Maintaining Partially Observed Systems With Imperfect Observation and Resource Constraint

The problem of finding the optimal maintenance policy for partially observed systems is considered, where only a limited number of maintenance actions can be performed. The maintenance is assumed to be imperfect in that the system can be only restored to a less deteriorated level rather than to a state as good as new. In addition, the true deterioration state is known just after each replacement action, but the deterioration state at other instants during the system's operation cannot be observed, evolving as a discrete-time Markov chain with a finite state space. In this paper, the described problem can be formulated as a partially observed Markov decision process (POMDP) over the infinite time horizon. To increase the computational efficiency, several key structural properties are developed through minimizing the total expected cost per unit time. The existence of the optimal threshold-type maintenance policy is strictly proved, and the monotonicity of the threshold is obtained. The effectiveness of the optimal policy can be verified by a numerical example.