Optimal policies with decreasing probability of imperfect maintenance

This study applies periodic preventive maintenance to three repair models: major repaired, minimal repaired, or fixed until perfect preventive maintenance upon failure. Two types of preventive maintenance are performed, namely imperfect preventive maintenance, and perfect preventive maintenance. The probability that preventive maintenance is perfect depends on the number of imperfect maintenance operations performed since the last renewal cycle. Mathematical formulas for the expected cost per unit time are obtained. For each model, the optimum preventive maintenance time T^*, which would minimize the cost rate, is discussed. Various special cases are considered. A numerical example is presented.