Thesis (MEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The demand for rail travel has increased over the years. As a result, it is becoming mandatory for railway industries to maintain very high availability of their assets to ensure that service levels are high. Railway industries require both their infrastructure and rolling stock assets maintained efficiently to sustain reliability. There has been on-going research on how maintenance can be carried out in a cost effective manner. However, the majority of this research has been done for infrastructure and the rolling stock maintenance has not been properly covered. The purpose of this research is to contribute to the maintenance sector of rolling stock for railway industries by developing a decision support model for rolling stock based on reliability and cost. The model is developed as an optimization problem of a system containing several components dependent on each other with different reliability characteristics. In this model, a mixed integer nonlinear problem is developed and solved using an exact method and metaheuristics methods. The Metrorail facility in Cape Town was chosen as a case study. Failure history and cost data were gathered from the facility and the information was applied to the model developed. The case study was investigated and different results were achieved using both exact and metaheuristics methods. The final result from the study is an optimal maintenance schedule based on reliability and cost. The developed model serves as a practical tool railway companies can adopt to schedule rolling stock maintenance to achieve a high level of reliability and at the same time maintaining minimum cost expenditure. / AFRIKAANSE OPSOMMING: Die vraag na spoorvervoer het oor die jare toegeneem. Dus het dit belangrik geword dat die spoorweg se bates hoogs toeganklik moet wees om te verseker dat die vlak van dienslewering hoog bly. Die spoorweg industrie besef dat hulle infrastruktuur, lokomotiewe, waens ens. effektief in stand gehou moet word sodat dit betroubaar kan wees. Navorsing word nog steeds gedoen oor hoe instandhouding op ’n koste-effektiewe wyse gedoen kan word. Die meeste van hierdie navorsing gaan egter oor infrastruktuur en instandhouding word nie ordentlik gedek nie. Die doel met hierdie navorsing is om by te dra tot die instandhoudingsektor van die spoorweg deur om ’n besluit-ondersteunende model vir lokomotiewe, waens, ens wat op betroubaarheid en koste gegrond is, te ontwikkel. Die model is ontwikkel as ’n optimasie probleem van ’n sisteem wat verskillende komponente wat van mekaar afhanklik is maar oor verskillende betroubaarheidskenmerke beskik, inluit. In hierdie model word ’n gemengde, heeltal nie-lineêre probleem ontwikkel en met ’n eksakte metode en metaheuristiese metodes opgelos. Die Metrorail fasiliteit in Kaapstad is vir die gevalle studie gekies. Die geskiedenis van mislukkings en koste data is by die fasiliteit versamel en die inligting is op die model wat ontwikkel is, toegepas. Die gevalle studie is ondersoek, en verskillende resultate is met eksakte en metaheuristiese metodes bereik. Die finale uitkomste van die studie is ’n optimale instandhoudingskedule wat op betroubaarheid en koste gegrond is. Die model wat ontwikkel is dien as ’n praktiese instrument wat spoormaatskappye kan gebruik om die instandhouding van lokomotiewe, waens ens. te reël sodat ’n hoë vlak van betroubaarheid bereik kan word en kostes terselfdertyd tot ’n minimum beperk kan word.

Thesis (MSc (Mathematical Sciences. Computer Science))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Since 2002 data tra c has overtaken voice tra c in volume [1]. Telecom / Network operators still generate most of their income carrying voice tra c. There is however a huge revenue potential in delivering reliable guaranteed data services. Network survivability and recovery from network failures are integral to network reliability. Due to the nature of the Internet, recovery from link failures needs to be distributed and dynamic in order to be scalable. Link failure recovery schemes are evaluated in terms of the survivability of the network, the optimal use of network resources, scalability, and the recovery time of such schemes. The need for recovery time to be improved is highlighted by real-time data tra c such as VoIP and video services carried over the Internet. The goal of this thesis is to examine existing link failure recovery schemes and evaluate the need for their extension, and to evaluate the performance of the proposed link failure recovery schemes. i / AFRIKAANSE OPSOMMING: Sedert 2002 het data verkeer die stem verkeer in volume verbygesteek [1]. Telekommunikasie / netwerk operateurs genereer egter steeds die meeste van hul inkomste met stem verkeer. Netwerk oorlewing en die herstel van netwerk mislukkings is integraal tot netwerk stabiliteit. Die samestelling van die Internet noodsaak dat die herstel van skakel mislukkings verspreid en dinamies van natuur moet wees. Die herstel-skema van skakel mislukkings word evalueer in terme van die oorleefbaarheid van die netwerk, die mees e ektiewe benutting van network bronne, aanpasbaarheid, en die herstel tydperk van die skema. Die vinnig moontlikste herstel tydperk word genoodsaak deur oombliklike data verkeer soos VoIP en beeld dienste wat oor die Internet gedra word. The doel van hierdie tesis is om bestaande skakel mislukking herstel skemas te evalueer, en dan verder ondersoek in te stel na hul uitbreiding. Daarna word die voorgestelde skakel mislukking skema se e ektiwiteit gemeet.

