Dissertations / Theses on the topic 'Stochastic deterioration'

Les travaux présentés contribuent à la modélisation stochastique de la maintenance de systèmes mono- ou multi-composants à détériorations et à modes de défaillances multiples en environnement dynamique. Dans ce cadre, les contributions portent d'une part sur la modélisation des processus de défaillance, et d'autre part sur la proposition de structures de décision de maintenance intégrant les différents types d'information de surveillance en ligne disponible sur le système (état de détérioration mesuré ou reconstruit, état de l'environnement, ...) et le développement des modèles mathématiques d'évaluation associés. Les modèles de détérioration et de défaillances proposés pour les systèmes mono-composants permettent de rendre compte de sources de détérioration multiples (chocs et détérioration graduelle) et d'intégrer les effets de l'environnement sur la dégradation. Pour les systèmes multi-composants, on insiste sur les risques concurrents, indépendants ou dépendants et sur l'intégration de l'environnement. Les modèles de maintenance développés sont adaptés aux modèles de détérioration proposés et permettent de prendre en compte la contribution de chaque source de détérioration dans la décision de maintenance, ou d'intégrer de l'information de surveillance indirecte dans la décision, ou encore de combiner plusieurs types d'actions de maintenance. Dans chaque cas, on montre comment les modèles développés répondent aux problématiques de la maintenance de turbines et de parcs éoliens<br>The thesis contributes to stochastic maintenance modeling of single or multi-components deteriorating systems with several failure modes evolving in a dynamic environment. In one hand, the failure process modeling is addressed and in the other hand, the thesis proposes maintenance decision rules taking into account available on-line monitoring information (system state, deterioration level, environmental conditions …) and develops mathematical models to measure the performances of the latter decision rules.In the framework of single component systems, the proposed deterioration and failure models take into account several deterioration causes (chocks and wear) and also the impact of environmental conditions on the deterioration. For multi-components systems, the competing risk models are considered and the dependencies and the impact of the environmental conditions are also studied. The proposed maintenance models are suitable for deterioration models and permit to consider different deterioration causes and to analyze the impact of the monitoring on the performances of the maintenance policies. For each case, the interest and applicability of models are analyzed through the example of wind turbine and wind turbine farm maintenance

Cette thèse explore l’utilisation des réseaux Bayésiens (RB) afin de répondre à des problématiques de dégradation en grandes dimensions concernant des infrastructures du génie civil. Alors que les approches traditionnelles basées l’évolution physique déterministe de détérioration sont déficientes pour des problèmes à grande échelle, les gestionnaires d’ouvrages ont développé une connaissance de modèles nécessitant la gestion de l’incertain. L’utilisation de la dépendance probabiliste se révèle être une approche adéquate dans ce contexte tandis que la possibilité de modéliser l’incertain est une composante attrayante. Le concept de dépendance au sein des RB s’exprime principalement de deux façons. D’une part, les probabilités conditionnelles classiques s’appuyant le théorème de Bayes et d’autre part, une classe de RB faisant l’usage de copules et corrélation de rang comme mesures de dépendance. Nous présentons à la fois des contributions théoriques et pratiques dans le cadre de ces deux classes de RB ; les RB dynamiques discrets et les RB non paramétriques, respectivement. Des problématiques concernant la paramétrisation de chacune des classes sont également abordées. Dans un contexte théorique, nous montrons que les RBNP permet de caractériser n’importe quel processus de Markov<br>This thesis explores high-dimensional deterioration-related problems using Bayesian networks (BN). Asset managers become more and more familiar on how to reason with uncertainty as traditional physics-based models fail to fully encompass the dynamics of large-scale degradation issues. Probabilistic dependence is able to achieve this while the ability to incorporate randomness is enticing.In fact, dependence in BN is mainly expressed in two ways. On the one hand, classic conditional probabilities that lean on thewell-known Bayes rule and, on the other hand, a more recent classof BN featuring copulae and rank correlation as dependence metrics. Both theoretical and practical contributions are presented for the two classes of BN referred to as discrete dynamic andnon-parametric BN, respectively. Issues related to the parametrization for each class of BN are addressed. For the discrete dynamic class, we extend the current framework by incorporating an additional dimension. We observed that this dimension allows to have more control on the deterioration mechanism through the main endogenous governing variables impacting it. For the non-parametric class, we demonstrate its remarkable capacity to handle a high-dimension crack growth issue for a steel bridge. We further show that this type of BN can characterize any Markov process

