Periodical Maintenance Modelling and Optimisation Assuming Imperfect Preventive Maintenance and Perfect Corrective Maintenance

Abstract: In this paper, a periodic maintenance model is formulated assumingcontinuous monitoring, imperfect preventive maintenance (PM) and perfect correctivemaintenance (CM) using three decision variables, (I, N, Z). The model is derived in aninfinite horizon context where the mean cost per unit time is modelled. PM actionsare performed N − 1 times at time instants iT for i = 1, ..., N − 1, where T = ∆T · Iand ∆T is a fixed positive number representing the minimum time allowed betweenPM actions and I is a time interval multiple representing the decision of how oftenPM actions should be performed. The N:th maintenance activity is either a plannedreplacement (if Z = 0) or a corrective replacement from letting the component runto failure (if Z = 1). Imperfect PM is modelled using age reductions, either using aconstant r or a factor γ. Previous research on assumptions of these types has beenlimited as the assumptions yield models of high complexity which are not analyticallytractable. However, assumptions of this type are considered more realistic than othermore thoroughly researched assumptions, using e.g. minimal CM. Therefore, twocomplimentary optimisation methods are proposed and evaluated, namely, completeenumeration and a specially derived genetic algorithm which can be used for differentproblem sizes respectively. Carefully determined solution bounds enabled completeenumeration to be applicable for many input parameter values which is a great strengthof the proposed model.