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Components are widely seen by software engineers as an important technology to address the "software crisis''. An important aspect of components in other areas of engineering is that system reliability can be estimated from the reliability of the components. We show how commonly proposed methods of reliability estimation and composition for software are inadequate because of differences between the models and the actual software systems, and we show where the assumptions from system reliability theory cause difficulty when applied to software. This thesis provides an approach to reliability that makes it possible, if not currently plausible, to compose component reliabilities so as to accurately and safely determine system reliability. Firstly, we extend previous work on input sub-domains, or partitions, such that our sub-domains can be sampled in a statistically sound way. We provide an algorithm to generate the most important partitions first, which is particularly important when there are an infinite number of input sub-domains. We combine analysis and testing to provide useful reliabilities for the various input sub-domains of a system, or component. This provides a methodology for calculating true reliability for a software system for any accurate statistical distribution of input values. Secondly, we present a calculus for probability density functions that permits accurately modeling the input distribution seen by each component in the system - a critically important issue in dealing with reliability of software components. Finally, we provide the system structuring calculus that allows a system designer to take components from component suppliers that have been built according to our rules and to determine the resulting system reliability. This can be done without access to the actual components. This work raises many issues, particularly about scalability of the proposed techniques and about the ability of the system designer to know the input profile to the level and kind of accuracy required. There are also large classes of components where the techniques are currently intractable, but we see this work as an important first step.

Components are widely seen by software engineers as an important technology to address the "software crisis''. An important aspect of components in other areas of engineering is that system reliability can be estimated from the reliability of the components. We show how commonly proposed methods of reliability estimation and composition for software are inadequate because of differences between the models and the actual software systems, and we show where the assumptions from system reliability theory cause difficulty when applied to software. This thesis provides an approach to reliability that makes it possible, if not currently plausible, to compose component reliabilities so as to accurately and safely determine system reliability. Firstly, we extend previous work on input sub-domains, or partitions, such that our sub-domains can be sampled in a statistically sound way. We provide an algorithm to generate the most important partitions first, which is particularly important when there are an infinite number of input sub-domains. We combine analysis and testing to provide useful reliabilities for the various input sub-domains of a system, or component. This provides a methodology for calculating true reliability for a software system for any accurate statistical distribution of input values. Secondly, we present a calculus for probability density functions that permits accurately modeling the input distribution seen by each component in the system - a critically important issue in dealing with reliability of software components. Finally, we provide the system structuring calculus that allows a system designer to take components from component suppliers that have been built according to our rules and to determine the resulting system reliability. This can be done without access to the actual components. This work raises many issues, particularly about scalability of the proposed techniques and about the ability of the system designer to know the input profile to the level and kind of accuracy required. There are also large classes of components where the techniques are currently intractable, but we see this work as an important first step.

This thesis presents a research project aimed at advancing the treatment of cold-formed steel (CFS) structural reliability in roof trusses. Structural design today relies almost exclusively on component-level design, so structural safety is assured by limiting the probability of failure of individual components. Reliability of the entire system is typically not assessed, so in a worst-case scenario the system reliability may be less than the component reliability, or in a best-case scenario the system reliability may be much greater than the component reliability. A roof truss itself, is a subsystem with several possible failure modes that are being studied in this test program. These trusses are constructed of CFS members that nest with one another at the truss nodes and are connected by drilling fasteners through the mated surfaces, as well as having steel sheathing fastened to the top chords for lateral bracing. Presented in this paper is a series of full-scale static tests on single cold-formed steel roof trusses with a unique experimental setup. The test specimens were carefully monitored to address multiple failure modes: buckling of the top chord, buckling of the truss webs, and any connection failures. This research includes the experimental results, the computed system reliability of the trusses as well as their relationship between the components reliability.

Large interruptions of power supply in the transmission system have considerable impact on modern society. The goal for the transmission system operator (TSO) is to prevent and mitigate such events with optimal decisions in design, planning, operation and maintenance. Identifying critical power components for system reliability provides one important input to this decision-making. This thesis develops quantitative component reliability importance indices applicable for identifying critical components in real transmission systems. Probabilistic models with component failure statistics are combined with detailed power system models evaluated with the AC power flow technique. In the presented method each system component is assigned three importance indices based on outage events expected probability and consequence to (i) reduced system security margin, (ii) interrupted load supply and (iii) disconnected generation units. By ranking components by each of the three interests, a more complete view of the risks to system reliability can be assessed than if, as traditionally, only (ii) is modelled. The impact on security margin is studied in well established critical transfer sections (CTS) supervised by the TSO. TSOs set the CTSs limits [MW] based on deterministic security criteria, with regard to thermal, voltage level, and system stability limits, and the CTSs' condition at post-contingency state is in the method used as an indicator of the system security margin. The methodology is extended with three indices modified to quantify the component importance for common-cause events initiated by acts of sabotage. The developed methods are applied on a significant part of the Great Britain transmission system, modelling 7000 components and 107 substation layouts. The study includes several load demand scenarios, 200 million initiating outage events and non-functioning protection equipment. The resulting component ranking provides an important input to the TSO's decision-making, and could be implemented as a complement to the existing deterministic N-1 criterion. With the methods applied a TSO can perform further and more detailed assessments on a few critical components in order to enhance system reliability for equipment failures and strengthen the system vulnerability against sabotage. / QC 20110920