Dans le contexte des systèmes commandés, l’effort de recherche est principalement porté sur la reconfiguration d’une loi de commande à l’apparition d’une situation de défaut. La reconfiguration a pour objectif de pallier au défaut et donc de maintenir les performances du système. La problématique principale de nos travaux est d’étudier ces systèmes du point de vue de leur sûreté de fonctionnement en s’interrogeant sur les causes qui engendrent une situation de défaut. Pour cela, il est supposé l’existence d’une relation étroite entre la commande d’un système, sa dégradation et ses défauts. Un cadre de modélisation stochastique de la dégradation est proposé intégrant l’usage du système ainsi que les différents modes de détérioration. Le pronostic de la durée de vie résiduelle RUL de l’actionneur -élément critique de ces systèmes- est dérivé de l’ensemble des modèles. La RUL est alors utilisée comme un outil de reconfiguration de la loi LQR (Linear Quadratic Regulator) d’un système mono-actionné dans le cadre d’une maintenance prédictive. L’impact de cette nouvelle politique de maintenance sur les performances statiques et dynamiques du système est évalué. Enfin, le comportement stochastique d’un système tolérant aux fautes basé sur une redondance d’actionneurs est étudié au travers des modèles développés<br>In the context of control systems, the research effort is focused on how to reconfigure the control law upon the occurrence of a faulty situation. The reconfiguration procedure aims to overcome the fault and thus to maintain system performances. The main issue of this thesis is to study these systems in terms of their dependability by questioning the causes that generate a fault. Then it is assumed a close relationship between the control of a system, its degradation and its faults. A stochastic modelling framework is proposed combining the use of the system and the various modes of deterioration. The actuator is assumed to be the most critical part of a system. The prognosis of its remaining life RUL is derived from these models. This RUL is then used as a tool for reconfiguring the LQR law (Linear Quadratic Regulator) of a system with a single actuator in the context of a predictive maintenance. The impact of this new maintenance policy on static and dynamic performances is assessed. Finally the stochastic behavior of a fault tolerant control system is studied by means of the achieved models

Cette thèse est une contribution à la prise de décision robuste pour la maintenance des systèmes soumis à dégradation graduelle. Dans une première contribution, nous développons un critère permettant l'évaluation conjointe de la performance économique moyenne et la robustesse de différents types de stratégies de maintenance. L'avantage du critère proposé est qu'il s'adapte à différents types de stratégies de maintenance et permet d'avoir accès à un modèle d'évaluation simple et pertinent. La deuxième contribution est dédiée au développement et l'évaluation d'une stratégie conjointe de maintenance prévisionnelle et de gestion des pièces de rechange qui s'applique à des systèmes à composants multiples ayant des qualités différentes. Pour la stratégie conjointe proposée, un indicateur de pronostic est utilisé à la fois pour la prise de décision en maintenance et en approvisionnement. Le critère d'évaluation proposé précédemment est utilisé pour l'évaluation de cette stratégie également. La troisième contribution correspond à la proposition de deux stratégies de maintenance conditionnelle à inspection hybrides pour la maintenance des systèmes à composants multiples ayant des qualités différentes et inconnues. Pour les stratégies proposées, les informations de la surveillance en ligne sont utilisées pour dévoiler la qualité des composants du système à maintenir en ayant recours à des techniques statistiques de classification et d'estimation<br>This thesis is a contribution to robust decision making in maintenance of systems subject to gradual degradation. Our first contribution is to develop a criterion allowing the joint evaluation of the mean economic performance and the robustness of different types of maintenance strategies. The advantage of the proposed criterion is that it adapts to different types of maintenance strategies and provides access to a simple and relevant evaluation model. The second contribution is devoted to the development and the evaluation of a joint maintenance and spares parts management strategy that applies to multi-component systems with different qualities. For the proposed joint strategy, prognostic indicator is used for both maintenance and procurement decision-making. The evaluation criterion proposed above is used for the evaluation of this policy as well. The third contribution corresponds to the proposal of two conditional maintenance strategies with hybrid inspections for the maintenance of multi-component systems with different and unknown qualities. For the strategies proposed, online monitoring information is used to disclose the quality of system components to be maintained using statistical techniques of classification and estimation

