Maintenance policies for protection systems with imperfect inspection and imperfect repair

In this study, we investigate the optimal maintenance policies for stochastically deteriorating protection systems with imperfect inspections and imperfect repairs. We model the system’s degradation as a continuous-time Markov chain with three states: good, poor, and failed. Six unique maintenance policies are considered, ranging from minimal intervention to immediate replacement upon any detected deviation from the good state. Our objective is to determine the optimal policy and inspection period that minimize the long-term maintenance cost rate. Through numerical examples, we demonstrate that maintenance policies which account for the inherent imperfections and are tailored to the system parameters can result in significant gains. We also assess the value of removing imperfections in the inspection or repair practices so that managers can focus their improvement efforts on the most promising activities. The original contribution of this study is the explicit construction and determination of the optimal maintenance policies specifically designed for protection systems that are subject to imperfect inspections and imperfect repairs. We develop a versatile model that facilitates a comparative evaluation of these policies, along with a sensitivity analysis regarding the uncertainty introduced by both the risky deterioration process and the imperfections in inspection and intervention actions.