Optimal maintenance models with minimal repair, periodic overhaul and complete renewal

This paper investigates the maintenance decision situation in which three actions, minimal repair, periodic overhaul and complete renewal, may be applied to the system under consideration. A new mathematical model is proposed to describe system improvement due to the maintenance action of an overhaul that differs from the virtual age approach by considering a direct reduction on the system’s failure rate. Based on this improvement model, two cost models for determining the optimal overhaul interval and the number of overhauls in a renewal cycle, that minimize the expected unit-time cost or the total discounted cost, are established. Existence conditions of optimal solutions are obtained and special cases of the two cost models are discussed.