The development and application of inventory models for deteriorating items is one of the main concerns of the experts in the domain, since the number and variety of deteriorating products are dramatically increasing. One of the major gaps in the deteriorating inventories literature is that researchers have not paid enough attention to two important features in their models: i) Considering stochastic conditions; especially stochastic lead time is almost overlooked since makes the mathematical challenges complicated, ii) designing innovative inventory policies by taking into account the environmental issues and particularly the CO2 emission as a new objective in a multi-objective framework that is quite new. In this thesis, we study replenishment policy for deteriorating products under stochastic conditions in form of three different problem areas. In the first one, we develop a continuous (r,Q) inventory model for a retailer that offers a deteriorating product by considering infinite planning horizon, stochastic lead time, constant demand rate and backordered shortages. For modeling the deterioration process, a non-linear holding cost is defined. Taking into consideration the stochastic lead time as well as a non-linear holding cost makes the mathematical model more complex. We therefore customize the proposed model for a uniform distribution function that could be tractable to solve optimally by an exact approach. In second problem, we study the strategy of pooling lead time risks by splitting replenishment orders among multiple suppliers simultaneously for a retailer that sells a deteriorating product. Finally, in the last problem, we consider inventory and transportation costs, as well as the environmental impacts in a centralized supply chain by taking into account uncertain demand and partial backordered shortages. In order to deal with demand uncertainty, a two stage stochastic programming approach is taken. Then, by considering transportation vehicles capacity, we develop a mixed integer mathematical model. In this way, the best transportation vehicles and replenishment policy are determined by finding a balance between financial and environmental criteria. A numerical example from the real world is also presented to show the applicability and effectiveness of the proposed model.

The implicit assumption in conventional inventory models is that the stored products maintain the same utility forever, i.e., they can be stored for an infinite period of time without losing their value or characteristics. However, generally speaking, almost all products experience some sort of deterioration over time. Some products have very small deterioration rates, and henceforth the effect of such deterioration can be neglected. Some products may be subject to significant rates of deterioration. Fruits, vegetables, drugs, alcohol and radioactive materials are examples that can experience significant deterioration during storage. Therefore the effect of deterioration must be explicitly taken into account in developing inventory models for such products. In most existing deteriorating inventory models, time is treated as a continuous variable, which is not exactly the case in practice. In real-life problems time factor is always measured on a discrete scale only, i.e. in terms of complete units of days, weeks, etc. In this research, we present several discrete-in-time inventory models and identify optimal ordering policies for a single deteriorating product by minimizing the expected overall costs over the planning horizon. The various conditions have been considered, e.g. periodic review, time-varying deterioration rate, waiting-time-dependent partial backlogging, time-dependent demand, stochastic demand etc. The objective of our research is two-fold: (a) To obtain optimal order quantity and useful insights for the inventory control of a single deteriorating product over a discrete time horizon with deterministic demand, variable deterioration rates and waiting-time-dependent partial backlogging ratios; (b) To identify optimal ordering policy for a single deteriorating product over a finite horizon with stochastic demand and partial backlogging. The explicit ordering policy will be developed for some special cases. Through computational experiments and sensitivity analysis, a thorough and insightful understanding of deteriorating inventory management will be achieved.

