariate general path model for analyzing degradation data with multiple degradation characteristics (DCs). The model incorporates covariates for modeling the nonlinear degradation path. It also includes random effects that are correlated among the multiple DCs to capture the unit-to-unit variation in the individual degradation paths and to model the interdependence among the multivariate measurements. An expectation-maximization algorithm combined with the Markov chain Monte Carlo simulation is developed for estimating the model parameters and predicting system reliability with quantified uncertainty. The performance of the developed method is evaluated and compared with existing methods through a simulation study. The implementation of the method is illustrated through two examples with different forms of reliability functions. The main motivating example analyzes the coating degradation data with a closed-form reliability function, while the second example on analyzing the Device-B data demonstrates a more general simulation approach for dealing with analytically intractable reliability functions.