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The study on the longest stretch of consecutive successes in \random" trials dates back to 1916 when the German philosopher Karl Marbe wrote a paper concerning the longest stretch of consecutive births of children of the same sex as appearing in the birth register of a Bavarian town. The result was actually used by parents to \predict" the sex of their children. The longest stretch of same-sex births during that time in 200 thousand birth registrations was actually 17 t log2(200 103): During the past century, the research of longest stretch of consecutive successes (longest runs) has found applications in various areas, especially in the theory of reliability. The aim of this thesis is to study large deviations on longest runs in the setting of Markov chains. More precisely, we establish a general large deviation principle for the longest success run in a two-state (success or failure) Markov chain. Our tool is based on a recent result regarding a general large deviation for the longest success run in Bernoulli trails. It turns out that the main ingredient in the proof is to implement several global and local estimates of the cumulative distribution function of the longest success run.

O trabalho apresentado sob o título \"Análise e Síntese de Sistemas Multiplexados: Uma Abordagem de Confiabilidade e Manutenabilidade Operacional\" tem como objetivo propor um modelo prático para a manutenção, baseado na confiabilidade e manutenabilidade de componentes. Os dados desse trabalho foram obtidos através de relatórios gerenciais da Empresa de Telecomunicações de São Paulo S/A, no período de janeiro/05 a junho/06, para as topologias de rede em anel e ponto a ponto da cidade de São Paulo, municípios da Grande São Paulo, Vale do Paraíba e Litoral do Estado de São Paulo. Com esses dados, foi utilizado o algoritmo de Weibull, cujo modelo probabilístico permite modelar vários tipos de resultados experimentais e operacionais. Dessa forma, foram determinados a confiabilidade operacional, o Tempo Médio de Bom Funcionamento (MTTF), a manutenabilidade, o Tempo Médio de Reparo (MTTR) e a disponibilidade para os componentes da rede externa óptica e dos equipamentos de rede da topologia de rede em anel e ponto a ponto. Observou-se que o equipamento de rede de Multiplexação Densa por Divisão do Comprimento de Onda (DWDM) apresenta uma confiabilidade operacional maior que a dos Equipamentos de Rede Tradicionais (ERT), independente da topologia de rede utilizada. Comparando-se o custo de implantação de uma rede óptica com DWDM e ERT, a uma taxa de transmissão de 2,5 Gbps, pode ser verificado que o custo é aproximadamente sete vezes menor quando se utiliza a rede óptica com DWDM. Por fim, foi feita uma comparação entre o custo total e médio da manutenção corretiva e preventiva para as topologias analisadas. Assim, pode ser concluído que a tecnologia DWDM é a opção mais vantajosa em termos de confiabilidade e manutenabilidade em relação ao ERT. / The work presented under the heading \"Analysis and Synthesis of Multiplexed Systems: An Approach of Reliability and Operational Maintainability\" has as objective to consider a practical model for the maintenance, based on the reliability and maintainability of components. The data of this work had been gotten through management reports of the Company of Telecommunications of São Paulo S/A, in the period of january/05 to june/06, for the in ring and point to point network topologies of the city of São Paulo, cities of the Great São Paulo, Valley of Paraíba and the coast of the State of São Paulo. With these data, it was used the algorithm of Weibull, whose probabilistic model allows to model many types of experimentals and operationals results. Of this form, were determined the operational reliability, the Mean Time To Failure (MTTF), the maintainability, the Mean Time To Repair (MTTR) and the availability for the components of the fiber optic external network and the network equipments of the in ring and point-to-point network topology. It was observed that the network equipment of Dense Wavelength Division Multiplexing (DWDM) presents a greater operational reliability that the Traditionals Network Equipments (ERT), independent of the network topology used. Comparing itself the cost of implantation of an fiber optic network with DWDM and ERT, to a rate of transmission of 2,5 Gbps, it could be verified that the cost is approximately seven times lesser when it is used the fiber optic network with DWDM. Finally, a comparison between the total and average cost of the corrective and preventive maintenance for the analyzed topologies was made. So, it can be concluded that the technology DWDM is the option most advantageous in terms of reliability and maintainability in relation to the ERT.