Les systèmes de piles à combustible offrent une solution durable à la production d'énergie électrique dans le secteur des transports, même s'ils rencontrent encore des problèmes de fiabilité et de durabilité. Le recours à des systèmes multi-piles à combustible (MFC) au lieu de piles à combustible uniques est une solution prometteuse pour surmonter ces limitations en répartissant de manière optimale la demande de puissance entre les différentes piles tout en tenant compte de leur état de santé, au moyen d'une stratégie de gestion de l'énergie (EMS) efficace. Dans ce travail, différentes stratégies ont été développées pour des applications automobiles, avec l'objectif d'optimiser la durée de vie du système de piles à combustible.Le premier défi est de développer un modèle reliant la détérioration de chaque pile avec la puissance délivrée, de manière à être en mesure de prédire l'effet d'une allocation de charge sur la détérioration de chaque pile, et ainsi prendre une décision post-pronostic pertinente. Plusieurs modèles stochastiques de détérioration, allant du modèle classique de processus Gamma à des modèles plus complexes avec des effets aléatoires, sont développés et adaptés aux spécificités des piles à combustible. Sur la base de ces modèles, plusieurs stratégies de décision post-pronostic pour une MFC sont proposées et, pour chacune d'entre elles, le problème d'optimisation associé est formulé.Tout d'abord, sous un profil de charge constant, en prenant en compte dans le processus de décision à la fois la consommation totale de combustible et la détérioration attendue, une stratégie de gestion de l'énergie tenant compte de la détérioration est proposée pour un système constitué de trois piles à combustible. Le problème d'optimisation multi-objectif associé à cette stratégie est résolu à l'aide d'un algorithme évolutionnaire, ce qui permet d'obtenir les allocations de charge optimisées pour chacune des piles du système. La durée de vie moyenne obtenue dans le cadre de la stratégie proposée s'avère plus longue que celle résultant de stratégies classiques (Average Load, Daisy Chain).De plus, sous un profil de charge dynamique aléatoire, et en prenant en compte les phénomènes de détérioration dus à la fois au niveau et aux variations de la charge, une stratégie de prise de décision est proposée pour un système de deux piles à combustible. La prise de décision est réalisée à chaque événement de modification de la demande, et les allocations de charge optimales sont obtenues en minimisant la fonction objectif qui est estimée sur la base de la prévision de la détérioration future du système. Une étude de l'influence des charges dynamiques aléatoires sur les performances de la stratégie proposée montre que la durée de vie moyenne obtenue dans le cas d’une durée inconnue entre deux modifications de demande est proche de celle obtenue avec une durée d'événement connue, ce qui prouve la robustesse de la stratégie proposée. De plus, il est montré que la durée de vie moyenne du système est augmentée par rapport au cas avec une stratégie de charge moyenne, sur plusieurs modèles de détérioration stochastique différents.Enfin, une étude plus exploratoire ouvre des perspectives de recherche dans le cas où le système multi-piles est composé de trois piles, dont deux seulement fonctionnent en même temps. Pour optimiser la durée de vie des piles, tout en répondant à la demande de charge, le système de gestion de l’énergie doit également optimiser le démarrage et l'arrêt des différentes piles. En fait, l'optimisation du remplacement des piles est également nécessaire pour une tâche d'exploitation à long terme. Par conséquent, cette étude ouvre la voie à des approches de maintenance pour les systèmes multi-piles<br>Fuel cell systems offer a sustainable solution to electrical power generation in the transportation sector, even if they still encounter reliability and durability issues. Resorting to Multi-stack Fuel Cells systems (MFC) instead of single fuel cells is a promising solution to overcome these limitations by optimally distributing the power demand among the different stacks while taking into account their state of health, by means of an efficient Energy Management Strategy (EMS). In this work, different strategies have been developed for vehicle applications, with the objective of optimizing the fuel cell system lifetime.The first challenge is to develop a model linking the deterioration trend of each stack with the power delivered by the stack, so as to predict the effect of a load allocation on each stack deterioration, and thus make a relevant post-prognostics decision. Several stochastic deterioration models, from the classical Gamma process model to more complex models with random effects are developed and tailored to the fuel cell specificities. Based on these models, several post-prognostics decision-making strategies for an MFC are proposed and, for each of them, the associated optimization problem is formulated.First, under a constant load profile, taking into consideration both the expected whole fuel consumption and the expected deterioration in the decision-making process, a deterioration-aware energy management strategy is proposed for a three-stack fuel cell system. The multi-objective optimization problem associated to this strategy is solved using an evolutionary algorithm, giving the optimized load allocations among stacks. The average lifetime obtained under the proposed strategy is demonstrated to be larger than those resulting from the classical Average Load and Daisy Chain strategies.Furthermore, under a random dynamic load profile, taking into consideration the deterioration phenomena due to both the load magnitude and the load variations, an event-based decision-making strategy is built for a two-stack fuel cell system. The optimal load allocations are obtained by minimizing the objective function which is estimated based on the prevision of the future system deterioration. An investigation on the influence of the random dynamic loads on the proposed strategy performance shows that the average lifetime obtained with unknown event duration is close to that with known event duration, which proves the robustness of the proposed strategy. Moreover, it is shown that the average system lifetime is increased when compared to the case with an Average Load strategy, on several different stochastic deterioration models.Lastly, a more exploratory study opening research perspectives in the case where the multi-stack system is composed of three stacks, only two of which are operating at the same time. To optimize the lifetime of the stacks, while meeting the load demand, the EMS must also optimize the start and stop of the different stacks. In fact, the optimization of stack replacement is also required for a long-term operation task. Therefore, this study opens the way to maintenance approaches to multi-stack systems

