Modeling systems with revealing and non-revealing failures undergoing periodic inspection

In this study, the inspection policy for a single-unit randomly failing system with alternating operating and inactivity periods is proposed. Failures are detected instantly for the former case, whereas in the latter case, inspections are required for failure detection. This article focuses on evaluating the general expressions for limiting availability and long-run average cost of the system undergoing periodic inspections. The distinctive characteristic of the proposed model is that the inspections are not perfect. Furthermore, it is supposed that inspection and maintenance time are non-negligible, and corrective maintenance results in as good as new unit. The optimal inspection problem is developed predicated on maximizing the availability and minimizing the cost. Numerical example of electric motor corresponding to different life distributions is also presented to justify the obtained results.