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The reliability of products has played a very important role for the competitiveness of enterprises. Foremost on the agricultural machinery area, where the reliability of the machinery will impact directly the production costs and profitability of farms. Agricultural tractors are complex machines with diverse systems and components interacting among themselves and establishing a dependency relationship among their performances. When these machines fail, are restored to recover their production capability. Many different techniques for reliability study have been developed based on components reliability studies, when testes under well defined conditions of bench tests to replicate well-known failure modes. Statistical distributions are used to represent the failures behavior of different kind of tests. Most of these studies, though, were developed for components that will be replaced when failed. Therefore they have to be analyzed under techniques that are suited for repairable systems. Many repairable systems have been analyzed with techniques that are only suited for non-repairable systems. This work proposes a comparison between the two techniques to analyze the differences and advantages of each one, and its applicability to the development of agricultural tractors / A confiabilidade dos produtos tem desempenhado um papel muito importante para a competitividade das empresas. Principalmente na área de máquinas agrícolas onde a confiabilidade do maquinário terá uma influência direta nos custos de produção e, conseqüentemente, na rentabilidade da mesma. Tratores agrícolas são máquinas complexas com diversos sistemas e componentes interagindo entre si e estabelecendo uma relação de dependência entre seus desempenhos. Quando estas máquinas falham, são restauradas para recuperar sua capacidade de produção. Muitas técnicas de estudo da confiabilidade têm sido desenvolvidas, baseadas em estudos de confiabilidade de componentes, quando submetidos a condições bem determinadas de solicitações, em testes de bancadas que reproduzem determinados modos de falha. Distribuições estatísticas são usadas para representar o comportamento de falhas de diversos tipos de ensaio. A maioria destes estudos, entretanto, foram desenvolvidos para componentes que irão ser substituídos quando falharem. Por isso devem ser analisados através de técnicas adequadas para sistemas reparáveis. Muitas análises de sistemas reparáveis têm sido feitas considerando técnicas desenvolvidas para sistemas não reparáveis. Este trabalho propõe uma comparação das duas técnicas para a análise das diferenças e vantagens de cada uma das técnicas e sua adequação ao desenvolvimento de tratores agrícolas. No final conseguimos concluir e comprovar a importância do conhecimento do embasamento matemático das diferentes técnicas para evitar análises de confiabilidade enganosas. A fácil disponibilidade e utilização de sofwares, permitem que engenheiros sem o devido embasamento teórico apresentado neste trabalho façam análises que levem a conclusões errôneas sobre a tendência da confiabilidade dos equipamentos analisados

Indiana University-Purdue University Indianapolis (IUPUI) / Recent years have seen a growth in research on system reliability and maintenance. Various studies in the scientific fields of reliability engineering, quality and productivity analyses, risk assessment, software reliability, and probabilistic machine learning are being undertaken in the present era. The dependency of human life on technology has made it more important to maintain such systems and maximize their potential. In this dissertation, some methodologies are presented that maximize certain measures of system reliability, explain the underlying stochastic behavior of certain systems, and prevent the risk of system failure. An overview of the dissertation is provided in Chapter 1, where we briefly discuss some useful definitions and concepts in probability theory and stochastic processes and present some mathematical results required in later chapters. Thereafter, we present the motivation and outline of each subsequent chapter. In Chapter 2, we compute the limiting average availability of a one-unit repairable system subject to repair facilities and spare units. Formulas for finding the limiting average availability of a repairable system exist only for some special cases: (1) either the lifetime or the repair-time is exponential; or (2) there is one spare unit and one repair facility. In contrast, we consider a more general setting involving several spare units and several repair facilities; and we allow arbitrary life- and repair-time distributions. Under periodic monitoring, which essentially discretizes the time variable, we compute the limiting average availability. The discretization approach closely approximates the existing results in the special cases; and demonstrates as anticipated that the limiting average availability increases with