An optimal maintenance policy for skipping imminent preventive maintenance for systems experiencing random failures

In this study we investigate systems that experience random failures and establish decision rules for performing renewal maintenance; that is, a preventive replacement (PR) policy. We seek a policy that is both simple to execute from the point of view of the maintenance planner but also a policy that is an improvement on existing schemes. We show that our policy is a hybrid of traditional time-based and age-based schemes and one that yields considerable cost savings. Our hybrid policy involves two decision variables. One decision variable is the time between PRs. Hence, for the maintenance planner, the times at which PRs are performed are chronologically fixed. Random failures can occur, however, and the machine receives an emergency renewal (ER) at these times. Hence, within these chronological times, a second decision time is identified. Should an ER occur between the start of a cycle and this second decision time, then the planned PR would still be performed at the end of the cycle. However, if the first ER occurs after this second decision time, then the PR at the end of the cycle is skipped over and the next planned PR would take place at the end of the subsequent cycle. With this simple mechanism, PRs that follow on too closely after an ER are avoided, thus saving the unnecessary expense. Numerical examples are given to examine the validity of the model, using four different failure density functions, namely Weibull, normal, uniform, and negative exponential.