Prognostics Based on Stochastic Degradation Process: The Last Exit Time Perspective

Degradation-model-based remaining useful life (RUL) estimation is essential for effective prognostic and health management; this method can provide information for enabling effective maintenance decisions pertaining to degrading systems to avoid or mitigate loss due to impending failures. According to existing studies that estimate degradation-model-based RUL, stochastic-process-based methods are widely advocated by many researchers because they can capture stochastic dynamics within the degradation processes of systems. However, most existing studies primarily utilize the first passage time (FPT) to define the lifetime/RUL. The definition is generally conservative; thus, the lifetime/RUL estimation may be underestimated. This is particularly true for nonmonotonic stochastic degradation processes. In some extreme cases, with strong fluctuations within the degradation processes, the estimated lifetime/RUL under the FPT can be significantly less than the actual lifetime/RUL. To address this limitation, this study investigates prognostic issues, based on the stochastic degradation process, from the last exit time (LET) perspective. In contrast to the FPT, the lifetime/RUL of the degrading system is defined as the LET of its degradation process, i.e., the instant at which the degradation process passes the failure threshold for the last time. Given the new definition, we consider the most widely used degradation process model (i.e., Wiener-process-based model) as an example to demonstrate how the lifetime/RUL is estimated. Two general methods of lifetime estimation for the Wiener-process-based model are given, and some examples with associated exact and closed-form solutions are also provided for better illustration. Finally, numerical examples and a practical case study are presented to substantiate the theoretical results and illustrate the superiority of the proposed method. The results imply that the proposed method exhibits the potential to prevent premature maintenance and resource wastage because the lifetime/RUL estimation from the LET perspective can help avoid conservative results from being obtained.