A computational model for determining the optimal preventive maintenance policy with random breakdowns and imperfect repairs

We consider a system that is subject to random failures, and investigate the decision rule for performing renewal maintenance or preventive replacement (PR). This type of maintenance policy involves two decision variables. The first decision variable is the time between preventive replacements, or a fixed cycle time. To avoid unnecessary renewals or replacements at the end of a cycle, a cut-off age is introduced as the second decision variable. At the end of every cycle, if the system's virtual age is equal to or greater than the cut-off age, it will undergo a renewal or replacement; otherwise the renewal decision will be postponed until the end of the next cycle. Random failures can occur, however; and the system receives emergency imperfect repairs (ER) at these times. Hence, within a PR cycle, a second decision time is identified. If an ER occurs 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, PR which follow on too closely after an ER are avoided, thus saving the unnecessary expense. We develop a computational model to determine the optimal maintenance policy with these two decision variables.