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

Some contributions to modeling usage sensitive warranty servicing strategies and their analyses

Providing a warranty as a part of a product\u27s sale is a common practice in industry. Parameters of such warranties (e.g., its duration limits, intensity of use) must be carefully specified to ensure their financial viability. A great deal of effort has been accordingly devoted in attempts to reduce the costs of warranties via appropriately designed strategies to service them. many such strategies, that aim to reduce the total expected costs of the warrantor or / and are appealing in other ways such as being more pragmatic to implement - have been suggested in the literature. Design, analysis and optimization of such servicing strategies is thus a topic of great research interest in many fields. In this dissertation, several warranty servicing strategies in two-dimensional warranty regimes, typically defined by a rectangle in the age-usage plane, have been proposed, analyzed and numerically illustrated. Two different approaches of modeling such usage sensitive warranty strategies are considered in the spirit of Jack, Iskandar and Murthy (2009) and Iskandar (2005). An `Accelerated Failure Time\u27 (AFT) formulation is employed to model product degradation resulting due to excessive usage rate of consumers. The focus of this research is on the analysis of warranty costs borne by the manufacturer (or seller or third party warranty providers) subject to various factors such as product\u27s sale price, consumer\u27s usage rate, types and costs of repair actions. By taking into account the impact of the rate of use of an item on its lifetime, a central focus of our research is on warranty cost models that are sensitive to the usage rate. Specifically, except the model in Chapter 4 where the rate at which an item is used is considered to be a random variable; all other warranty servicing policies that we consider, have usage rate as a fixed parameter, and hence are policies conditional on the rate of use. Such an approach allows us to examine the impact of a consumer\u27s usage rate on the expected warranty costs. For the purpose of designing warranties, exploring such sensitivity analysis may in fact suggest putting an upper limit on the rate of use within the warranty contract, as for example in case of new or leased vehicle warranties. A Bayesian approach of modeling 2-D Pro-rated warranty (PRW) with preventive maintenance is considered and explored in the spirit of Huang and Fang (2008). A decision regarding the optimal PRW proportion (paid by the manufacturer to repair failed item) and optimal warranty period that maximizes the expected profit of the rm under different usage rates of the consumers is explored in this research. A Bayesian updating process used in this context combines expert opinions with market data to improve the accuracy of the parameter estimates. The expected profit model investigated here captures the impact of juggling decision variables of 2-D pro-rated warranty and investigates the sensitivity of the total expected profit to the extent of mis-specification in prior information

Commande optimale stochastique appliquée à la gestion de capacité des systèmes dynamiques en environnement manufacturier