Orientador: Helio Waldman / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e Computação / Made available in DSpace on 2018-08-07T03:14:56Z (GMT). No. of bitstreams: 1 Mello_DarliAugustodeArruda_D.pdf: 2229379 bytes, checksum: e813cff8c9fed2550e1d237c195fd740 (MD5) Previous issue date: 2006 / Resumo: A tese propõe conceitos e ferramentas matemáticas para a alocação eficiente de conexões com habilidade de sobrevivência diferenciada. Utilizamos a disponibilidade como critério na escolha dos mecanismos de proteção e restauração que atuam no controle da habilidade de sobrevivência. Diante da carência de métodos de estimação de disponibilidade acurados, propusemos aproximações baseadas em um modelo markoviano. Obtivemos também limitantes à disponibilidade que permitem calcular erros de estimação. Desenvolvemos então um algoritmo para a alocação de conexões com disponibilidade garantida. Com ele verificamos, usando simulações, a aplicabilidade da proteção por compartilhamento de caminhos de reserva (SBPP) e da proteção de caminho dedicada (DPP) em redes de dimensões nacionais (rede italiana) e continentais (rede estadunidense). Em redes de dimensões nacionais a SBPP oferece ganhos de compartilhamento. Em redes de dimensões continentais a SBPP e a DPP mostraram-se inviáveis devido às restrições de disponibilidade. Por fim, sugerimos utilizar a distribuição da disponibilidade de intervalo e da duração de períodos de inoperância na formulação de contratos de níveis de serviço. Computamos a distribuição das duas métricas por métodos numéricos existentes, e analiticamente, respectivamente / Abstract: This thesis proposes concepts and mathematical formulations for the efficient allocation of connections with differentiated survivability. We use availability to found the choice of adequate protection or restoration mechanisms for survivability differentiation. Given a lack of accurate methods for availability estimation, we proposed approximations based on Markov models. We also derived bounds to the availability that allow to calculate estimation errors. We then developed an algorithm for allocating connections with guaranteed availability. It allowed us to verify the applicability of the shared backup path protection (SBPP) and dedicated path protection (DPP) schemes in networks of national (Italian network) and continental (American NSFNet) dimensions. In networks of national dimensions SBPP allows capacity gains. In networks of continental dimensions the use of both SBPP and DPP has shown to be impractical due to availability constraints. Finally, we suggested to employ the interval availability and outage duration distributions for the elaboration of service level agreements. We computed the distributions using existing numerical methods, and analytically, respectively / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

Orientador: Antonio Carlos Moretti / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T06:41:26Z (GMT). No. of bitstreams: 1 AraujoNeto_JoseEvangelista_M.pdf: 2884766 bytes, checksum: c57ca36e07463336bdf238ea6b35e234 (MD5) Previous issue date: 2011 / Resumo: Uma empresa de energia elétrica tem por obrigação garantir a continuidade e a qualidade do serviço prestado. A fim de incentivar a qualidade do serviço, a ANEEL introduziu penalidades nos contratos com as concessionárias de serviços públicos de transmissão de energia elétrica caso as instalações de transmissão sejam desligadas, por acidente, falha de equipamento ou manutenção programada. Abordagens tradicionais de manutenção em sistemas de transmissão de energia elétrica se baseiam em ações realizadas periodicamente, ou programadas, de acordo com uma análise de necessidades. Embora essas abordagens tenham o objetivo de melhorar o desempenho destes sistemas, geralmente não há uma avaliação precisa do impacto das ações de manutenção na confiabilidade dos mesmos relacionada aos recursos empregados, bem como penalidades legais decorrentes. O objeto assim formulado caracteriza-se como um problema de otimização combinatória com o objetivo de encontrar o encadeamento das ações de manutenções que minimizem os recursos utilizados em manutenções e garanta um nível de confiabilidade desejado para o Sistema Elétrico. Este trabalho propõe uma abordagem para enfrentar este problema baseada na relação confiabilidade/custo com a perspectiva de encontrar as melhores estratégias para a realização de manutenções em equipamentos (ativos) de