We consider a machine which generates income at rate I during its operating time. The machine is composed of N independent stochastically failing units. A failure of each one of the units causes a breakdown of the machine.
The machine's status (good or failed) is observed continuously, by a controller, at zero cost. In the event of a breakdown, exactly one unit is failed, and a series of inspections is performed, in order to identify the failed unit and the reasons for its failure. At any time along the inspection process only one unit can be tested.
An inspection of a given unit is characterized by its cost rate and inspection time. At the end of the inspection process, the failed unit is repaired at a known cost, and a new operating cycle is started.
Our objective is to formulate an optimal inspection strategy under two optimality criteria: long-run average net income, and total expected discounted net income.