Optimal inspection and preventive maintenance of units with revealed and unrevealed failures

The maintenance of a single unit system that alternates operating and idle periods is studied. In the former case the failures are detected as soon as they occur and only by special testing or inspection in the latter. This paper aims at minimizing the cost per unit of time for an infinite time span by selection of a unique interval, for both inspection and maintenance. A special feature of this model is the possibility of a less than perfect testing as the inspections may fail and give a wrong result. It is further assumed that both preventive and corrective maintenance make the unit as good as new with the durations of inspections and maintenances being negligible. The existence of an optimum interval and how it depends on both the cost parameters and the reliability characteristics of the unit is discussed.