transmissão de energia elétrica, apresentando um modelo matemático para a confecção de um calendário viável (que respeite às restrições do Sistema Elétrico) para programação de manutenção nestes ativos e metodologia de otimização para encontrar as melhores soluções em um determinado horizonte de planejamento / Abstract: A eletric power company is required to ensure continuity and quality of the provided service. To promote the quality of service, ANEEL introduced penalties in contracts with the electric power companies if transmission facilities are turned off by accident, equipment failure or programmed maintenance. Traditional approaches to maintenance of electric energy transmission systems are based on actions performed periodically, or programmed, in agreement with an analysis of needs. Although these approaches have the goal of improving the performance of these systems, generally there is not an accurate assessment of the impact of maintenance actions on the reliability of those actions related to the employed resources, as well as current legal penalties. The object thus formulated is characterized as a combinatorial optimization problem with the objective to find the sequence of maintenance actions that minimize the resources used in maintenance, ensuring a level of reliability desired for the Electric System. This work proposes an approach to address this problem based on the relationship reliability/ cost with the prospect of finding the best strategies for performing maintenance on equipment (assets) of electricity transmission, presenting a mathematical model for finding a feasible schedule (which respects the constraints of the Electric System) maintenance programming for these assets and optimization methodology to find the best solutions in a given planning horizon / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

Orientadores: José Ricardo Pelaquim Mendes, Kazuo Miura / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências / Made available in DSpace on 2018-08-21T13:11:36Z (GMT). No. of bitstreams: 1 DaFonseca_TiagoCardoso_M.pdf: 2105397 bytes, checksum: 938187b300de7b315fa5e2dcca4fef13 (MD5) Previous issue date: 2012 / Resumo: Integridade de poço pode ser entendida como sua capacidade de evitar vazamentos para o meio ambiente e é uma importante característica de um poço de petróleo. Uma das formas de evitar vazamentos durante a fase de produção é realizar intervenções de manutenção que conservem os poços em situações seguras e com barreiras de segurança sobressalentes. A previsão de custos relativos às intervenções para manutenção deve ser levada em conta nas fases iniciais dos projetos de Desenvolvimento da Produção, quando se planeja e se avalia técnica e economicamente a campanha de construção de poços. Este trabalho apresenta uma metodologia para análise de integridade de poços de Desenvolvimento da Produção que considera a existência de estados intermediários, onde não há perda de integridade, mas o sistema poço encontra-se degradado, fundamentando-se nos conceitos de Conjuntos Solidários de Barreiras (CSB) propostos por Miura (2004) e em técnicas de Engenharia de Confiabilidade. A metodologia pode ser utilizada na previsão de recursos para as intervenções de manutenção de uma campanha de construção e operação de poços. Através do tempo esperado para falha de cada um dos CSB presentes na configuração de completação é possível se estimar quando o estado de integridade do poço passará a depender de um único Conjunto Solidário de Barreiras e qual a expectativa para que haja vazamento (ausência de CSB) / Abstract: Well integrity may be defined as its capability to prevent leaks to the environment and is therefore a very important feature for oil and gas wells. One way to avoid leaks during the well operation is to perform maintenance interventions, seeking to keep redundancy in the well's safety barriers. Cost assessment regarding the wells maintenance interventions shall be done during the initial phases of the Production Development project, when the wells construction campaign is both technically and economically evaluated. This work presents a methodology for petroleum wells integrity analysis considering the existence of intermediate stages, when the integrity has not been lost but the well is considered to be in a degraded status. The method is based on the Barrier Integrated Sets (BIS), proposed by Miura (2004, in Portuguese) and described by Miura et al. (2006 [1]), and on Reliability Engineering techniques. The methodology may be used for maintenance interventions resource assessment considering a well construction campaign. Through the computation of the mean time to failure of each BIS identified in the completion configuration it is possible to estimate when the well is in a degraded status, relying in a single Barrier Integrated Set and well the well is expected to leak (no BIS) / Mestrado / Explotação / Mestre em Ciências e Engenharia de Petróleo

