Cost Optimization of Periodic Preventive Maintenance

Most preventive maintenance(PM) models assume that the hazard function of a system after each PM occurrence is restored to like new or to some specified level. Thus, there is no provision for system degradation with time. Operation of many systems causes stress which results in system degradation and hence an increase in the level of the hazard function with time. PM is assumed to relieve stress temporarily and hence slow the rate of system degradation. However, this type of activity does not reverse degradation; so the hazard function is monotone. A hazard function is developed in this paper consistent with this concept of PM effect. The special case for which PM reduces the operational stress to that of a new system is considered in greater detail (eg, a new system begins operation with the full benefit of a PM activity; each subsequent PM completely restores the benefits). It is shown for this case that the hazard function under PM is approximately a 2-parameter Weibull with shape parameter 2 for systems with strictly increasing hazard without PM. Cost optimization of the PM intervention interval is obtained by determining the average cost-rate of system operation. When the hazard function without PM is unknown, optimization may be achieved through an iterative process. This avoids the necessity of estimating system failure characteristics without PM; such testing can be destructive or use expensive equipment.