Le travail presente dans cette these porte sur I'approche integree de gestion optimale de production, de capacite, de remplacement, de maintenance corrective et preventive des ressources d'un systeme manufacturier. Lesdites ressources sont sujettes a une degradation progressive dans un environnement caracterise par des incertitudes. Le travail est developpe en quatre (04) phases. Dans la premiere phase, une etude est menee sur I'impact de I'introduction des strategies de maintenance corrective des equipements sur les decisions d'acquisition de capacite et de planification de la production. Le systeme constitue de plusieurs machines est modelise par un processus qui depend de la politique de maintenance corrective. Le probleme d'optimisation est ensuite resolu par des methodes numeriques. L'introduction des stratégies de maintenance corrective dans le modele propose permet d'ameliorer la disponibilite des machines et reduit le cout total encouru, compare aux modeles existants. Cependant, dans cette premiere phase, nous ne tenons pas compte de la degradation de la machine, phenomene pourtant inherent en contexte manufacturier. En effet, les machines des systemes de production sont remplacees a long terme, ce qui demontre qu'il y a une degradation progressive. La deuxieme phase du travail a permis de prendre en compte cette realite. Pour cela, nous avons travaille sur des machines pour lesquelles le vieillissement se traduit par l'age que prend la machine chaque fois qu'une piece est fabriquee. De plus, le temps de reparation de ces machines croit avec le nombre de pannes. Une approche de recherche simultanee des strategies de production, de reparation et du remplacement de la machine est utilisee pour determiner les politiques optimales de reparation, de remplacement et de production. Bien que les temps de reparation deviennent de plus en plus longs au fil des reparations, dans cette phase, nous considerons que les activites de maintenance permettent de remettre l'age de la machine a zero, ce qui n'est pas realiste. D'ou I'apport de la prochaine phase. Dans la troisieme phase, les machines apres reparation ont un age non nul, appele age virtuel de la machine. Une approche hierarchique de prise de decision permettant au premier niveau de determiner la politique de reparation/remplacement de la machine et au second niveau la politique de production est utilisee. EUe montre que sous des hypotheses raisonnables, les decisions de reparation ou de remplacement peuvent etre fondees sur I'age de la machine et le nombre de paimes. Le niveau operatioimel de gestion peut ensuite determiner un plan de production pour le systeme en tenant compte de ces decisions. Les phases deux (02) et trois (03) de notre travail apportent une contribution importante. Elles permettent de montrer que le nombre de pieces a mettre en stock pour se proteger des penuries durant les periodes de non production n'augmente pas seulement avec l'age de la machine, mais qu'il augmente egalement avec le nombre de paimes. Nous ne pouvions conclure ce travail sans explorer l'impact de I'introduction des stratégies de maintenance preventive. En effet, la maintenance preventive est une des pratiques les plus courantes dans I'industrie manufacturiere. Elle permet d'ameliorer la disponibilite des equipements lorsque ces demiers subissent une degradation progressive et nous 1'avons integree dans la demiere phase. Dans la quatrieme phase de ce travail, nous introduisons la strategic de maintenance preventive et analysons son effet sur les differentes politiques. Le systeme est modelise par un processus qui prend en compte la deterioration et la maintenance preventive. Le modele est resolu par des methodes numeriques. Des analyses de sensibilite sont elaborees pour montrer la pertinence de I'approche et I'impact de I'introduction des strategies de maintenance preventive

Semi-Markov and delay time models of maintenance

This thesis is concerned with modelling inspection policies of facilities which Qraduallv deteriorate in time. The context of inspection policies lends itself readily to probabilistic modelling. Indeed, many of the published theoretical models to be found in the literature adopt a Markov approach, where states are usually 'operating', 'operating but fault present', and 'failed'. However, most of these models fail to discuss the 'fit' of the model to data,a nd virtually no exampleso f actual applications or case-studiesa re to be found. hi a series of recent papers dating from 1984, a robust approach to solve these problems has been introduced and developed as the Delay Time Model (DTM). The central concept for this model is the delay time, h, of a fault which is the time lapse from when a fault could first be noticed until the time when its repair can be delayed no longer because of unacceptable consequences. The bottle neck in delay time modelling is how to estimate the delay time distribution parameters. Two methods for estimating these parameters have been developed. namely the subjective method and the objective method. Markov models have the advantage of an extensive body of theory. 'fliere are, however. difficulties of definition, measurement, and calculation when applying Markov models to real-world situations within a maintenance context. Indeed. this problem has motivated the current research which ainis to explore the two modelling methodologies in cases where comparison is valid, and also to gain an insight as to how robust Markov inspection models can be as decision-aids where Markovian properties are not strictly satisfied. It Nvill be seen that a class of inspection problems could be solved by a serni- Markov model using the delay time concept. In this thesis, a typical senii-i%Ia, rkov inspection model based upon the delay time concept is presented for a complex repairable systein that may fail during the course of its service lifetime and the results are compared. Finally, a case study of the senii-Markov inspection model and the delay time model is discussed

Finite production rate model with backlogging, service level constraint, rework, and random breakdown

In most real-life production systems, both random machine breakdown and the production of nonconforming items are inevitable, and adopting a backlogging policy with a predetermined minimum acceptable service level can sometimes be an effective strategy to help the management reduce operating cost or smoothen the production schedule. With the aim of addressing the aforementioned practical situations in production, this study explores the optimal production runtime for the finite production rate (FPR) model with allowable backlogging and service level constraint, rework of defective products, and random machine breakdown. Mathematical modelling is employed along with optimization techniques to derive the optimal production runtime that minimizes the long-run average system costs for the proposed FPR model. The joint effects of the allowable backlogging with a planned service level, rework, and random machine breakdown on optimal runtime decision have been carefully investigated through a numerical example and sensitivity analysis. As a result, important insights regarding various system parameters are revealed in order to enable the management to better understand, plan, and control such a practical production system

