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In this study, we comparatively evaluate various maintenance policies for systems subject to continuous-time Markovian deterioration, which may result in non-self-announcing failures. The decision maker inspects the system periodically at the decision epochs, identifies the current state, i.e., good, poor, or failed, and chooses an available action, i.e., do-nothing, repair, or replace. When the system fails, failure will not be detected until the next inspection epoch. The objective is to minimize the expected long-run cost rate, which consists of various components such as inspection, downtime, and maintenance costs. We provide numerical examples to analyze the effect of various cost parameters on the optimum inspection period and policy, and to demonstrate a practical application.
Keleş et al. (Mon,) studied this question.