Abstract: A method was proposed to determine preventive maintenance time for repairable and maintainable systems. The life cycle was defined by building the joint density function of working time and maintenance time. Considering the profit during working time and the loss during maintenance time， the function between unit time profit expectation and preventive maintenance time T in a life cycle was confirmed by applying the theory of mathematical expectation of random variable function. The optimal objective is to maximize the unit time profit expectation. Newton’s method was used to confirm the optimal preventive maintenance time， then the corresponding reliability would be confirmed based on the optimal objective. A numerical example showed that the proposed model is valid.The distribution parameter effect on the optimum preventive maintenance time was analyzed.

Key words: preventive maintenance time, unit time profit expectation, optimization, working time, maintenance time