An optimal inspection policy for a storage system with three types of hazard rate functions

A system such as missiles and spare parts of aircrafts has to perform a normal operation in a severe environment at any time when it is used. However, the system is in storage for a long time from the transportation to the usage and its reliability goes down with time. Thus, a system in storage should be inspected and maintained at periodic times to hold a high reliability. But, the authors do not wish to inspect a system too often because each inspection involves a cost and sometimes degrades it. Therefore, they have to establish an optimal inspection policy for such a storage system. This paper considers a periodic inspection policy for a storage system with unit 1 and unit 2: Unit 1 is inspected and maintained at each inspection, however, unit 2 is degraded with time and at each inspection. Three hazard rate functions of the system are defined and its reliability is derived. Using this result, the mean time to failure and the expected number of inspections before failure are computed. Further, the expected total cost until detection of failure is obtained and an optimal policy to minimize it is discussed. Numerical examples are finally given.