Optimization of Preventive Maintenance Interval Mohamed Grida, Zagazig University Abdelnaser Zaid, Zagazig University Ghada Kholief, Egyptian Radio and Television Union Key Words: 3-out-of-4 repairable system, Availability, preventive maintenance interval, total cost. SUMMARY & CONCLUSIONS This paper combines the normalized cost and availability metrics into one new metric: availability/normalized cost. The new metric provides single optimization objective that is used to evaluate different maintenance policies. In addition, a non- dimensional time interval is introduced to test the effect of maintenance frequency on a system performance. A Monte- Carlo simulation model is developed to investigate the performance of staggered maintenance policy versus the traditional simultaneous policy. In general, the simulation results show that the staggered policy outperforms the simultaneous one except for systems with very lengthy repairs. 1. INTRODUCTION Preventive maintenance (PM) is utilized to improve the system availability by reducing the probability of unpredictable failures [1]. Preventive maintenance consists of a set of technical, administrative and management actions to reset the components' ages to reduce the failure probability. These actions can be characterized by their effects on the component age: resetting it completely to consider the component to be ‘as good as new', reducing the component age, or just ensuring its necessary operating conditions and the component remaining appears to be ‘as bad as old' [2] and [3]. Age replacement preventive maintenance affects both system availability and expected system cost. The traditional methods focus on a single measure of performance, either cost [2], [3], [4], [5], [6], [7], [8], [9],[10] and [11], or availability [12], [1], [13], [14], [15] and [16], and do not offer a way to consider these two important system performance measures simultaneously [17], [18] and [19]. The optimum preventive maintenance interval for any system depends on factors such as failure rate, repair and maintenance time. The objective of optimizing preventive maintenance interval is to minimize the overall costs using the optimum age replacement model under assuming that components have an increasing failure rate and the cost of preventive maintenance is less than the cost of corrective maintenance. As a performance criterion of repairable systems, availability is defined as the probability that the system is properly operating when it is required for use. In risky environments, it is vital to guaranty the highest possible availability. This paper presents mathematical models, which can be used to evaluate the optimum preventive maintenance interval considering both of system costs and its availability. The model is used to investigate the effect of both of the failure probability density functions of the system components and the adoption different maintenance policies on the time interval between successive preventive maintenance actions. 2. BENEFIT AND COST MODELS OF different MAINTENANCE POLICIES In order to have a benefit / cost ratio evaluation formula, the system availability and the normalized cost per unit time are formulated. The failure of systems components is assumed to be described by Weibull distribution with shape factor β and scale factor (characteristic time) η. Notation A Availability C PM Cost of preventive maintenance per unit time C R Cost of corrective maintenance per unit time CPU Total cost per unit time f (t) Failure probability density function F(t) Failure probability function R(t) Reliability function PM Preventive maintenance h Hazard rate or failure rate t Time, t > 0 Te Expected duration of system uptime β Shape factor of Weibull distribution η Scale parameter of Weibull distribution τ Length of time interval between two consecutive maintenance actions μ PM Expected duration of PM work in each cycle μ R Expected duration of repair work in each cycle μ F Mean time to failure of the system ρ PM Ratio of μPM to η ρ R Ratio of μR to η ρa Ratio of μR to μPM = ρR / ρPM ρc Ratio of CR to CPM ρ = ρa * ρc ψ Normalized cost ratio (CPU / CPM) θ τ / η ξ t / τ The Total Cost per unit time can be calculated as [14] and [18]: