A unified methodology of maintenance management for repairable systems based on optimal stopping theory

This dissertation focuses on the study of maintenance management for repairable systems based on optimal stopping theory. From reliability engineering’s point of view, all systems are subject to deterioration with age and usage. System deterioration can take various forms, including wear, fatigue, fracture, cracking, breaking, corrosion, erosion and instability, any of which may ultimately cause the system to fail to perform its required function. Consequently, controlling system deterioration through maintenance and thus controlling the risk of system failure becomes beneficial or even necessary. Decision makers constantly face two fundamental problems with respect to system maintenance. One is whether or when preventive maintenance should be performed in order to avoid costly failures. The other problem is how to make the choice among different maintenance actions in response to a system failure. The whole purpose of maintenance management is to keep the system in good working condition at a reasonably low cost, thus the tradeoff between cost and condition plays a central role in the study of maintenance management, which demands rigorous optimization. The agenda of this research is to develop a unified methodology for modeling and optimization of maintenance systems. A general modeling framework with six classifying criteria is to be developed to formulate and analyze a wide range of maintenance systems which include many existing models in the literature. A unified optimization procedure is developed based on optimal stopping, semi-martingale, and lambda-maximization techniques to solve these models contained in the framework. A comprehensive model is proposed and solved in this general framework using the developed procedure which incorporates many other models as special cases. Policy comparison and policy optimality are studied to offer further insights. Along the theoretical development, numerical examples are provided to illustrate the applicability of the methodology. The main contribution of this research is that the unified modeling framework and systematic optimization procedure structurize the pool of models and policies, weed out non-optimal policies, and establish a theoretical foundation for further development

An study of cost effective maintenance policies: Age replacement versus replacement after N minimal repairs

In this paper we consider the inspection and maintenance of a system under two types of age-dependent failures, revealed minor failures (R) and unrevealed catastrophic failures (U). Periodic inspections every T units of time are carried out to detect U failures, leading to the system replacement when one is discovered. R failures are followed by a minor repair. In addition the system is preventively replaced at MT or after the Nth R failure whichever comes first. The costs of minimal repair and replacement after N minor failures depend on age and history of failures. Non-perfect inspections are assumed, providing false positives when no U failure has happened or false negatives when a U failure is present. The long-run cost per unit of time along with the optimum policy (T*, M*, N*) are obtained. We explore conditions under which both strategies of preventive maintenance are profitable, comparing with suboptimal policies when only one of them is performed. Maintenance of infrastructures illustrates the model conditions

Maintenance Strategies Design and Assessment Using a Periodic Complexity Approach

People become more dependent on various devices, which do deteriorate over time and their operation becomes more complex. This leads to higher unexpected failure chance, which causes inconvenience, cost, time, and even lives. Therefore, an efficient maintenance strategy that reduces complexity should be established to ensure the system performs economically as designed without interruption. In the current research, a comprehensive novel approach is developed for designing and evaluating maintenance strategies that effectively reduce complexity in a cost efficient way with maximum availability and quality. A proper maintenance strategy application needs a rigorous failure definition. A new complexity based mathematical definition of failure is introduced that is able to model all failure types. A complexity-based metric, complication rate , is introduced to measure functionality degradation and gradual failure. Maintenance reduces the system complexity by system resetting via introducing periodicity. A metric for measuring the amount of periodicity introduced by maintenance strategy is developed. Developing efficient maintenance strategies that improve system performance criteria, requires developing the mathematical relationships between maintenance and quality, availability, and cost. The first relation relating the product quality to maintenance policy is developed using the virtual age concept. The aging intensity function is then deployed to develop the relation between maintenance and availability. The relation between maintenance and cost is formulated by investigating the maintenance effect on each cost element. The final step in maintenance policy design is finding the optimum periodicity level. Two approaches are investigated; weighted sum integrated with AHP and a comfort zones approach. Comfort zones is a new developed physical programming based optimization heuristic that captures designer preferences and limitations without substantial efforts in tweaking or calculating weights. A mining truck case study is presented to explain the application of the developed maintenance design approach and compare its results to the traditional reward renewal theory. It is shown that the developed approach is more capable of designing a maintenance policy that reduces complexity and simultaneously improves some other performance measures. This research explains that considering complexity reduction in maintenance policy design improves system functionality, and it can be achieved by simple industrially applicable approach

Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair

We analyze the optimal replacement policy for a system subject to a general failure and repair model. Failures can be of one of two types: catastrophic or minor. The former leads to the replacement of the system, whereas minor failures are followed by repairs. The novelty of the proposed model is that, after repair, the system recovers the operational state but its condition is worse than that just prior to failure (worse than old). Undertrained operators or low quality spare parts explain this deficient maintenance. The corresponding failure process is based on the Generalized Pólya Process which presents both the minimal repair and the perfect repair as special cases. The system is replaced by a new one after the first catastrophic failure, and also undergoes two sorts of preventive maintenance based on age and after a predetermined number of minor failures whichever comes first. We derive the long-run average cost rate and study the optimal replacement policy. Some numerical examples illustrate the comparison between the as bad-as-old and the worse than old conditions

Optimal Periodic Inspection of a Stochastically Degrading System

This thesis develops and analyzes a procedure to determine the optimal inspection interval that maximizes the limiting average availability of a stochastically degrading component operating in a randomly evolving environment. The component is inspected periodically, and if the total observed cumulative degradation exceeds a fixed threshold value, the component is instantly replaced with a new, statistically identical component. Degradation is due to a combination of continuous wear caused by the component\u27s random operating environment, as well as damage due to randomly occurring shocks of random magnitude. In order to compute an optimal inspection interval and corresponding limiting average availability, a nonlinear program is formulated and solved using a direct search algorithm in conjunction with numerical Laplace transform inversion. Techniques are developed to significantly decrease the time required to compute the approximate optimal solutions. The mathematical programming formulation and solution techniques are illustrated through a series of increasingly complex example problems

Using a Novel Hierarchical Coloured Petri Net to Model and Optimise Fleet Spare Inventory, Cannibalisation and Preventive Maintenance

Spare part availability is crucial to restoring inoperative platforms to the working state. Platforms failing during operation undergo corrective maintenance to replace failed components with spares. To reduce the frequency of this unplanned, corrective maintenance, platforms are inspected periodically and degraded components preventively replaced. Maintenance delays occur when spares are unavailable but cannibalisation can reduce these delays by allowing working components to be removed from inoperative platforms and used to restore other inoperative platforms. Fleets can be deployed across multiple bases that are served by one or more depots. Failed components that cannot be repaired at a base are sent to a depot for repair, along with associated requests for spares, which are satisfied by depot inventories.The management of fleet corrective and preventive maintenance, cannibalisation, spare inventories, provision of spares to bases and depots, and response of the depot to spare requests is a complex problem for fleet maintenance managers and critical to ensuring acceptable fleet performance. This paper presents a novel hierarchical coloured Petri net (HCPN) model of a fleet spare inventory system, which accounts for these issues alongside fleet deployment and mission-oriented operation. The application of the model is demonstrated using case studies of two example fleets

Determining Optimal Machine Replacement Events with Periodic Inspection Intervals

This research will examine the optimal maintenance and replacement policies for a generic machine with periodic inspection intervals. The considered reliability models consist of a single machine that can fail during operation or else may be found to be inoperative during regularly-scheduled maintenance inspections. A distinction will be made between spontaneously-occurring failures during operation and those that are discovered during inspections. Since the elapsed time between inspections is constant, the resulting stochastic reliability process becomes non-Markovian, and thus a Semi-Markov Decision Process (SMDP) framework must be employed in order to determine the cost-optimal stationary policy consisting of repair and replace decisions and inspection intervals. Using the methodology developed here, a system controller will be able to readily develop an inspection-based strategy to optimize the overall costs of maintaining systems with a variety of failure characteristics over a finite time horizo

Prognostics-Based Two-Operator Competition for Maintenance and Service Part Logistics

Prognostics and timely maintenance of components are critical to the continuing operation of a system. By implementing prognostics, it is possible for the operator to maintain the system in the right place at the right time. However, the complexity in the real world makes near-zero downtime difficult to achieve partly because of a possible shortage of required service parts. This is realistic and quite important in maintenance practice. To coordinate with a prognostics-based maintenance schedule, the operator must decide when to order service parts and how to compete with other operators who also need the same parts. This research addresses a joint decision-making approach that assists two operators in making proactive maintenance decisions and strategically competing for a service part that both operators rely on for their individual operations. To this end, a maintenance policy involving competition in service part procurement is developed based on the Stackelberg game-theoretic model. Variations of the policy are formulated for three different scenarios and solved via either backward induction or genetic algorithm methods. Unlike the first two scenarios, the possibility for either of the operators being the leader in such competitions is considered in the third scenario. A numerical study on wind turbine operation is provided to demonstrate the use of the joint decision-making approach in maintenance and service part logistics