The risk-based life-cycle management of engineering systems in a nuclear power plant is intended to ensure safe and economically efficient operation of energy generation infrastructure over its entire service life. An important element of life-cycle management is to understand, model and forecast the effect of various degradation mechanisms affecting the performance of engineering systems, structures and components. The modeling of degradation in nuclear plant components is confounded by large sampling and temporal uncertainties. The reason is that nuclear systems are not readily accessible for inspections due to high level of radiation and large costs associated with remote data collection methods. The models of degradation used by industry are largely derived from ordinary linear regression methods. The main objective of this thesis is to develop more advanced techniques based on stochastic process theory to model deterioration in engineering components with the purpose of providing more scientific basis to life-cycle management of aging nuclear power plants. This thesis proposes a stochastic gamma process (GP) model for deterioration and develops a suite of statistical techniques for calibrating the model parameters. The gamma process is a versatile and mathematically tractable stochastic model for a wide variety of degradation phenomena, and another desirable property is its nonnegative, monotonically increasing sample paths. In the thesis, the GP model is extended by including additional covariates and also modeling for random effects. The optimization of age-based replacement and condition-based maintenance strategies is also presented. The thesis also investigates improved regression techniques for modeling deterioration. A linear mixed-effects (LME) regression model is presented to resolve an inconsistency of the traditional regression models. The proposed LME model assumes that the randomness in deterioration is decomposed into two parts: the unobserved heterogeneity of individual units and additive measurement errors. Another common way to model deterioration in civil engineering is to treat the rate of deterioration as a random variable. In the context of condition-based maintenance, the thesis shows that the random variable rate (RV) model is inadequate to incorporate temporal variability, because the deterioration along a specific sample path becomes deterministic. This distinction between the RV and GP models has profound implications to the optimization of maintenance strategies. The thesis presents detailed practical applications of the proposed models to feeder pipe systems and fuel channels in CANDU nuclear reactors. In summary, a careful consideration of the nature of uncertainties associated with deterioration is important for credible life-cycle management of engineering systems. If the deterioration process is affected by temporal uncertainty, it is important to model it as a stochastic process.

Infrastructure systems are critical to a country’s prosperity. It is extremely important to manage the infrastructure systems efficiently in order to avoid wastage and to maximize benefits. Deterioration of infrastructure systems is one of the primary issues in civil engineering today. This problem has been widely acknowledged by engineering community in numerous studies. We need to evolve efficient strategies to tackle the problem of infrastructure deterioration and to efficiently operate infrastructure. In this research, we propose stochastic models to predict the process of deterioration in engineering systems and to perform life-cycle analysis (LCA) of deteriorating engineering systems. LCA has been recognized, over the years, as a highly informative tool for helping the decision making process in infrastructure management. In this research, we propose a stochastic model, SSA, to accurately predict the effect of deterioration processes in engineering systems. The SSA model addresses some of the important and ignored areas in the existing models such as the effect of deterioration on both capacity and demands of systems and accounting for different types of failures in assessing the life-span of a deteriorating system. Furthermore, this research proposes RTLCA, a renewal theory based LCA model, to predict the life-cycle performance of deteriorating systems taking into account not only the life-time reliability but also the costs associated with operating a system. In addition, this research investigates the effect of seismic degradation on the reliability of reinforced concrete (RC) bridges. For this purpose, we model the seismic degradation process in the RC bridge columns which are the primary lateral load resisting system in a bridge. Thereafter, the RTLCA model along with SSA model is used to study the life-cycle of an example RC bridge located in seismic regions accounting for seismic degradation. It is expected that the models proposed in this research will be helpful in better managing our infrastructure systems.