Modelling condition monitoring inspection using the delay-time concept

In the literature on inspection modelling, the failure distribution traditionally plays a fundamental role in model construction in that it is assumed that system failures occur instantly at random time points from new with a known pdf. of time to failure. Numerous models have been built on this basis. However, Professor Christer challenged this traditional idea and proposed the concept of delay time. The idea, which is an essential part of most engineers' experience, assumes that defects do not just appear as failures, but are present for a while before becoming sufficiently obvious to be noticed and declared as failures. The time lapse from when a defect could first be identified at an inspection to consequential failure has been termed the "delay time". It is this idea which can be captured to reveal the nature and scope for preventive maintenance or inspection. It appears that the concept is now being taken up by many other authors. In this thesis, various models for condition monitoring inspection are built on the basis of delay time analysis. Extensions and further developments are made here to enrich the delay-time modelling. Since the distribution of the delay time is important to delay time modelling, a new approach to estimate the delay time distribution is proposed. This technique, which contrasts with the previous subjective data estimation technique, is based upon objective data. Assuming the distribution of the delay time is known, models of condition monitoring inspection are fully discussed for both perfect and imperfect inspections, and for infinite and finite time horizons. Based upon the models for perfect inspection, algorithms are presented to find the optimal solution. Numerical examples are presented in each Chapter to illustrate how models and algorithms work

Warranty cost analysis under imperfect repair

Cataloged from PDF version of article.Increasing market competition forces manufacturers to offer extensive warranties. Faced with the challenge of keeping the associated costs under control, most companies seek efficient rectification strategies. In this study, we focus on the repair strategies with the intent of minimizing the manufacturer’s expected warranty cost expressed as a function of various parameters such as product reliability, structure of the cost function and the type of the warranty contract. We consider both one- and two-dimensional warranties, and use quasi renewal processes to model the product failures along with the associated repair actions. We propose static, improved and dynamic repair policies, and develop representative cost functions to evaluate the effectiveness of these alternative policies. We consider products with different reliability structures under the most commonly observed types of warranty contracts. Experimental results indicate that the dynamic policy generally outperforms both static and improved policies on highly reliable products, whereas the improved policy is the best performer for products with low reliability. Although, the increasing number of factors arising in the analysis of two-dimensional policies renders generalizations difficult, several insights can be offered for the selection of the rectification action based on empirical evidence.Samatlı, GülayM.S

Production and maintenance planning of deteriorating manufacturing systems taking into account the quality of products

The research work presented in this thesis addresses the integration of quality aspects in the development of stochastic dynamic programming models. The goal is to determine the joint optimal production planning, and several maintenance strategies for an unreliable and deteriorating manufacturing system. In particular, we conjecture that deterioration has a severe influence on various aspects of the machine, thus this leads to divide our research work in three (3) phases. In the first one, we analyze the simultaneous production planning and quality control problem for an unreliable manufacturing system. The machine is subject to deterioration whose effect is observed mainly on the quality throughput. The quality related decisions involves a major overhaul strategy that counters the effect of deterioration. A simulation optimization approach is applied to determine the optimal control policy, providing a better understanding about the influence of quality deterioration on such system. The second phase of the research analyzes the fact where the deterioration of the production system is originated by a combination of several factors. We consider that the system deteriorates by the combined effect of the wear of the machine and imperfect repairs. Multiple operational states are implemented to model variations on the rate of defectives. Furthermore at failure, either a repair or a major overhaul can be conducted; however the machine deteriorates even more following repairs. We use a Semi-arkov decision model, since the rate of defectives is depended of the machine’s history denoted by the number of repairs and the set of multiple operational states. Then the simultaneous production plan, and repair/overhaul switching strategy are determined through numerical methods. The third phase complements the previous models by considering that the deterioration of the production systems has a twofold effect that decreases the quality of the parts produced and also increases the failure intensity. We employ the age of the machine to denote the progressive deterioration. At failure it is conducted a minimal repair that leaves the machine at the same level of deterioration before failure. To counter completely the effect of deterioration it can be performed a major overhaul. Moreover, this phase introduces preventive maintenance strategies to reduce partially the level of deterioration. This set of characteristics yields to formulate a Semi-Markov model that thorough numerical methods, we determine the joint optimal production plan and the overhaul and preventive maintenance strategies. This model clarifies the role of quality aspects on the optimal control policy. In this way our research deepens the effects of quality aspects and deterioration on the optimal control policy, and provides interesting contributions to the domain of stochastic control of manufacturing systems. Additionally, a number of numerical examples are conducted as illustration, and extensive sensitivity analyses are presented with the purpose to confirm the structure and validity of the obtained control policies. The models developed in this thesis provide further insights into the relations between the production policy and quality aspects in the context of deterioration, and also contribute to a better understanding about the behavior of stochastic manufacturing systems