Reliability prediction of components operating in complex systems has historically been conducted in a statistically isolated manner. Current physics-based, i.e. mechanistic, component reliability approaches focus more on component-specific attributes and mathematical algorithms and not enough on the influence of the system. The result is that significant error can be introduced into the component reliability assessment process. The objective of this study is the development of a framework that infuses the influence of the system into the process of conducting mechanistic-based component reliability assessments. The formulated framework consists of six primary steps. The first three steps, identification, decomposition, and synthesis, are qualitative in nature and employ system reliability and safety engineering principles for an appropriate starting point for the component reliability assessment. The most unique steps of the framework are the steps used to quantify the system-driven local parameter space and a subsequent step using this information to guide the reduction of the component parameter space. The local statistical space quantification step is accomplished using two newly developed multivariate probability tools: Multi-Response First Order Second Moment and Taylor-Based Inverse Transformation. Where existing joint probability models require preliminary statistical information of the responses, these models combine statistical information of the input parameters with an efficient sampling of the response analyses to produce the multi-response joint probability distribution. Parameter space reduction is accomplished using Approximate Canonical Correlation Analysis (ACCA) employed as a multi-response screening technique. The novelty of this approach is that each individual local parameter and even subsets of parameters representing entire contributing analyses can now be rank ordered with respect to their contribution to not just one response, but the entire vector of component responses simultaneously. The final step of the framework is the actual probabilistic assessment of the component. Variations of this final step are given to allow for the utilization of existing probabilistic methods such as response surface Monte Carlo and Fast Probability Integration. The framework developed in this study is implemented to conduct the finite-element based reliability prediction of a gas turbine airfoil involving several failure responses. The framework, as implemented resulted in a considerable improvement to the accuracy of the part reliability assessment and an increased statistical understanding of the component failure behavior.

A confiabilidade de um sistema de componentes depende da confiabilidade de cada componente. Assim, a estimação da função de confiabilidade de cada componente do sistema é de interesse. No entanto, esta não é uma tarefa fácil, pois quando o sistema falha, o tempo de falha de um dado componente pode não ser observado, isto é, um problema de dados censurados. Neste trabalho, propomos modelos Bayesianos paramétricos para estimação das funções de confiabilidade de componentes e sistemas em quatro diferentes cenários. Inicialmente, um modelo Weibull é proposto para estimar a distribuição do tempo de vida de um componente de interesse envolvido em sistemas coerentes não reparáveis, quando estão disponíveis o tempo de falha do sistema e o estado do componente no momento da falha do sistema. Não é imposta a suposição de que os tempos de vida dos componentes sejam identicamente distribuídos, mas a suposição de independência entre os tempos até a falha dos componentes é necessária, conforme teorema anunciado e devidamente demonstrado. Em situações com causa de falha mascarada, os estados dos componentes no momento da falha do sistema não são observados e, neste cenário, um modelo Weibull com variáveis latentes no processo de estimação é proposto. Os dois modelos anteriormente descritos propõem estimar marginalmente as funções de confiabilidade dos componentes quando não são disponíveis ou necessárias as informações dos demais componentes e, por consequência, a suposição de independência entre os tempos de vida dos componentes é necessária. Com o intuito de não impor esta suposição, o modelo Weibull multivariado de Hougaard é proposto para a estimação das funções de confiabilidade de componentes envolvidos em sistemas coerentes não reparáveis. Por fim, um modelo Weibull para a estimação da função de confiabilidade de componentes de um sistema em série reparável com causa de falha mascarada é proposto. Para cada cenário considerado, diferentes estudos de simulação são realizados para avaliar os modelos propostos, sempre comparando com a melhor solução encontrada na literatura até então, em que, em geral, os modelos propostos apresentam melhores resultados. Com o intuito de demonstrar a aplicabilidade dos modelos, análises de dados são realizadas com problemas reais não só da área de confiabilidade, mas também da área social. / The reliability of a system of components depends on reliability of each component. Thus, the initial statistical work should be the estimation of the reliability of each component of the system. This is not an easy task because when the system fails, the failure time of a given component can be not observed, that is, a problem of censored data. We propose parametric Bayesian models for reliability functions estimation of systems and components involved in four scenarios. First, a Weibull model is proposed to estimate component failure time distribution from non-repairable coherent systems when there are available the system failure time and the component status at the system failure moment. Furthermore, identically distributed failure times are not a required restriction. An important result is proved: without the assumption that components\' lifetimes are mutually independent, a given set of sub-reliability functions does not identify the corresponding marginal reliability function. In masked cause of failure situations, it is not possible to identify the statuses of the components at the moment of system failure and, in this second scenario, we propose a Bayesian Weibull model by means of latent variables in the estimation process. The two models described above propose to estimate marginally the reliability functions of the components when the information of the other components is not available or necessary and, consequently, the assumption of independence among the components\' failure times is necessary. In order to not impose this assumption, the Hougaard multivariate Weibull model is proposed for the estimation of the components\' reliability functions involved in non-repairable coherent systems. Finally, a Weibull model for the estimation of the reliability functions of components of a repairable series system with masked cause of failure is proposed. For each scenario, different simulation studies are carried out to evaluate the proposed models, always comparing then with the best solution found in the literature until then. In general, the proposed models present better results. In order to demonstrate the applicability of the models, data analysis are performed with real problems not only from the reliability area, but also from social area.

