Degradation Modeling Using Stochastic Filtering for Systems under Imperfect Maintenance

Wiener process with a linear drift has been extensively studied in degradation modeling, mainly due to the existence of an analytical expression of the first hitting time distribution which permits feasible mathematical developments. However, a fundamental problem related to the stationary Wiener process is that it can only describe linearly drifted diffusion processes. This article is devoted to characterizing degradation phenomena with non-stationary Wiener processes. A new treatment is initiated to characterize the efficiency of imperfect maintenance, i.e., extending the improvement factor method on the degradation rate function. A stochastic filtering technique is employed to dynamically update the estimate of the degradation rate. A numerical example is given to illustrate the potential applications in real practice.