An inspection-repair-replacement model for a deteriorating system with unobservable state

In this paper, an inspection-repair-replacement (IRR) model for a deteriorating system with unobservable state is studied. Assume that the system state can only be diagnosed by inspection and an inspection is imperfect. After inspection, if the system is diagnosed as being in a down state, a minimal repair will be undertaken, otherwise we do nothing. Assume further that the system lifetime is a random variable having increasing failure rate. A feasible IRR policy is studied. An algorithm is then suggested for determining an optimal feasible IRR policy for minimizing the long-run average cost per unit time after a finite-step search.