A condition-based preventive replacement policy with imperfect manual inspection for a two-stage deterioration process

This article proposes a novel preventive replacement policy based on condition monitoring and imperfect manual inspection for systems subject to a two-stage deterioration process, where the two-stage deterioration process is modeled by the white noise process and Brownian motion with a drift, respectively. The proposed preventive replacement policy is implemented using two thresholds: a failure threshold and a preventive threshold. Specifically, if the condition monitoring measurement is observed to cross the failure threshold, then the failure replacement will be carried out; and, if the condition monitoring measurement is observed to cross the preventive threshold while lower than the failure threshold, then the system needs to be checked by manual inspection, and the preventive replacement will be carried out once the system is found to be in the defective state. In this article, we consider that manual inspection is imperfect, namely, there is a probability that the defect will be unnoticed. By minimizing the expected cost per unit time, we obtain the optimal condition monitoring interval and preventive threshold. A numerical example is provided to demonstrate the performance of the proposed condition-based replacement policy. Comparisons are made with the existing work, which shows the effectiveness and superiority of the proposed policy.