additional spare unit and/or repair facility. In Chapter 3, the system experiences two types of sporadic impact: valid shocks that cause damage instantaneously and positive interventions that induce partial healing. Whereas each shock inflicts a fixed magnitude of damage, the accumulated effect of k positive interventions nullifies the damaging effect of one shock. The system is said to be in Stage 1, when it can possibly heal, until the net count of impacts (valid shocks registered minus valid shocks nullified) reaches a threshold $m_1$. The system then enters Stage 2, where no further healing is possible. The system fails when the net count of valid shocks reaches another threshold $m_2 (> m_1)$. The inter-arrival times between successive valid shocks and those between successive positive interventions are independent and follow arbitrary distributions. Thus, we remove the restrictive assumption of an exponential distribution, often found in the literature. We find the distributions of the sojourn time in Stage 1 and the failure time of the system. Finally, we find the optimal values of the choice variables that minimize the expected maintenance cost per unit time for three different maintenance policies. In Chapter 4, the above defined Stage 1 is further subdivided into two parts: In the early part, called Stage 1A, healing happens faster than in the later stage, called Stage 1B. The system stays in Stage 1A until the net count of impacts reaches a predetermined threshold $m_A$; then the system enters Stage 1B and stays there until the net count reaches another predetermined threshold $m_1 (>m_A)$. Subsequently, the system enters Stage 2 where it can no longer heal. The system fails when the net count of valid shocks reaches another predetermined higher threshold $m_2 (> m_1)$. All other assumptions are the same as those in Chapter 3. We calculate the percentage improvement in the lifetime of the system due to the subdivision of Stage 1. Finally, we make optimal choices to minimize the expected maintenance cost per unit time for two maintenance policies. Next, we eliminate the restrictive assumption that all valid shocks and all positive interventions have equal magnitude, and the boundary threshold is a preset constant value. In Chapter 5, we study a system that experiences damaging external shocks of random magnitude at stochastic intervals, continuous degradation, and self-healing. The system fails if cumulative damage exceeds a time-dependent threshold. We develop a preventive maintenance policy to replace the system such that its lifetime is utilized prudently. Further, we consider three variations on the healing pattern: (1) shocks heal for a fixed finite duration $\tau$; (2) a fixed proportion of shocks are non-healable (that is, $\tau=0$); (3) there are two types of shocks---self healable shocks heal for a finite duration, and non-healable shocks. We implement a proposed preventive maintenance policy and compare the optimal replacement times in these new cases with those in the original case, where all shocks heal indefinitely. Finally, in Chapter 6, we present a summary of the dissertation with conclusions and future research potential.

Submitted by Rafael Santana (rafael.silvasantana@ufpe.br) on 2017-04-19T18:10:57Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_Versão Final.pdf: 1475057 bytes, checksum: 12f4f23219e2dd8cfd695075bb204ac4 (MD5) / Made available in DSpace on 2017-04-19T18:10:57Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_Versão Final.pdf: 1475057 bytes, checksum: 12f4f23219e2dd8cfd695075bb204ac4 (MD5) Previous issue date: 2016-08-23 / CAPES / Este trabalho trata de sistemas reparáveis que sofrem reparo imperfeito, utilizando uma classe de modelos de processos estocásticos conhecida como Processo de Renovação Generalizado (PRG), que é um modelo de idade virtual que determina a classificação do reparo de acordo com o grau de redução que este proporciona sob a idade real do equipamento, mensurada através de um parâmetro de rejuvenescimento, , e este modelo permite inserir uma maior flexibilidade quanto ao tratamento de dados de falhas. Foi proposto um modelo PRG com base na distribuição -Exponencial ( -PRG), onde o sucesso da Exponencial deve-se, em parte, à sua capacidade de exposições a caudas pesadas e fenômenos de lei de potência. Os estimadores de máxima verossimilhança não apresentaram expressões analíticas e, então, a estimação dos parâmetros -PRG foi realizada por meio do algoritmo evolucionário Differential Evolution (DE), que é algoritmo estocástico para resolver problemas de otimização global de funções não lineares, ou seja, é um método para minimizar funções não lineares e não diferenciáveis em um espaço contínuo de busca. Com base no método DE, foram realizadas simulações a partir de dados de falha extraídos da literatura. A partir das simulações executadas utilizando o método bootstrap paramétrico, mesmo existindo valores discrepantes, o processo de simulação manteve as características