A new age-dependent degradation model based on diffusion process

Abstract

The last decades have witnessed the development of degradation modeling based remaining useful life (RUL) estimation, especially for Wiener process based degradation models. However, most researchers paid their attention to the drift coefficient representing the degradation rate, while much fewer eyes focus on the diffusion coefficient. The under consideration of diffusion process may cause bias in degradation modeling and RUL estimation, when the concerned system has volatile degradation path. Therefore, this paper construct a new kind of age-dependent degradation model based on diffusion process with time-dependent drift and diffusion coefficient. Unlike most existing models, the degradation process' temporal variance is assumed to be proportional to the instantaneous expectation of the degradation process. By doing so, volatile degradation process can be modelled. The exact lifetime and RUL distributions under the concept of first hitting time (FHT) are derived, and normal random-effect are incorporated to depict the unit-to-unit variability within degradation process. The maximum likelihood estimation method based on historical degradation data is presented. Through a specific degradation model and its application to the data of accelerators, the presented degradation model has been illustrated and validated.