Multi-State System Reliability: A New and Systematic Review

AbstractReliability analysis considering multiple possible states is known as multi-state (MS) reliability analysis. Multi-state system reliability models allow both the system and its components to assume more than two levels of performance. Through multi-state reliability models provide more realistic and more precise representations of engineering systems, they are much more complex and present major difficulties in system definition and performance evaluation. MSS reliability has received a substantial amount of attention in the past four decades. This article presents a new and systematic review about multi-state system reliability. A timely review is an effective work related to improving the development of MSS theory. The review about the latest studies and advances about multi-state system reliability evaluation, multi-state systems optimization and multi-state systems maintenance is summarized in this paper

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

Reliability and Condition-Based Maintenance Analysis of Deteriorating Systems Subject to Generalized Mixed Shock Model

For successful commercialization of evolving devices (e.g., micro-electro-mechanical systems, and biomedical devices), there must be new research focusing on reliability models and analysis tools that can assist manufacturing and maintenance of these devices. These advanced systems may experience multiple failure processes that compete against each other. Two major failure processes are identified to be deteriorating or degradation processes (e.g., wear, fatigue, erosion, corrosion) and random shocks. When these failure processes are dependent, it is a challenging problem to predict reliability of complex systems. This research aims to develop reliability models by exploring new aspects of dependency between competing risks of degradation-based and shock-based failure considering a generalized mixed shock model, and to develop new and effective condition-based maintenance policies based on the developed reliability models. In this research, different aspects of dependency are explored to accurately estimate the reliability of complex systems. When the degradation rate is accelerated as a result of withstanding a particular shock pattern, we develop reliability models with a changing degradation rate for four different shock patterns. When the hard failure threshold reduces due to changes in degradation, we investigate reliability models considering the dependence of the hard failure threshold on the degradation level for two different scenarios. More generally, when the degradation rate and the hard failure threshold can simultaneously transition multiple times, we propose a rich reliability model for a new generalized mixed shock model that is a combination of extreme shock model, δ-shock model and run shock model. This general assumption reflects complex behaviors associated with modern systems and structures that experience multiple sources of external shocks. Based on the developed reliability models, we introduce new condition-based maintenance strategies by including various maintenance actions (e.g., corrective replacement, preventive replacement, and imperfect repair) to minimize the expected long-run average maintenance cost rate. The decisions for maintenance actions are made based on the health condition of systems that can be observed through periodic inspection. The reliability and maintenance models developed in this research can provide timely and effective tools for decision-makers in manufacturing to economically optimize operational decisions for improving reliability, quality and productivity.Industrial Engineering, Department o

A Condition-Based Maintenance Model for Assets with Accelerated Deterioration Due to Fault Propagation

Complex industrial assets such as power transformers are subject to accelerated deterioration when one of its constituent component malfunctions, affecting the condition of other components, which is a phenomenon called fault propagation. In this paper, we present a novel approach for optimizing condition-based maintenance policies for such assets by modelling their deterioration as a multiple dependent deterioration path process. The aim of the policy is to replace the malfunctioned component and mitigate accelerated deterioration at minimal impact to the business. The maintenance model provides guidance on determining inspection and maintenance strategies to optimize asset availability and operational cost.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TR.2015.243913

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

Quantifying Preventive Maintenance Efficacy: A Baltimore City Use Case

Existing preventive maintenance efficacy research heavily focuses on quantifying system degradation in deterministic, probabilistic, and policy-based models, yet in a data centric age they inadequately address data requirements, the linchpin for improving preventive maintenance and graduating to predictive maintenance. Using Baltimore City’s public facility maintenance work orders, this study demonstrates the impact of data requirements on frequency, time and cost key performance indicators (KPI) and addresses omitted variable bias introduced by lack of condition-based data. Overall results show that maintenance cost has annually increased by $6,520 despite a sharp drop in 2018. Facilities in poor condition with persistently high repair needs present an opportunity for Baltimore to tailor its preventive maintenance strategy using condition-based data and separating money for a narrower definition of functional maintenance, potentially making better use of up to$14 million. Data requirements such as tracking corrective and preventive maintenance work for the same system and parts, combining facilities condition index (FCI) scores with work order frequency, prioritizing which facilities get preventive maintenance using return on investment thresholds, and enforcing data quality discipline compose the road map to these insights

