Optimal maintenance policy considering imperfect repairs and non-constant probabilities of inspection errors

During system operation, inspections are usually scheduled to detect the signals of defects. Due to the human, measurement or environment errors, inspections are generally imperfect which reveal the real states of the system with non-constant probabilities. When an inspection concludes a defect, necessary preventive maintenance actions should be carried out. In most existing literatures, perfect preventive maintenance, like replacement, is studied. However, in practice, most defects are imperfectly repaired rather than being replaced because of limitations of resources, technologies or time. Thus, considering both imperfect inspections and imperfect repairs, a novel preventive maintenance policy is investigated for a three-state system. Cost rate and reliability of the system are derived by a recursive method. The problem of optimal maintenance policy is formulated by minimizing the cost rate over an infinite time horizon. An algorithm is proposed to obtain the optimal inspection interval and preventive replacement interval. Finally, several numerical examples are given to illustrate the proposed method and verify the correctness of the method.