O trabalho apresentado sob o título \"Análise e Síntese de Sistemas Multiplexados: Uma Abordagem de Confiabilidade e Manutenabilidade Operacional\" tem como objetivo propor um modelo prático para a manutenção, baseado na confiabilidade e manutenabilidade de componentes. Os dados desse trabalho foram obtidos através de relatórios gerenciais da Empresa de Telecomunicações de São Paulo S/A, no período de janeiro/05 a junho/06, para as topologias de rede em anel e ponto a ponto da cidade de São Paulo, municípios da Grande São Paulo, Vale do Paraíba e Litoral do Estado de São Paulo. Com esses dados, foi utilizado o algoritmo de Weibull, cujo modelo probabilístico permite modelar vários tipos de resultados experimentais e operacionais. Dessa forma, foram determinados a confiabilidade operacional, o Tempo Médio de Bom Funcionamento (MTTF), a manutenabilidade, o Tempo Médio de Reparo (MTTR) e a disponibilidade para os componentes da rede externa óptica e dos equipamentos de rede da topologia de rede em anel e ponto a ponto. Observou-se que o equipamento de rede de Multiplexação Densa por Divisão do Comprimento de Onda (DWDM) apresenta uma confiabilidade operacional maior que a dos Equipamentos de Rede Tradicionais (ERT), independente da topologia de rede utilizada. Comparando-se o custo de implantação de uma rede óptica com DWDM e ERT, a uma taxa de transmissão de 2,5 Gbps, pode ser verificado que o custo é aproximadamente sete vezes menor quando se utiliza a rede óptica com DWDM. Por fim, foi feita uma comparação entre o custo total e médio da manutenção corretiva e preventiva para as topologias analisadas. Assim, pode ser concluído que a tecnologia DWDM é a opção mais vantajosa em termos de confiabilidade e manutenabilidade em relação ao ERT. / The work presented under the heading \"Analysis and Synthesis of Multiplexed Systems: An Approach of Reliability and Operational Maintainability\" has as objective to consider a practical model for the maintenance, based on the reliability and maintainability of components. The data of this work had been gotten through management reports of the Company of Telecommunications of São Paulo S/A, in the period of january/05 to june/06, for the in ring and point to point network topologies of the city of São Paulo, cities of the Great São Paulo, Valley of Paraíba and the coast of the State of São Paulo. With these data, it was used the algorithm of Weibull, whose probabilistic model allows to model many types of experimentals and operationals results. Of this form, were determined the operational reliability, the Mean Time To Failure (MTTF), the maintainability, the Mean Time To Repair (MTTR) and the availability for the components of the fiber optic external network and the network equipments of the in ring and point-to-point network topology. It was observed that the network equipment of Dense Wavelength Division Multiplexing (DWDM) presents a greater operational reliability that the Traditionals Network Equipments (ERT), independent of the network topology used. Comparing itself the cost of implantation of an fiber optic network with DWDM and ERT, to a rate of transmission of 2,5 Gbps, it could be verified that the cost is approximately seven times lesser when it is used the fiber optic network with DWDM. Finally, a comparison between the total and average cost of the corrective and preventive maintenance for the analyzed topologies was made. So, it can be concluded that the technology DWDM is the option most advantageous in terms of reliability and maintainability in relation to the ERT.