dos dados iniciais, de modo que informações sobre as falhas não foram perdidas. Com as simulações, concluiu-se que para tamanhos amostrais maiores, as abordagens bootstrap utilizadas tendem a fornecer estimativas intervalares semelhantes para os parâmetros -PRG. Além disso, foi possível obter alguns resultados estatísticos para os estimadores como a ausência de normalidade e estimar o parâmetro de rejuvenescimento do PRG. / This work deals with repairable systems that undergo imperfect repair, using a class of stochastic process models known as Generalized Renewal Process (GRP), which is a virtual age model that determines the classification of the repair according to the degree of reduction that This provides, under the real age of the equipment, measured through a rejuvenation parameter, , and this model allows to insert a greater flexibility in the treatment of data of failures. A GRP model was proposed based on the -Exponential distribution ( -GRP), where -Exponential success is due, in part, to its ability to expose heavy tails and power law phenomena. The maximum likelihood estimators did not present analytical expressions and, therefore, the estimation of the -GRP parameters was performed using the evolutionary algorithm Differential Evolution (DE), which is a stochastic algorithm to solve problems of global optimization of non-linear functions, that is, is a method to minimize non-linear and non-differentiable functions in a continuous search space. Based on the DE method, simulations were performed based on fault data extracted from the literature. From the simulations performed using the parametric bootstrap method, even if there were discrepant values, the simulation process maintained the characteristics of the initial data, so that information about the failures was not lost. With the simulations, it was concluded that for larger sample sizes, the bootstrap approaches used tend to provide similar interval estimates for the -GRP parameters. In addition, it was possible to obtain some statistical results for the estimators such as the absence of normality and to estimate the GRP rejuvenation parameter.

<p>Recent years have seen a growth in research on system reliability and maintenance. Various studies in the scientific fields of reliability engineering, quality and productivity analyses, risk assessment, software reliability, and probabilistic machine learning are being undertaken in the present era. The dependency of human life on technology has made it more important to maintain such systems and maximize their potential. In this dissertation, some methodologies are presented that maximize certain measures of system reliability, explain the underlying stochastic behavior of certain systems, and prevent the risk of system failure.</p> <p><br></p> <p>An overview of the dissertation is provided in Chapter 1, where we briefly discuss some useful definitions and concepts in probability theory and stochastic processes and present some mathematical results required in later chapters. Thereafter, we present the motivation and outline of each subsequent chapter.</p> <p><br></p> <p>In Chapter 2, we compute the limiting average availability of a one-unit repairable system subject to repair facilities and spare units. Formulas for finding the limiting average availability of a repairable system exist only for some special cases: (1) either the lifetime or the repair-time is exponential; or (2) there is one spare unit and one repair facility. In contrast, we consider a more general setting involving several spare units and several repair facilities; and we allow arbitrary life- and repair-time distributions. Under periodic monitoring, which essentially discretizes the time variable, we compute the limiting average availability. The discretization approach closely approximates the existing results in the special cases; and demonstrates as anticipated that the limiting average availability increases with additional spare unit and/or repair facility.</p> <p><br></p> <p>In Chapter 3, the system experiences two types of sporadic impact: valid shocks that cause damage instantaneously and positive interventions that induce partial healing. Whereas each shock inflicts a fixed magnitude of damage, the accumulated effect of k positive interventions nullifies the damaging effect of one shock. The system is said to be in Stage 1, when it can possibly heal, until the net count of impacts (valid shocks registered minus valid shocks nullified) reaches a threshold $m_1$. The system then enters Stage 2, where no further healing is possible. The system fails when the net count of valid shocks reaches another threshold $m_2  (> m_1)$. The inter-arrival times between successive valid shocks and those between successive positive interventions are independent and follow arbitrary distributions. Thus, we remove the restrictive assumption of an exponential distribution, often found in the literature. We find the distributions of the sojourn time in Stage 1 and the failure time of the system. Finally, we find the optimal values of the choice variables that minimize the expected maintenance cost per unit time for three different maintenance policies.