Structural Property of Inspection and Maintenance Policies for Partially Observable Systems with Three Deterioration States

This research deals with an optimization problem for condition-based maintenance which makes it possible to prevent system failures and troubles. In condition-based maintenance, the deterioration state of the target system is continuously observed by a monitoring device, and an appropriate maintenance is performed based on the observation information. However, sometimes it is difficult to fully grasp the deterioration state of the system from the information obtained from the monitoring device. Therefore, it is necessary to determine maintenance policies that consider the incomplete observation. In this research, the deterioration process of a system with one failure state and three deterioration states is represented by a hidden Markov chain. The optimal maintenance decision-making problem is formulated by a partially observable Markov decision process (POMDP). Based on the incomplete observation information and maintenance history, the decision-maker decides whether or not to carry out inspections and replacements. The structure properties of the optimal maintenance policy that minimizes the total expected discount cost over an infinite horizon is discussed widely. Most of the previous research assumes that the transition probability matrix representing the deterioration state has a property of totally positive of order 2. In this study, we relax this condition to a property of stochastically increasing. We also assume that the observation matrix that expresses the accuracy of the monitoring device has the property of totally positive of order 2. Under these conditions, we derive that the optimal maintenance policy is given by a policy under which the information space is divided into at most three regions. In addition, we provide discussions on inspection behaviors and optimal policies based on some simulation results.