Residual Useful Life Estimation Based on a Time-Dependent Ornstein-Uhlenbeck Process

Abstract

Residual useful life plays a core role in the field of the prognostics and health management of systems. For deteriorating systems or devices it can be estimated by establishing a good-fitting stochastic process model and solving corresponding first passage problem with the given failure level. In this paper, providing that the mean and variance function of the degradation process are given or obtained directly from observed data by statistical/empirical techniques, we propose a time-dependent Ornstein-Uhlenbeck process whose mean and variance are equal to the given mean and variance respectively. Based on this diffusion process, when a failure level is considered, the first passage failure distribution can be solved by a Volterra integral equation of second class. Furthermore, with the help of numerical methods, the residual useful life estimation is considered for a real case.