This paper proposes a joint optimal policy of inspection and age based replacement based on a three-stage failure process to jointly optimize the inspection and replacement intervals. The three-stage failure process divides the failure process of system into three stages: namely normal, minor defective and severe defective. When the minor defective stage is identified, the subsequent inspection interval is halved. Once identifying the severe defective stage, the maintenance action is carried out immediately. The system is replaced once it reaches the certain age. Finally, a numerical example is presented to demonstrate the efficiency of the proposed model.
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