Submitted in fulfillment of the requirements for the degree of Master of Engineering, Durban University of Technology, Durban, South Africa, 2017. / Much equipment in the eThekwini Electricity network has been in use for several decades. Failure of this equipment could critically impact electricity supply to customers, and result in high costs associated with loss of load and/or component replacement. The fundamental motive for any power utility is to plan, operate, and maintain power infrastructure such that customers receive reliable electric services at the minimum expense possible. For this dissertation, the Reliability Centered Maintenance (RCM) model was implemented in the eThekwini Electricity network. This model emphasises the importance of long-term planning and allocation of resources over the life time of a transformer, or any other component. RCM is an ongoing process that entails gathering data from operating systems performance, and using this data to improve design, operation, and maintenance of the system. The eThekwini Power network failure statistics for the previous five years were collected and thoroughly analysed to identify critical components associated with higher failure rates, and associated consequences. Upon examination, it was determined that the power transformer is a critical component of the system. The transformer plays a significant role in the power system due to its remarkable effect on overall reliability, in addition to the fact that it is a major cost factor in the power grid. Transformer management comprises of identifying the appropriate type and frequency of maintenance, and the appropriate time to replace the transformer in a cost-effective manner. The Markov model for ascertaining the transformer’s remaining service life was applied on the identified critical transformer. The transformer deterioration process is modelled by representing the oil insulation by discrete stages. Using the Institute of Electrical and Electronics Engineers (IEEE) standard for interpreting the transformer insulation, the transformer under review was found to be at stage two. Further analysis was performed on system unavailability rates versus mean time to first failure (MTTFF). The analyses indicated that the higher the MTTFF, the longer the system availability whereas the lower the MTTFF, the more reduced the system availability. Improving the MTTFF rates of a system will enhance reliability. The effective application of RCM will optimise the maintenance processes with reasonable expenditures. / M

La prolifération des électroniques et des émetteurs radiofréquences rend de plus en plus compliqué le processus de conception des systèmes sur le plan CEM. Ce processus doit aboutir à limiter le risque d’interférences ou de défauts au niveau le plus faible notamment dans le contexte des interférences électromagnétiques intentionnelles (IEMI). Ces défauts CEM doivent alors être anticipés lors de la phase de conception. Cependant, du fait de la dispersion des valeurs prises par certains paramètres du système, la modélisation déterministe éprouve quelques difficultés à identifier le risque encouru. La mauvaise connaissance de l’effet des incertitudes associées au système, aboutit alors à prendre des marges de conception considérables conduisant à des surcoûts de fabrication. Pour cette raison, il est devenu important de prendre en compte l’impact des incertitudes des différents paramètres constitutifs d’un système (en phase de conception). Ces paramètres sont essentiellement géométriques (e.g. position de câblages) ou électromagnétiques (e.g. caractéristiques intrinsèques de matériaux). Ils influent par nature sur les performances CEM de ce système. Ces travaux de thèse portent sur l’analyse de la propagation des incertitudes relatives à ces paramètres sur des sorties de modèles de CEM. Le but visé, consiste à quantifier sous une forme probabiliste, le risque de défaut d’un