Statistical Modeling and Reliability Analysis for Degradation Processes Indexed by Two Scales

Degradation is an important phenomenon for industrial products, which manifests as the gradually deterioration of some performance characteristics. The degradation process is often relevant to both time and usage, and indexing the degradation process merely by the time or usage cannot characterize the process accurately. Considering a stochastic usage process, this study proposes a degradation process model indexed by two scales, i.e., the time and the usage, where the degradation along the two scales are modeled as correlated nonlinear Wiener processes. We develop two simulation-based algorithms for reliability evaluation and study the model inference problems for the proposed model. The estimation procedure and the reliability assessment algorithms are validated by simulations. The performance of the proposed model is justified with an application to a real degradation dataset of outdoor coating materials, which shows that indexing the degradation process by two scales can considerably improve the degradation modeling performance.