Degradation modeling and RUL prediction with Wiener process considering measurable and unobservable external impacts

•A Wiener process considering measurable and unobservable external impacts is proposed.•The time-varying measurable covariate is modeled by an OU process.•The impact from unobservable factors is modeled as an time-varying degradation rate.•We develop the model estimation procedure and RUL prediction approach for the model. Degradation of products in field depends heavily on the external operating environment. The external factors, such as temperature and working load, are often time-varying or stochastic, which bring more uncertainty in the degradation process in addition to the inherent randomness. According to the availability of these factors in degradation modeling, they can be classified into the measurable covariates and the unobservable ones. In this study, we incorporate the influence of both kinds of factors into the degradation modeling using the Wiener process. We model the measurable time-varying covariate by an Ornstein-Uhlenbeck process and link it to the degradation rate through an exponential covariate-effect function, and model the impact of the unobservable factors through a time-varying degradation rate using a Brownian motion. Thus, the impacts of both the measurable covariate and the unobservable factors are accounted for in the degradation modeling. We develop the maximum likelihood estimation for the model, and propose a simulation-based algorithm for remaining useful life prediction. A simulation study is implemented to validate the performance of the proposed model, and applications to the battery degradation dataset and the outdoor coating weathering dataset are used to justify the advantages of the proposed model over the existing methods.