système contenant de nombreux paramètres incertains. Ce type d’étude statistique devrait également permettre, via des analyses de sensibilité, des stratégies de conception de systèmes « fiables » ou à moindres coûts. Dans le contexte des applications visées, les approches dites « fiabilistes » et la méthode dite de « stratification contrôlée », ont été identifiées comme intéressantes, du point de vue de l’analyse d’événements extrêmes. Dans un premier temps, nous nous sommes consacrés à la transposition des méthodes fiabilistes dans un contexte CEM. Ces techniques permettent de quantifier la probabilité de défaillance d’un système, définie comme le dépassement d’un seuil de risque, et renseignent, via une analyse de sensibilité locale, sur les paramètres clés à ajuster. Dans un second temps, nous nous sommes intéressés à la méthode de stratification contrôlée, non appliquée à ce jour à notre connaissance en CEM. L’objectif de cette approche consiste à estimer un quantile extrême de la réponse d’intérêt d’un modèle rigoureux, via l’utilisation d’un modèle simple beaucoup moins coûteux en termes de temps de calcul. Ce processus permet d’accélérer l’obtention d’observations extrêmes, nécessaires à l’estimation du quantile recherché. Les deux techniques ont été mises en oeuvre sur un problème complexe dans un contexte IEMI, pour estimer la probabilité d’occurrence d’événements d’interférences extrêmes. Elles ont permis de dégager des tendances similaires, quant à l’importance de certains paramètres d’entrée incertains sur les événements rares. Les deux méthodes, bien appliquées, pourraient constituer un apport considérable en matière de conception CEM. / The proliferation of electronic and radio frequency transmitters makes more complicated the system design process on the EMC point of view. This process should lead to limit the risk of interferences or defects to lowest level particularly in the context of intentional electromagnetic interferences (IEMI). Therefore, these EMC defects have to be anticipated during the design stage. However, due to the dispersion of the values taken by some parameters of the system, the deterministic modeling presents some difficulties to identify the involved risk. The poor knowledge of the uncertainties effect associated with the system, leads then to take important design margins at the price of additional costs of manufacturing. For this reason, it has become important to take into account the impact of uncertainties of the various constituent parameters of a system (at the design stage). These parameters are essentially geometric (e.g. position of wirings) or electromagnetic (e.g. intrinsic characteristics of materials) ones. They influence by nature the EMC performance of this system. This thesis work deals with the analysis of the propagation of uncertainties of these parameters on EMC model outputs. It aims at quantifying in a probabilistic form, the default risk of a system containing numerous uncertain parameters. This type of statistical analysis should also allow through sensitivity analyses, design strategies of “reliable” systems or at lower cost. In the context of targeted applications, the so-called “reliability approaches” and the “controlled stratification” method have been identified as interesting from the point of view of the analysis of extreme events. Firstly, we are dedicated to the transposition of reliability methods in an EMC context. These techniques are used to quantify the probability of failure of a system, defined as the probability of exceeding a threshold of risk. They inform through a local sensitivity analysis, on the key parameters to adjust. Secondly, we have focused our work on the controlled stratification method, not yet applied in EMC as far as we know. The objective of this approach is to estimate an extreme quantile of the interest response of a rigorous model, using of a much cheaper simple model in terms of computation time. This process allows to speed up the identification of extreme observations required for the estimation of the researched quantile. Both techniques have been applied on a complex problem in an IEMI context, to estimate the probability of occurrence of extreme interference events. They have revealed similar trends as regards to the importance of some uncertain input parameters on rare events. Both methods, properly applied, could provide a significant contribution in terms of EMC design strategy.