Integration of production, maintenance and quality : Modelling and solution approaches

Dans cette thèse, nous analysons le problème de l'intégration de la planification de production et de la maintenance préventive, ainsi que l'élaboration du système de contrôle de la qualité. Premièrement, on considère un système de production composé d'une machine et de plusieurs produits dans un contexte incertain, dont les prix et le coût changent d'une période à l'autre. La machine se détériore avec le temps et sa probabilité de défaillance, ainsi que le risque de passage à un état hors contrôle augmentent. Le taux de défaillance dans un état dégradé est plus élevé et donc, des coûts liés à la qualité s’imposent. Lorsque la machine tombe en panne, une maintenance corrective ou une réparation minimale seront initiées pour la remettre en marche sans influer ses conditions ou le processus de détérioration. L'augmentation du nombre de défaillances de la machine se traduit par un temps d'arrêt supérieur et un taux de disponibilité inférieur. D'autre part, la réalisation des plans de production est fortement influencée par la disponibilité et la fiabilité de la machine. Les interactions entre la planification de la maintenance et celle de la production sont incorporées dans notre modèle mathématique. Dans la première étape, l'effet de maintenance sur la qualité est pris en compte. La maintenance préventive est considérée comme imparfaite. La condition de la machine est définie par l’âge actuel, et la machine dispose de plusieurs niveaux de maintenance avec des caractéristiques différentes (coûts, délais d'exécution et impacts sur les conditions du système). La détermination des niveaux de maintenance préventive optimaux conduit à un problème d’optimisation difficile. Un modèle de maximisation du profit est développé, dans lequel la vente des produits conformes et non conformes, les coûts de la production, les stocks tenus, la rupture de stock, la configuration de la machine, la maintenance préventive et corrective, le remplacement de la machine et le coût de la qualité sont considérés dans la fonction de l’objectif. De plus, un système composé de plusieurs machines est étudié. Dans cette extension, les nombres optimaux d’inspections est également considéré. La fonction de l’objectif consiste à minimiser le coût total qui est la somme des coûts liés à la maintenance, la production et la qualité. Ensuite, en tenant compte de la complexité des modèles préposés, nous développons des méthodes de résolution efficaces qui sont fondées sur la combinaison d'algorithmes génétiques avec des méthodes de recherches locales. On présente un algorithme mimétique qui emploi l’algorithme Nelder-Mead, avec un logiciel d'optimisation pour déterminer les valeurs exactes de plusieurs variables de décisions à chaque évaluation. La méthode de résolution proposée est comparée, en termes de temps d’exécution et de qualités des solutions, avec plusieurs méthodes Métaheuristiques. Mots-clés : Planification de la production, Maintenance préventive imparfaite, Inspection, Qualité, Modèles intégrés, MétaheuristiquesIn this thesis, we study the integrated planning of production, maintenance, and quality in multi-product, multi-period imperfect systems. First, we consider a production system composed of one machine and several products in a time-varying context. The machine deteriorates with time and so, the probability of machine failure, or the risk of a shift to an out-of-control state, increases. The defective rate in the shifted state is higher and so, quality related costs will be imposed. When the machine fails, a corrective maintenance or a minimal repair will be initiated to bring the machine in operation without influencing on its conditions or on the deterioration process. Increasing the expected number of machine failures results in a higher downtime and a lower availability rate. On the other hand, realization of the production plans is significantly influenced by the machine availability and reliability. The interactions between maintenance scheduling and production planning are incorporated in the mathematical model. In the first step, the impact of maintenance on the expected quality level is addressed. The maintenance is also imperfect and the machine conditions after maintenance can be anywhere between as-good-as-new and as-bad-as-old situations. Machine conditions are stated by its effective age, and the machine has several maintenance levels with different costs, execution times, and impacts on the system conditions. High level maintenances on the one hand have greater influences on the improvement of the system state and on the other hand, they occupy more the available production time. The optimal determination of such preventive maintenance levels to be performed at each maintenance intrusion is a challenging problem. A profit maximization model is developed, where the sale of conforming and non-conforming products, costs of production, inventory holding, backorder, setup, preventive and corrective maintenance, machine replacement, and the quality cost are addressed in the objective function. Then, a system with multiple machines is taken into account. In this extension, the number of quality inspections is involved in the joint model. The objective function minimizes the total cost which is the sum of maintenance, production and quality costs. In order to reduce the gap between the theory and the application of joint models, and taking into account the complexity of the integrated problems, we have developed an efficient solution method that is based on the combination of genetic algorithms with local search and problem specific methods. The proposed memetic algorithm employs Nelder-Mead algorithm along with an optimization package for exact determination of the values of several decision variables in each chromosome evolution. The method extracts not only the positive knowledge in good solutions, but also the negative knowledge in poor individuals to determine the algorithm transitions. The method is compared in terms of the solution time and quality to several heuristic methods. Keywords : Multi-period production planning, Imperfect preventive maintenance, Inspection, Quality, Integrated model, Metaheuristic

