Optimal preventive maintenance policy for a system subject to two-phase imperfect inspections

Inspections are essential to finding the health status of a system. However, inspections are usually imperfect, which may not always reveal the true state of the system. Most of research on imperfect inspections of degrading systems focuses on one-phase inspections, but a multi-phase inspection strategy may be more flexible and efficient. In this paper, a two-phase imperfect inspection strategy is considered along with a hybrid preventive maintenance policy for a three-state system. To minimize the maintenance cost, the optimal inspection interval and number of inspections in each phase are obtained based on the renewal reward theorem. Numerical examples are provided to illustrate the proposed method and to explore some managerial insights. To show the advantages of the proposed method, several special models, such as perfect inspection model, one-phase inspection model, and pure inspection model, are presented for comparison. One can see that taking account of imperfect inspections in maintenance management is important, the two-phase inspection policy is generally better than the one-phase inspection, and the pure inspection model might be cost-optimal for the system with a constant defect rate.