Consider a single machine that produces N items each period. This machine which deteriorates over time needs occasional maintenance to restore it to its "new" condition. Our only indication that such deterioration has occurred is an increase in the incidence of defective items produced by the machine. The more periods that pass without maintenance, the higher the chances that the machine has deteriorated and will start producing more inferior items. We suppose that in the beginning of each period, the decision maker has three options: (1) To let the machine produce during that period without interfering with its production or inspecting it. (2) To inspect n items produced that period. If the inspected items are bad, maintenance is done at the end of the period on the machine to restore its "new" condition before the start of the next period. (3) To automatically do a maintenance on the machine at the start of the period without inspecting any of the items or doing any production. This choice must be made taking into account: (a) The machine deterioration rate, (b) The type of inspection that can be done and (c) The costs involved, e.g. inspection, maintenance, bad items produced, lost revenues, etc. Our thesis considers two different finite time horizon discounted dynamic programming models that can be used to optimally choose the correct option each period. The first model assumes that any inspection data obtained in a given period is only used in that period. The second model assumes that a single summary statistic of all past and present data is kept, and employed in making the decision. For both models, we proved the existence of a set of sufficient conditions based exclusively on input data that assure that the optimal policy has a special simple structure. In the first model, the optimal policy indicates that it is optimal to do nothing for the first few periods since the last maintenance, inspect before making a decision for the next few period, and if no maintenance is chosen in those periods, then automatically maintain in the following period. This structure is called a three tier policy. The second model's special structure says that for any given summary statistics, the optimal policy also has a three tier structure. In addition, for any given period, the optimal policy is to do nothing for the "best" summary statistics, inspect for the "next best" summary statistics and automatically maintain for the worst summary statistics.

碩士<br>國立臺灣科技大學<br>工業管理系<br>106<br>This paper deals with two specific inventory models for deteriorating items with a stochastic demand rate and a fixed shelf lifetime. Many researchers have been studied deterioration phenomenon as the deteriorating items always appear ubiquitously. In practice, the expiration date is a problem of deteriorating items that must be sold before their fixed shelf lifetime, or that only can be used within a certain period after being unpacked. As a result, consideration of the expiry date could help enterprise to avoid profit loss without waste of the orders. Most of current inventory models dealing with deterioration would assume a certain or a constant demand function. This is certainly unreasonable in a prevailing market of stochastic demand which conforms to our daily reality, therefore stochastic demand must be considered. Here, we present ordering policies for two such inventory models. In model I, ordering would be immediately replenished when the inventory level drops to zero even before the expiration date. Namely, the stock shortage is not allowed. In model II, shortage is allowed and the items are not backlogged even after the stock depletes. Only at the expiration date can the replenishment arrived instantaneously. Furthermore, because of the effect of the stochastic demand condition, we must consider two cases for each model in this paper. In the first case, due to lack of demand, the stock remains even at expiration date. The remainder is assumed to be discarded with cost. In the second case, the stock depletes earlier before the expiration date during the period of high demand. In this case, model II occurs shortage until replenishment arrived at expiration date. Finally, we provide the approximated solution for optimal ordering quantity for both models. In order to maximize expected relevant total profit, we also present sensitivity analysis of the expected total relevant profit influenced by prices, expiration dates …etc. by the help of numerical examples. It shows that our approximated solutions from the assumed models that mentioned above gives conditions and the results very close to the optimal solution obtained from computation. Moreover, these results reveal the impact of various parameters on the optimal policy and the profit.

