Abstract: In general, every system is in one of the three states: normal, abnormal, or failure state. When the system is diagnosed as abnormal state, it needs predictive maintenance. If the system fails, an identical new one will replace it. The predictive maintenance cannot make the system “as good as new”. Under these assumptions, the reliability index and the inspection-replacement policy of a system were studied. The explicit expression of the reliability index and the average income rate (i.e., the long-run average income per unit time) are derived by using probability analysis and vector Markov process method. The criterion of feasibility for the optimal inspection-replacement policy under the maximum average income rate is obtained. The numerical example shows the optimal inspection-replacement policy can raise the average income rate when the optimal inspection-replacement policy is feasible.

Key words: Inspection-replacement policy, Inspection and diagnosis, Monotone stochastic process, Reliability index, Vector Markov process method

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