2022 Volume 7 Issue 2 Pages 89-101
Condition-based maintenance is preventive maintenance in which an appropriate maintenance action is taken on the basis of the system’s underlying condition before failure. The underlying condition is continuously or periodically observed by a sensor. In most research on condition-based maintenance, the accuracy of the sensor was assumed to not change over time. However, in actuality, not only the system but also the sensor deteriorates over time. In this research, we considered a multi-state system that deteriorates in accordance with a discrete-time Markov chain. It is assumed that the underlying deterioration state is observed periodically by a sensor with accuracy that degrades over time. After each observation, a decision maker chooses one of three actions: continue operating system, replace only system, and replace both system and sensor. We formulated the optimization problem of condition-based maintenance for both the system and sensor using a partially observable Markov decision process. The objective is to minimize the total expected discounted costs (both operation and maintenance of system and sensor) over an infinite horizon. We analytically show that, under certain sufficient conditions, the total expected discounted costs are monotonically non-decreasing with respect to the state probability vector of the system and the age of the sensor. Moreover, the optimal policy has a threshold-type structure. We also provide a numerical example illustrating the properties obtained. These properties are useful for many practical purposes, such as determining thresholds for changing the maintenance action.