Les travaux présentés dans ce manuscrit traitent de la détermination de classes de systèmes selon leur mode de vieillissement dans l'objectif de prévenir une défaillance et de prendre une décision de maintenance. L’évolution du niveau de dégradation observée sur un système peut être modélisée par un processus stochastique paramétré. Un modèle usuellement utilisé est le processus Gamma. On s’intéresse au cas où tous les systèmes ne vieillissent pas identiquement et le mode de vieillissement est dépendant du contexte d’utilisation des systèmes ou des propriétés des systèmes, appelé ensemble de covariables. Il s’agit alors de regrouper les systèmes vieillissant de façon analogue en tenant compte de la covariable et d’identifier les paramètres du modèle associé à chacune des classes.Dans un premier temps la problématique est explicitée avec notamment la définition des contraintes: incréments d’instants d’observation irréguliers, nombre quelconque d’observations par chemin décrivant une évolution, prise en compte de la covariable. Ensuite des méthodes sont proposées. Elles combinent un critère de vraisemblance dans l’espace des incréments de mesure du niveau de dégradation, et un critère de cohérence dans l’espace de la covariable. Une technique de normalisation est introduite afin de contrôler l’importance de chacun de ces critères. Des études expérimentales sont effectuées pour illustrer l'efficacité des méthodes proposées / The work presented in this thesis deals with the problem of determination of classes of systems according to their aging mode in the aim of preventing a failure and making a decision of maintenance. The evolution of the observed deterioration levels of a system can be modeled by a parameterized stochastic process. A commonly used model is the Gamma process. We are interested in the case where all the systems do not age identically and the aging mode depends on the condition of usage of systems or system properties, called the set of covariates. Then, we aims to group the systems that age similarly by taking into account the covariate and to identify the parameters of the model associated with each class.At first, the problem is presented especially with the definition of constraints: time increments of irregular observations, any number of observations per path which describes an evolution, consideration of the covariate. Then the methods are proposed. They combine a likelihood criterion in the space of the increments of deterioration levels, and a coherence criterion in the space of the covariate. A normalization technique is introduced to control the importance of each of these two criteria. Experimental studies are performed to illustrate the effectiveness of the proposed methods

Cette thèse concerne les systèmes de surveillance des turboréacteurs. Le développement de tels systèmes nécessite une phase d’évaluation et d’optimisation des performances, préalablement à la mise en exploitation. Le travail a porté sur cette phase, et plus précisément sur les performances des fonctions de détection et de pronostic de deux systèmes. Des indicateurs de performances associés à chacune de ces fonctions ainsi que leur estimation ont été définis. Les systèmes surveillés sont d’une part la séquence de démarrage pour la fonction de détection et d’autre part la consommation d’huile pour la fonction de pronostic. Les données utilisées venant de vols en exploitation sans dégradations, des simulations ont été nécessaires pour l’évaluation des performances. L’optimisation des performances de détection a été obtenue par réglage du seuil sur la statistique de décision en tenant compte des exigences des compagnies aériennes exprimées en termes de taux de bonne détection et de taux d’alarme fausse. Deux approches ont été considérées et leurs performances ont été comparées pour leurs meilleures configurations. Les performances de pronostic de surconsommations d’huile, simulées à l’aide de processus Gamma, ont été évaluées en fonction de la pertinence de la décision de maintenance induite par le pronostic. Cette thèse a permis de quantifier et d’améliorer les performances des fonctions considérées pour répondre aux exigences. D’autres améliorations possibles sont proposées comme perspectives pour conclure ce mémoire / This thesis deals with monitoring systems of turbojet engines. The development of such systems requires a performance evaluation and optimization phase prior to their introduction in operation. The work has been focused on this phase, and more specifically on the performance of the detection and the prognostic functions of two systems. Performances metrics related to each of these functions as well as their estimate have been defined. The monitored systems are, on the one hand, the start sequence for the detection function and on the other hand, the oil consumption for the prognostic function. The used data come from flights in operation without degradation, simulations of degradation were necessary for the performance assessment. Optimization of detection performance was obtained by tuning a threshold on the decision statistics taking into account the airlines requirements in terms of good detection rate and false alarm rate. Two approaches have been considered and their performances have been compared for their best configurations. Prognostic performances of over oil consumption, simulated using Gamma processes, have been assessed on the basis of the relevance of maintenance decision induced by the prognostic. This thesis has allowed quantifying and improving the performance of the two considered functions to meet the airlines requirements. Other possible improvements are proposed as prospects to conclude this thesis

Component failures can result in catastrophic behaviors in safety critical embedded systems, sometimes resulting in loss of life. Component failures can be treated as off nominal behaviors (ONBs) with respect to the components and sub systems involved in an embedded system. A lot of research is being carried out to tackle the problem of ONBs. These approaches are mainly focused on the states (i.e., desired and undesired states of a system at a given point of time to detect ONBs). In this paper, an approach is discussed to detect component failures and critical components of an embedded system. The approach is based on fault tree analysis (FTA), applied to the requirements specification of embedded systems at design time to find out the relationship between individual component failures and overall system failure. FTA helps in determining both qualitative and quantitative relationship between component failures and system failure. Analyzing the system at design time helps in detecting component failures and critical components and helps in devising strategies to mitigate component failures at design time and improve overall safety and reliability of a system.