A confiabilidade de um sistema de componentes depende da confiabilidade de cada componente. Assim, a estimação da função de confiabilidade de cada componente do sistema é de interesse. No entanto, esta não é uma tarefa fácil, pois quando o sistema falha, o tempo de falha de um dado componente pode não ser observado, isto é, um problema de dados censurados. Neste trabalho, propomos modelos Bayesianos paramétricos para estimação das funções de confiabilidade de componentes e sistemas em quatro diferentes cenários. Inicialmente, um modelo Weibull é proposto para estimar a distribuição do tempo de vida de um componente de interesse envolvido em sistemas coerentes não reparáveis, quando estão disponíveis o tempo de falha do sistema e o estado do componente no momento da falha do sistema. Não é imposta a suposição de que os tempos de vida dos componentes sejam identicamente distribuídos, mas a suposição de independência entre os tempos até a falha dos componentes é necessária, conforme teorema anunciado e devidamente demonstrado. Em situações com causa de falha mascarada, os estados dos componentes no momento da falha do sistema não são observados e, neste cenário, um modelo Weibull com variáveis latentes no processo de estimação é proposto. Os dois modelos anteriormente descritos propõem estimar marginalmente as funções de confiabilidade dos componentes quando não são disponíveis ou necessárias as informações dos demais componentes e, por consequência, a suposição de independência entre os tempos de vida dos componentes é necessária. Com o intuito de não impor esta suposição, o modelo Weibull multivariado de Hougaard é proposto para a estimação das funções de confiabilidade de componentes envolvidos em sistemas coerentes não reparáveis. Por fim, um modelo Weibull para a estimação da função de confiabilidade de componentes de um sistema em série reparável com causa de falha mascarada é proposto. Para cada cenário considerado, diferentes estudos de simulação são realizados para avaliar os modelos propostos, sempre comparando com a melhor solução encontrada na literatura até então, em que, em geral, os modelos propostos apresentam melhores resultados. Com o intuito de demonstrar a aplicabilidade dos modelos, análises de dados são realizadas com problemas reais não só da área de confiabilidade, mas também da área social. / The reliability of a system of components depends on reliability of each component. Thus, the initial statistical work should be the estimation of the reliability of each component of the system. This is not an easy task because when the system fails, the failure time of a given component can be not observed, that is, a problem of censored data. We propose parametric Bayesian models for reliability functions estimation of systems and components involved in four scenarios. First, a Weibull model is proposed to estimate component failure time distribution from non-repairable coherent systems when there are available the system failure time and the component status at the system failure moment. Furthermore, identically distributed failure times are not a required restriction. An important result is proved: without the assumption that components\' lifetimes are mutually independent, a given set of sub-reliability functions does not identify the corresponding marginal reliability function. In masked cause of failure situations, it is not possible to identify the statuses of the components at the moment of system failure and, in this second scenario, we propose a Bayesian Weibull model by means of latent variables in the estimation process. The two models described above propose to estimate marginally the reliability functions of the components when the information of the other components is not available or necessary and, consequently, the assumption of independence among the components\' failure times is necessary. In order to not impose this assumption, the Hougaard multivariate Weibull model is proposed for the estimation of the components\' reliability functions involved in non-repairable coherent systems. Finally, a Weibull model for the estimation of the reliability functions of components of a repairable series system with masked cause of failure is proposed. For each scenario, different simulation studies are carried out to evaluate the proposed models, always comparing then with the best solution found in the literature until then. In general, the proposed models present better results. In order to demonstrate the applicability of the models, data analysis are performed with real problems not only from the reliability area, but also from social area.