For the past decade the Australian Customs Service (ACS) has been regarded as an organisation in decline. Customs' history has been sporadically influenced by numerous reports that identify many instances of 'maladministration'. More recently, instances, such as the 'Midford Paramount Affair', have brought media and public notoriety to Customs followed by the establishment of the Review of the ACS in May 1993 (The Conroy Report). This, the latest and most comprehensive report undertaken on the ACS, documented administrative malfunctions of a major kind. Each report, using its own rationale has recommended more advanced levels of information technology (IT) application. To study these protracted administrative issues, the author has used, as the basis of analysis, a dynamic contingent decision-paths schema as well as furthering the theoretical constructs of organisational 'reliability' theory. The dynamic contingent decision-paths schema is designed to provide a conceptual framework regarding public (and private) sector situations of agency decline, evaluation, strategic response and finally 'turnaround' policy and implementation. The ACS is now implementing a comprehensive turnaround strategy, which includes new and novel information technologies. Organisational 'reliability' theory relates to organisations that are required to be highly reliable in their daily work-related activities otherwise crises of some major magnitude may occur. These organisations need to practice near perfect organisational and decision-making performance, and tend to be highly technical, relying increasingly in turn on information technology in managing their respective systems or operations. Customs was an early innovator in using Electronic Data Interchange and is now pursuing e-commerce, which in part is being outsourced, to EDS, a multinational company. The study initially reviews the recent history of the ACS - 'mapping' the nature of the organisation's decline, raising relevant factors which the author argues may be seen as successive 'crisis points', and lastly, addresses the strategic 'turnaround' policies of the organisation. The author believes the nadir for Customs has been reached and there are now positive signs that the ACS has commenced its organisational 'turnaround'. Organisational design matters including structural and cultural issues have been addressed which has allowed Customs to forge new relationships with its clients, as well as fostering 'new' management philosophies. These new philosophies and relationships, together with participation with an industry lead advisory team and a new internal management team, have provided the catalyst for change and recovery. Political and industry pressure and their formal involvement in a recovery strategy provide a high level of confidence for Customs' future and the strategic and operational changes being implemented.

Submitted by Admir José Giacon Junior null (juniorgiacon@gmail.com) on 2018-03-06T14:12:14Z No. of bitstreams: 1 Análise probabilística da estabilidade de taludes via teoria da confiabilidade - GIACON JUNIOR - 2018.pdf: 4258233 bytes, checksum: 777c3f6fb0d3f477af5650ac6adc895a (MD5) / Approved for entry into archive by Maria Marlene Zaniboni null (zaniboni@bauru.unesp.br) on 2018-03-07T17:37:24Z (GMT) No. of bitstreams: 1 giaconjunior_aj_me_bauru.pdf: 4258233 bytes, checksum: 777c3f6fb0d3f477af5650ac6adc895a (MD5) / Made available in DSpace on 2018-03-07T17:37:24Z (GMT). No. of bitstreams: 1 giaconjunior_aj_me_bauru.pdf: 4258233 bytes, checksum: 777c3f6fb0d3f477af5650ac6adc895a (MD5) Previous issue date: 2018-01-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Devido às consequências negativas associadas à ruptura e deslizamentos de taludes, a análise de estabilidade desses assume uma parte primordial na área da engenharia geotécnica. A maioria dessas análises é realizada de maneira determinística, não incorporando as incertezas inerentes ao sistema. A constatação dessas incertezas em projetos de taludes associa-se a previsão de uma probabilidade de falha no desempenho de taludes quanto à segurança. Nesse contexto, esta dissertação busca avaliar a segurança de taludes através de uma abordagem probabilística, simulando taludes com geometrias e solos variados, verificando ainda a influência da elevação da posição do nível d´água. Para essa finalidade foram realizadas análises probabilísticas utilizando First Order Reliability Method (FORM) com base nos métodos de Equilíbrio Limite, através dos programas computacionais acadêmicos RASS (análises determinísticas) e RELgen (análises probabilísticas). Com base nos resultados, verificou-se que as superfícies críticas obtidas pelos métodos determinísticos podem não coincidir com as superfícies que apresentam a maior probabilidade de falha. Isto é verificado ainda na análise de inclinação da superfície do talude, em que inclinações apresentando fatores de segurança admissíveis, apresentaram probabilidades de falha não aceitáveis. Estas divergências são atribuídas às incertezas inerentes ao sistema. Sendo assim, as análises de estabilidade de talude baseadas apenas nos resultados de análises determinísticas não apresentam todas as variáveis presentes no contexto do projeto. Por fim, através dos resultados obtidos nesta pesquisa é possível inferir que a adoção da análise probabilística em projeto de taludes auxilia de uma forma consistente a avaliação da segurança dos taludes, contribuindo de maneira satisfatória na prática de projetos de engenharia geotécnica. / Due to the negative consequences associated with slope rupture and landslides, the stability analysis of these slopes plays an important role in geotechnical engineering. Most of these analyzes are carried out in a deterministic manner, not incorporating the uncertainties inherent to the system. The observation of these uncertainties in slope projects is associated with the forecast of a probability of failure in slope performance in terms of safety. In this context, this paper present research seeks to evaluate slope safety in a probabilistic manner, simulating slopes with varied geometries and soils, also verifying the influence of elevation of the water level position. For this purpose, were performed probabilistic analyzes using First Order Reliability Method (FORM), based on the Limit Equilibrium methods, RASS (deterministic analysis) and RELgen (probabilistic analyzes). Based on the results, it was found that the critical surfaces obtained by the deterministic methods may not coincide with the highest most probability surfaces to fail. This is still verified in surface slope analysis, where inclinations with acceptable safety factors presented probabilities of failure unacceptable. These divergences are attributed to the uncertainties inherent in the system. Therefore, slope stability analyzes based only on the results of deterministic analyzes do not present all the variables present in the project context. Finally, through the results obtained in this research it is possible to infer that the adoption of probabilistic analysis in slope design assists in a consistent way the assessment of slope safety, contributing in a satisfactory way in the practice of geotechnical engineering projects.

