Optimal Preventive Maintenance Policies for Unreliable Queueing and Production Systems

Title of Dissertation: OPTIMAL PREVENTIVE MAINTENANCE POLICIES FOR UNRELIABLE QUEUEING AND PRODUCTION SYSTEMS Xiaodong Yao, Doctor of Philosophy, 2003 Dissertation directed by: Professors Steve I. Marcus and Michael C. Fu Department of Electrical and Computer Engineering Preventive Maintenance (PM) models have traditionally concentrated on utilizing machine “technical” state information such as the degree of deterioration. However, in real manufacturing systems, additional system operational information such as work-in-process (WIP) inventory levels critically impact actual PM decisions. Surprisingly, the literature on models incorporating this important aspect is relatively sparse. This thesis attempts to fill some of the research gaps in this area by considering problems of optimal preventive maintenance explicitly under the context of unreliable queueing and production-inventory systems. We propose a two-level hierarchical modeling framework for PM planning and scheduling problems. In the higher level, our objective is to characterize structure of optimal PM policies. We start with a simple case in which queueing is not taken into account in the model. We show that a randomized PM policy, like the widely used “time-window” policy in industry, is in general not optimal. We then consider the problem of optimal PM policies for an M/G/1 queueing system with an unreliable server. The decision problem is formulated as a semi-Markov decision process. We establish some structural properties, e.g., “control-limit” type structure, that optimal policies will satisfy. We then take the optimal PM problem a step further by considering optimal joint PM and production control policies for unreliable production-inventory systems with time-dependent or operation-dependent failures. We show the optimal joint policies retain the “control-limit” type structure in terms of the PM portion of the policy. For the production portion of the policy, some properties are also derived, but numerical studies show that in general optimal policies have more complicated structure than the simple control-limit form. The last part of the thesis is devoted to the lower level of the framework where the objective is to optimally schedule multiple PM tasks across a group of tools. We take into account information such as interdependence of PM tasks, WIP data and resource constraints, and formulate the problem as a mixedinteger program. Results of a simulation study comparing the performance of the model-based PM schedule with that of a baseline reference schedule are presented to illustrate the fitness of our solutions. OPTIMAL PREVENTIVE MAINTENANCE POLICIES FOR UNRELIABLE QUEUEING AND PRODUCTION SYSTEMS