碩士<br>國立屏東商業技術學院<br>行銷與流通管理系<br>96<br>The paper mainly considers a retailer who sales deteriorating items about the price and quantity with deteriorating items, assumption with two periods of the planning horizon. Besides, we consider a single product which is subject to continues decay and a demand which is a function of price and quantity. An inventory model of periodical stocktaking allow the selling price and can freely decide to rise or fall, in order to respond to the product life cycle which is demand or supply on the market. This research tries using dynamic programming to demonstrate the model and solves with the number research. Also use a data to deal with the condition of the character and the adjustment of the research price of strategy structure. The numerical result shows that the solution generated by the flexibility policy outperforms that by the fixed policy in maximizing discounting profit.

博士<br>中原大學<br>工業與系統工程研究所<br>99<br>Inventory problems have been investigated extensively in recent years. One form of industrial issues causing inventory problems is production system reliability. Since production system is not continuously reliable, some consequences such as inventory lost sales, and product rejects can occur. Due to the condition, this research studies inventory models dealing with unreliable production system. The study develops economic production quantity (EPQ) models for deteriorating items under unreliable production systems such as machine unavailability and breakdown. In this research, five production inventory models for deteriorating items are developed. The first model presents an EPQ model with random machine unavailability. Machine can be unavailable randomly due to some reasons such as regular preventive maintenance. Lost sales and backorder case are also included in the first model. The second model shows an EPQ model with random machine breakdown. Subsequently, the third model integrates the first and the second model. The third model considers both the random machine breakdown and random machine unavailability. While the fourth and fifth models deal with production process problems that affect the product’s quality. The production process can not consistently produce good quality products, hence some products are rejected. The fourth model assumes that defective products are reworked immediately at the end of the production process. This system is called as the last in first out (LIFO) system. After the rework process, the machine is maintained in random time where there is a possibility that the machine is not available when needed. Contrary, the fifth model considers the first in first out (FIFO) system instead of the LIFO system. From the first to the fifth model, two types of distribution models for random machine unavailability: upper-bound and bound distribution types are considered This study develops EPQ models for deteriorating items with stochastic maintenance and corrective time, and rework. Since these mathematical models are complex, their closed form solutions cannot be derived. To solve the models, the simple search method is employed using Maple 8 software. All models are convex in the assumed conditions. Numerical examples are provided for each model to illustrate the theorems. Sensitivity analyses are presented to demonstrate the effects of key parameters changes to production up time and cost. The results of the sensitivity analyses show that some parameters have significant effects on the optimal total cost and the optimal production time. Some management insights to handle unreliable production system are given in Chapter 8.

In today's competitive environment, the importance of continuous production, quality improvement, and fast delivery has forced production and delivery processes to become highly reliable. Keeping equipment in good condition through maintenance activities can ensure a more reliable system. However, maintenance leads to temporary reduction in capacity that could otherwise be utilized for production. Therefore, the coordination of maintenance and production is important to guarantee good system performance. The central thesis of this dissertation is that integrating maintenance and production decisions increases efficiency by ensuring high quality production, effective resource utilization, and on-time deliveries. Firstly, we study the problem of integrated maintenance and production planning where machines are preventively maintained in the context of a periodic review production system with uncertain yield. Our goal is to provide insight into the optimal maintenance policy, increasing the number of finished products. Specifically, we prove the conditions that guarantee the optimal maintenance policy has a threshold type. Secondly, we address the problem of integrated maintenance planning and production scheduling where machines are correctively maintained in the context of a dynamic aircraft repair shop. To solve the problem, we view the dynamic repair shop as successive static repair scheduling sub-problems over shorter periods. Our results show that the approach that uses logic-based Benders decomposition to solve the static sub-problems, schedules over longer horizon, and quickly adjusts the schedule increases the utilization of aircraft in the long term. Finally, we tackle the problem of integrated maintenance planning and production scheduling where machines are preventively maintained in the context of a multi-machine production system. Depending on the deterioration process of machines, we design decomposed techniques that deal with the stochastic and combinatorial challenges in different, coupled stages. Our results demonstrate that the integrated approaches decrease the total maintenance and lost production cost, maximizing the on-time deliveries. We also prove sufficient conditions that guarantee the monotonicity of the optimal maintenance policy in both machine state and the number of customer orders. Within these three contexts, this dissertation demonstrates that the integrated maintenance and production decision-making increases the process efficiency to produce high quality products in a timely manner.