An Optimal Imperfect Maintenance Policy for a Partially Observed System With Obvious Failures and Limited Repairs

In this paper, we investigate an imperfect maintenance optimization problem for a multi-state, Markovian deterioration system with obvious failures under repair restriction based on those non-periodically collected sensor information. Our aim is to adaptively schedule observations and other maintenance actions with taking imperfect maintenance effect into consideration. Different from most existing works, imperfect maintenance here means that repair action can not only restore the system to a less deteriorated level instead of the good-as-new state but also accelerate the deterioration process so that the system can be repaired only a limited number of times before it must be replaced with a new one. Assuming that the system's deterioration state evolves as a discrete-time Markov chain with a finite state space, and then choosing the information state together with the number of completed repair times as state variable, we formulate the problem as a Markov decision process over an infinite time horizon. In order to increase the computational efficiency, several key structural properties are developed by minimizing the long-run average cost per unit time. Then, special algorithms are proposed to find the optimal maintenance policies. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithms.