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.