Modeling of Degradation Processes to Obtain an Optimal Solution for Maintenance and Performance

This paper presents an approach to represent equipment degradation and various maintenance decision processes based on Markov processes. Non-exponential holding time distributions are approximated by inserting multiple intermediate states between the two different degradation states based on a phase-type distribution. Overall system availability then is numerically calculated by recursively solving the balance equations of the Markov process. Preliminary simulation results show that the optimal preventive maintenance intervals for two repairable components system can be achieved by means of the proposed method. By having an adequate model representing both deterioration and maintenance processes, it is also possible to obtain different optimal maintenance policies to maximize the availability or productivity for different configurations of components. INTRODUCTION Since modern manufacturing systems have become highly automated and mechanized, the impact of unplanned downtime caused by system failures are worse than ever. Unplanned downtime of equipment might not only reduce line productivity but also affect the quality control of the products. Another consequence of system failures is the escalation of maintenance expenses due to unpredictable maintenance. Therefore, identifying a cost effective maintenance program is becoming one of the key objectives in the production line [1-4]. It has been recognized that maintenance is not an isolated technical discipline but an integral part of the competitive plant operations [5]. To examine the trade-offs between maintenance and operation costs, a mathematical model should be developed to estimate an appropriate maintenance policy and relevant system performance measurements. A set of Markov processes has been used to mimic the effect of non-exponential holding time distributions that are often needed in the maintenance policy. Even though semiMarkov processes have been employed to model multi-state deteriorating systems by allowing the holding time distributions to be non-exponential, it is well-known that the mathematical formulations of semi-Markov models [6, 7] are so complicated that they are not analytically tractable. Non-exponential holding time distributions can be approximated by inserting multiple intermediate states between the two degradation states [8-11]. In general, the system consists of more than a single unit. If all units in the system are stochastically independent of one another, a maintenance policy for the single unit model [12, 13] may be applied to the multi-unit maintenance problems. On the other hand, if any units in the system are stochastically dependent on each other, then an optimal decision on maintenance of one unit is not necessarily the optimum for the entire system [14]. A decision must be made to improve the whole system rather than any single subsystem. Therefore, we must also investigate optimal maintenance policies for a multiunit system, which may or may not depend on each other. Although the complexity of a multi-unit system poses challenges in finding the optimal maintenance policies, this may introduce an opportunity for a group replacement of several components provided that a joint replacement cost is less than that of the separate replacements of the components [15]. For a system consisting of only two identical components which are subject to exponential failure, Berg [16,