Integrated Workload Allocation and Condition-based Maintenance Threshold Optimisation

Effective asset management is considered key to reducing total costs of asset ownership while enhancing machine availability, guaranteeing security, and increasing productivity. Amongst all the activities involved in asset management, maintenance has been one of the major focus areas of academic research due to its potential in helping manufacturers to generate the most value from their assets. The emergence of condition-based maintenance (CBM) in which decisions are made based on the real-time condition of assets, has opened up new possibilities in developing more comprehensive approaches to improve the performance of production systems. For instance, a trend has been observed where attempts are made to couple CBM decisions with those on other production-related factors such as inventory control, spare parts management, and labour routing. The intrinsic link between the degradation behaviour of and the workload allocated to an asset, however, has not been sufficiently studied. Consequently, the potential benefits of intervening in machine degradation, either in the context of a single asset or a fleet of assets, are rarely explored. It is therefore essential that a systematic approach is at hand to improve system performance by exploiting the inter-relationship between production and maintenance. This thesis is dedicated to developing a dynamic integrated decision-making model to improve the system-level performance of a fleet of parallel assets. The aim of the model is to realise the potential benefits, mainly in the form of lower maintenance costs and reduced penalty costs incurred due to loss of production, by simultaneously optimising workload allocation and the CBM threshold. The decision-making model is implemented using an agent-based system involving two types of agents - 1) machine agents that reside within each individual machine; and 2) a coordinator agent that oversees the entire system. The integrated decision-making model is constituted of two components - 1) a workload-dependent condition-based maintenance optimisation model based on Gamma Process at the asset level through a machine agent; and 2) a workload allocation strategy at the system level implemented by a coordinator agent. Numerical analysis is performed to demonstrate the rationale behind the decision-making process, which is to reach the most desirable balance between maintenance costs and penalty costs incurred by loss of production. The capability of the model to reduce total costs is demonstrated via comparison with traditional strategies such as uniform and random workload allocation. Additionally, the sensitivity analysis conducted has helped to reveal the respective factors that impact the potential reduction in maintenance costs and that in penalty costs, which include the sensitivity of asset degradation to workloads, heterogeneity of assets, penalty cost for a unit of production loss, redundancy of the system, etc. The model presented in this study not only assists operation and maintenance managers to make decisions on the optimal combination of workload allocation and maintenance plans for assets in a production system, but also provides guidance on whether they should invest in workload control capabilities. Furthermore, the proposed approach allows practitioners to evaluate the long-term impacts of sudden events such as an increase in demand, a decrease in the number of redundant machines, and a change in the cost of maintenance actions