</p> <p><br></p> <p>In Chapter 4, the above defined Stage 1 is further subdivided into two parts: In the early part, called Stage 1A, healing happens faster than in the later stage, called Stage 1B. The system stays in Stage 1A until the net count of impacts reaches a predetermined threshold $m_A$; then the system enters Stage 1B and stays there until the net count reaches another predetermined threshold $m_1 (>m_A)$. Subsequently, the system enters Stage 2 where it can no longer heal. The system fails when the net count of valid shocks reaches another predetermined higher threshold $m_2 (> m_1)$. All other assumptions are the same as those in Chapter 3. We calculate the percentage improvement in the lifetime of the system due to the subdivision of Stage 1. Finally, we make optimal choices to minimize the expected maintenance cost per unit time for two maintenance policies.</p> <p><br></p> <p>Next, we eliminate the restrictive assumption that all valid shocks and all positive interventions have equal magnitude, and the boundary threshold is a preset constant value. In Chapter 5, we study a system that experiences damaging external shocks of random magnitude at stochastic intervals, continuous degradation, and self-healing. The system fails if cumulative damage exceeds a time-dependent threshold. We develop a preventive maintenance policy to replace the system such that its lifetime is utilized prudently. Further, we consider three variations on the healing pattern: (1) shocks heal for a fixed finite duration $\tau$; (2) a fixed proportion of shocks are non-healable (that is, $\tau=0$); (3) there are two types of shocks---self healable shocks heal for a finite duration, and non-healable shocks. We implement a proposed preventive maintenance policy and compare the optimal replacement times in these new cases with those in the original case, where all shocks heal indefinitely.</p> <p><br></p> <p>Finally, in Chapter 6, we present a summary of the dissertation with conclusions and future research potential.</p>

L'analyse prévisionnelle des risques d'un système complexe repose aujourd'hui sur une modélisation de la dynamique du système vis-à-vis des défaillances et réparations de ses composants. L'analyse qualitative d'un tel système consiste à rechercher et à analyser les scénarios conduisant à la panne. En raison de leur nombre, il est courant de ne s'intéresser qu'aux scénarios les plus caractéristiques, les Séquences de Coupe Minimales (SCM). L'absence de formalisation de ces SCM a généré soit des définitions spécifiques à certains outils de modélisation soit des définitions informelles. Les travaux présentés dans cette thèse proposent: i) un cadre et une définition formelle des séquences de coupe minimales, tout deux indépendants de l'outil de modélisation de fiabilité utilisé, ii) une méthode permettant leur calcul, méthode basée sur des propriétés déduites de leur définition, iii) l'extension des premières définitions aux composants multimodes. Ce cadre permet le calcul des SCM pour des installations décrites avec les Boolean logic Driven Markov Processes (BDMP). Sous l'hypothèse que l'ensemble des scénarios représentés implicitement via le modèle de sûreté établi peut être modélisé à l'aide d'un automate fini, ces travaux définissent la notion de cohérence des systèmes dynamiques et réparables, et le moyen d'obtenir une représentation minimale de l'ensemble des scénarios menant à la défaillance du système. / Preventive risk assessment of a complex system rely on a dynamic models which describe the link between the system failure and the scenarios of failure and repair events from its components. The qualitative analyses of a binary dynamic and repairable system is aiming at computing and analyse the scenarios that lead to the system failure. Since such systems describe a large set of those, only the most representative ones, called Minimal Cut Sequences (MCS), are of interest for the safety engineer. The lack of a formal definition for the MCS has generated multiple definitions either specific to a given model (and thus not generic) or informal. This work proposes i) a formal framework and definition for the MCS while staying independent of the reliability model used, ii) the methodology to compute them using property extracted from their formal definition, iii) an extension of the formal framework for multi-states components in order to perform the qualitative analyses of Boolean logic Driven Markov Processes (BDMP) models. Under the hypothesis that the scenarios implicitly described by any reliability model can always be represented by a finite automaton, this work is defining the coherency for dynamic and repairable systems as the way to give a minimal representation of all scenarios that are leading to the system failure.

