Condition-based maintenance policy for deteriorating systems based on Wiener process with heterogeneous spare unit population and partial observation

We consider a single-unit system that deteriorates following a Wiener process. The deterioration state is partially observed by a monitoring device at equally spaced time intervals. Based on this information, one of two actions, replacement or keep operating, is selected. Under operation, the unit for replacement deteriorates at different rates due to population heterogeneity, which is reflected in the assumption that the unique deterioration rate of each spare unit follows a general distribution. The unit deterioration rate and state are estimated based on the history of partial observations. Considering both uncertainties, we formulated the optimal decision-making problem for condition-based maintenance using a partially observable Markov decision process. We showed that the total expected discounted cost is non-increasing in operating time and non-decreasing in both the observed deterioration state and the believed deterioration state. We also showed that the optimal maintenance policy that minimizes the total expected discounted cost over an infinite horizon, is a control limit policy. A case study on lithium-ion batteries demonstrated that the optimal policy can be obtained by solving the optimal decision-making problem. Sensitivity analysis with population heterogeneity and partial observation revealed that the proposed optimal maintenance policy is superior to two heuristic policies.