Optimal periodic preventive maintenance schedules with improvement factors depending on number of preventive maintenances

This paper considers a periodic preventive maintenance policy under which each preventive maintenance reduces the hazard rate of the repairable system, while keeping the pattern of hazard rate unchanged. For this model, the hazard rate at a given time t is affected by the improvement factor which depends on the number of PMs conducted until t. In addition to the periodic preventive maintenance, the system undergoes the minimal repair at each failure between the preventive maintenances. We derive mathematical formulas to evaluate the expected cost rate per unit time by computing the expected number of failures depending on the hazard rate of the underlying life distribution of the system. Assuming that the system is replaced by a new one at the N-th preventive maintenance, the optimal values of N and the preventive maintenance period, which minimize the expected cost rate, are solved and thus the best schedules for the periodic preventive maintenance policy are established. Explicit solutions for the optimal schedule for the periodic preventive maintenance are presented when the failure times follow the Weibull distribution.