Submitted by Daniele Amaral (daniee_ni@hotmail.com) on 2016-09-15T15:15:11Z No. of bitstreams: 1 DissCCF.pdf: 1472861 bytes, checksum: 937810926b98a08677085a559d13aec9 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-16T19:51:30Z (GMT) No. of bitstreams: 1 DissCCF.pdf: 1472861 bytes, checksum: 937810926b98a08677085a559d13aec9 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-16T19:51:36Z (GMT) No. of bitstreams: 1 DissCCF.pdf: 1472861 bytes, checksum: 937810926b98a08677085a559d13aec9 (MD5) / Made available in DSpace on 2016-09-16T19:51:41Z (GMT). No. of bitstreams: 1 DissCCF.pdf: 1472861 bytes, checksum: 937810926b98a08677085a559d13aec9 (MD5) Previous issue date: 2015-09-15 / Não recebi financiamento / The usual models in repairable systems are minimal, perfect and imperfect repair, and, in the literature, the minimum repair model is the most explored. In repairable systems it is common that the same type of components are studied and in these cases is relevant to verify the heterogeneity between them. According to Vaupel et al. (1979), the standard methods for analysis of repairable systems data ignore the heterogeneity not observed and in some cases this should be considered. Such variability can be estimated from frailty models, characterized by using a random e ect. It is proposed that the minimum repair model with frailty in order to estimate the heterogeneity not observed between systems. For this model it was conducted a simulation study in order to analyze the frequentist properties of the estimation process. The application of a real data set showed the applicability of the proposed model, in which the estimation of the parameters were determined from maximum likelihood and Bayesian approaches. / Os modelos de sistemas reparáveis usuais são os de reparo mí nimo, perfeito e imperfeito, sendo que, na literatura, o modelo de reparo mí nimo e o mais explorado. Em sistemas reparáveis e comum que componentes do mesmo tipo sejam estudados e nestes casos é relevante verifi car a heterogeneidade entre eles. Segundo Vaupel et al. (1979), os métodos padrões em análise de dados de sistemas reparáveis ignoram a heterogeneidade não observada e em alguns casos esta deveria ser considerada. Tal variabilidade pode ser estimada a partir dos modelos de fragilidade, caracterizados pela utilização de um efeito aleat ório. Propõe-se o modelo de reparo mí nimo com fragilidade, a fi m de estimar a heterogeneidade não observada entre sistemas. Para este modelo foi realizado um estudo de simula ção com o objetivo de analisar as propriedades frequentistas do processo de estimação. A aplicação em um conjunto de dados reais mostrou a aplicabilidade do modelo proposto, em que a estima ção dos parâmetros foram determinadas a partir das abordagens de m áxima verossimilhan ça e Bayesiana.

The aim of this thesis is to define and study stochastic models of repairable systems and the application of these models to biological systems, especially for cell survival after irradiation with ionizing radiation.