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

Optimal Maintenance for Stochastically Degrading Satellite Constellations

This thesis develops a methodology to determine an optimal policy for maintaining a satellite constellation that degrades over time. Previous work has developed a methodology to compute an optimal replacement policy for a satellite constellation in which satellites were viewed as binary entities, either operational or failed. This research extends the previous models by developing an optimal maintenance policy for satellite constellations in which each satellite may operate in a finite number of degraded states. The constellation is assumed to consist of a finite number of satellites, each with a finite number of functions with distinct failure mechanisms. Assuming each function lifetime is exponentially distributed, the stochastic degradation process is modelled as a discrete-time Markov chain. The degradation process is subsequently used to formulate an optimization problem as a finite planning horizon Markov decision process in which the total expected loss of utility is minimized. The maintenance actions considered include on-orbit repairs and satellite replacements, each of which have an associated level of risk. Numerical examples are presented to illustrate the model, and a parametric sensitivity analysis is performed using notional data to determine conditions for which the resulting policy consists of only replacements, only on-orbit repairs, or mixtures of replacements and on-orbit repairs

Modelo para un sistema multi estado reparable con tasas de reparación y fallas variables en el tiempo utilizando modelos de dinámica de sistemas equivalente

This paper treats with the reliability assessment of a Repairable Multi-State System (RMSS) by means of a Nonhomogeneous Continuous-Time Markov Chain (NH-CTMC). A RMSS run on different operating conditions that may be considered acceptable or unacceptable according to a defined demand level. In these cases, the commonly used technique is Homogeneous Continuous-Time Markov Chain (H-CTMC), since its solution is mathematically tractable. However, the H-CMTC involve that the time between state transitions is exponentially distributed, and the failure and repair rates are constants. It's certainly not true if the system components age with the operation or if the repair activities depend on the instant of time when the failure occurred. In these cases, the failure and repair rates are time-varying and the NH-CTMC is needed to be considered. Nevertheless, for these models the analytical solution may not exist and the use of others techniques is required. This paper proposes the use of an Equivalent Systems Dynamics Model (ESDM) to model a NH-CTMC. A ESDM represent the Markov Model (MM) by means of the language and the tools of the Systems Dynamics (SD), and the results are obtained by simulation. As an example, an RMSS with three components, failure rates associated with the Weibull distribution and repair rates associated with the Log-logistic distribution is developed. This example serves to identify the advantages and disadvantages of a ESDM to make model a RMSS and evaluate some reliability measures.This paper treats with the reliability assessment of a Repairable Multi-State System (RMSS) by means of a Nonhomogeneous Continuous-Time Markov Chain (NH-CTMC). A RMSS run on different operating conditions that may be considered acceptable or unacceptable according to a defined demand level. In these cases, the commonly used technique is Homogeneous Continuous-Time Markov Chain (H-CTMC), since its solution is mathematically tractable. However, the H-CMTC involve that the time between state transitions is exponentially distributed, and the failure and repair rates are constants. It's certainly not true if the system components age with the operation or if the repair activities depend on the instant of time when the failure occurred. In these cases, the failure and repair rates are time-varying and the NH-CTMC is needed to be considered. Nevertheless, for these models the analytical solution may not exist and the use of others techniques is required. This paper proposes the use of an Equivalent Systems Dynamics Model (ESDM) to model a NH-CTMC. A ESDM represent the Markov Model (MM) by means of the language and the tools of the Systems Dynamics (SD), and the results are obtained by simulation. As an example, an RMSS with three components, failure rates associated with the Weibull distribution and repair rates associated with the Log-logistic distribution is developed. This example serves to identify the advantages and disadvantages of a ESDM to make model a RMSS and evaluate some reliability measures

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