An optimal condition-based maintenance policy for nonlinear stochastic degrading systems

Prognostics and system health management (PHM) has attracted increasing attention from both scholars and engineers with interests in improving the reliability, availability, and profitability of industrial systems. Recognized as the two prominent challenges in the prognostics of complicated degrading systems, temporal nonlinearity and stochastic dynamics have incentivized numerous research on nonlinear degradation modeling-based prognostic approaches such as diffusion-process-based models. Comparatively, much less research on how to incorporate the corresponding prognosis information into the decision making on health management has been conducted. In this paper, an optimal condition-based maintenance (CBM) policy for stochastic degrading systems characterized by a diffusion-process-based model has been presented. The CBM policy is firstly converted into a Markovian decision process (MDP) based on the expected discounted cost function (EDCF) within the infinite horizon. Then, the structural properties of the optimal CBM policy have been thoroughly investigated, and the value-based iteration algorithm to solve the optimal CBM problem is proposed. It is proved that the optimal CBM policy for a periodically inspected nonlinear degrading system governed by a diffusion process is a control limit policy, which neither increases in the degradation state nor decreases in the age of the system. Finally, the proposed optimal CBM policy has been illustrated and validated by a case study on the gyroscopes.