Dans les travaux existants, les analyses basées sur les modèles de la Sûreté de Fonctionnement (SdF) d'un système automatisé sont généralement focalisées uniquement sur la partie procédé. Aussi, les stratégies de reconfiguration du procédé - réalisées par le contrôle-commande - ne sont souvent pas modélisées, sinon de manière imprécises et sans échec possible. Pourtant, ces stratégies ont un impact certain sur la SdF du système bouclé, qui doit être pris en compte dans les modèles afin d'améliorer la pertinence des analyses. Le travail dont rend compte cette thèse contribue à la modélisation et à l'analyse de la SdF des systèmes dynamiques, réparables et reconfigurables. Premièrement, un nouveau formalisme de modélisation est proposé pour prendre en compte avec précision les différentes stratégies de reconfiguration du système avec leurs possibles échecs. Ce formalisme développe et généralise le principe des BDMP (Boolean logic Driven Markov Processes en anglais), auxquels il associe des machines de Moore afin de spécifier formellement les stratégies de reconfiguration. Dans un second temps, deux techniques d'analyse basées sur un modèle GBDMP (BDMP Généralisé) sont décrites. Ces techniques permettent d'obtenir un résultat qualitatif : l'ensemble des plus courtes Séquences de Coupe Minimales (SCM), ainsi qu'un résultat quantitatif : indicateur probabiliste de la disponibilité du système. Finalement, la modélisation GBDMP et l'analyse de SdF basée sur un modèle GBDMP sont expérimentées sur un cas d'étude représentatif de plusieurs problématiques industrielles liées au secteur de la production d'énergie électrique. / Existing works on Model Based Safety Analysis of an automated system generally focus on the process part. Process reconfiguration strategies that are driven by the control are often modeled without failure and with a lack of accuracy. However these strategies have a real impact on the safety of the closed-loop system. In order to improve the relevance of analysis, this impact has to be captured in models. This thesis contributes to modeling and analysis of dynamic repairable reconfigurable systems. Firstly a new modeling formalism is proposed to relevantly take into account different reconfiguration strategies that can fail. This formalism develops and generalizes the principle of Boolean logic Driven Markov Processes (BDMP), and enriches it with Moore machine for formally specifying reconfiguration strategies. In a second stage, two analysis techniques based on a Generalized BDMP (GBDMP) model are described. These techniques allow to obtain a qualitative result: the set of shortest Minimal Cut Sequences (MCS), and a quantitative result: probabilistic indicator of system availability. Finally, a case study coming from the electric power production field is addressed. This case study shows how several industrial problems can be solved in GBDMP framework.

Reliability analysis plays an important role in keeping manufacturers in a competitive position. It can be applied in many areas such as warranty predictions, maintenance scheduling, spare parts provisioning, and risk assessment. This dissertation focuses on statistical modeling and predictions based on lifetime data, degradation data, and recurrent event data. The datasets used in this dissertation come from the field, and have complicated structures. The dissertation consists of three main chapters, in addition to Chapter 1 which is the introduction chapter, and Chapter 5 which is the general conclusion chapter. Chapter 2 consists of the traditional time-to-failure data analysis. We propose a statistical method to address the failure data from an appliance used at home with the consideration of retirement times and delayed reporting time. We also develop a prediction method based on the proposed model. Using the information of retirement-time distribution and delayed reporting time, the predictions are more accurate and useful in the decision making. In Chapter 3, we introduce a nonlinear mixed-effects general path model to incorporate dynamic covariates into degradation data analysis. Dynamic covariates include time-varying environmental variables and usage condition. The shapes of the effect functions of covariates may be constrained to be, for example, monotonically increasing (i.e., higher temperature is likely to cause more damage). Incorporating dynamic covariates with shape restrictions is challenging. A modified alternative algorithm and the corresponding prediction method are proposed. In Chapter 4, we introduce a multi-level trend-renewal process (MTRP) model to describe component-level events in multi-level repairable systems. In particular, we consider two-level repairable systems in which events can occur at the subsystem level, or the component (within the subsystem) level. The main goal is to develop a method for estimation of model parameters and a procedure for prediction of the future replacement events at component level with the consideration of the effects from the subsystem replacement events. To explain unit-to-unit variability, time-dependent covariates as well as random effects are introduced into the heterogeneous MTRP model (HMTRP). A Metropolis-within-Gibbs algorithm is used to estimate the unknown parameters in the HMTRP model. The proposed method is illustrated by a simulated dataset. / Ph. D.