Preventive Maintenance of a Two-Unit Priority Standby System with Repair

Abstract

Optimal maintenance policies play an important role in the reliability analysis of repairable systems. This paper examines a two-unit priority standby system with a repair facility, where the priority unit is subject to preventive maintenance. In the general case, we derive necessary and sufficient conditions under which maintenance increases the mean time to system failure. When the hazard rate of the priority unit has either a bathtub-shaped or an upside-down bathtub-shaped form, we establish conditions for the existence of both a threshold time, beyond which maintenance improves the mean time to system failure, and the optimal maintenance time. Expressions to find these quantities are provided in terms of the hazard rate and the mean residual life function. Furthermore, stochastic ordering techniques are used to compare two independent systems under this model, along with their respective threshold times and optimal maintenance times.