A Preventive Maintenance Model with Periodic and Random Inspection Policy for a Three-stage Failure Process

Inspection is an effective method to guarantee the safety and reliability of the components and systems. For some systems executing jobs with random working times, implementing a comprehensive inspection at fixed periodic interval would disrupt the ongoing job. Therefore it would be cost-effective to inspect these systems thoroughly at the completion of every N jobs, which is named as random inspection policy. Considering such systems, a new model is proposed by combining the random and periodic inspection policy based on a three-stage failure process. The whole life cycle of the system is divided into three independent phases: normal, minor and severe defective stages. Two-level inspections are employed in this model. The minor inspections are performed at a fixed periodic interval, which can identify the minor defective stage with a certain probability but detect the severe defective stage perfectly. The major inspections are performed when every N jobs is completed, which can completely reveal both minor and severe defective stages. When the system is found in minor defective stage, the minor inspection interval will be shortened. If the severe defective stage is identified, instead of maintaining the system immediately, the maintenance action will be postponed to the completion of the current job. Numerical examples and comparisons with other models are presented to demonstrate the correctness, generality and economy of the model.