Nonlinear Step-Stress Accelerated Degradation Modeling and Remaining Useful Life Estimation Considering Multiple Sources of Variability

In the absence of sufficient degradation data of long-lifetime and highly reliable products, a step-stress accelerated degradation model based on nonlinear diffusion process is proposed to estimate the remaining useful life (RUL), with the advantage of requiring small sample size and short test time. For multiple uncertainties caused by inherent properties, individual differences, measurement equipment performance and artificial deviations in the degradation process, this model considers the temporal variability, unit-to-unit variability and measurement errors in both performance degradation and covariates. To estimate the RUL, we derive an analytical approximation to the first hitting time (FHT) of the nonlinear diffusion process crossing a predetermined threshold with the consideration of measurement errors. Based on maximum likelihood estimation (MLE), a modified simulation and extrapolation (SIMEX) method, called MLE-SIMEX, is developed for estimating unknown parameters in the established model. The usefulness of the proposed model is demonstrated by a simulation case and a real-world example. The results reveal that considering nonlinearity and multiple sources of variability in the step-stress accelerated degradation process can improve the model fitting and the accuracy of RUL estimation.