Organisationen wie Feuerwehren, med. Rettungsdienste oder Spezialeinheiten der Polizei zeigen auch in Situationen, die durch Unsicherheit, unvollständige Informationen oder eine sehr hohe Dynamik gekennzeichnet sind, eine effiziente und effektive Leistungsfähigkeit. Sie können deswegen als Hochleistungssysteme (HLS) bezeichnet werden. Im vorliegenden Artikel wird dargestellt wie sich Erkenntnisse der High Reliabilty Theory auf die Untersuchung von Hochleistungssystemen auswirken und welche Gemeinsamkeiten und Parallelen bestehen. Dabei wird insbesondere ein Schwerpunkt auf die Thematik des Lernens gelegt.

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.

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Στην παρούσα διατριβή επεκτείνουμε και γενικεύουμε γνωστές κατανομές ροών. Για το σκοπό αυτό μελετούμε κατανομές απλών σχηματισμών χρησιμοποιώντας τη μέθοδο εμφύτευσης σε Μαρκοβιανή αλυσίδα. Με την ίδια μεθοδολογική προσέγγιση μελετούμε τόσο τις μεταβλητές διωνυμικού τύπου, όσο και τις αντίστοιχες χρόνου αναμονής. Στο Πρώτο Κεφάλαιο παρουσιάζουμε μια ανασκόπηση της ερευνητικής δουλειάς των τελευταίων δεκαετιών σε κατανομές ροών. Στο Δεύτερο Κεφάλαιο μελετούμε κατανομές απλών σχηματισμών, οι οποίες αποτελούν επεκτάσεις και γενικεύσεις κατανομές ροών. Η μελέτη αυτή γίνεται στην περίπτωση που οι δοκιμές είναι ανεξάρτητες. Η υπόθεση αυτή αντικαθίσταται στο Τρίτο Κεφάλαιο από τη γενικότερη υπόθεση δοκιμών που παρουσιάζουν Μαρκοβιανή εξάρτηση πρώτης τάξης και κάτω από αυτό το νέο πλαίσιο μελετούνται κατανομές χρόνου αναμονής. Στο Τέταρτο Κεφάλαιο παρουσιάζεται μια ανασκόπηση των συνεχόμενων συστημάτων στη Θεωρία Αξιοπιστίας. Στη συνέχεια εισάγονται και μελετούνται δύο νέα συστήματα, τα αποία οποία επεκτείνουν και γενικεύουν γνωστά συνεχόμενα συστήματα. Στο Πέμπτο Κεφάλαιο γενικεύεται ένα κλασικό πρόβλημα περιορισμένης χωρητικότητας, το οποίο αναφέρεται συχνά στη Θεωρία Ροών και μας απασχολεί συχνά στο Πρώτο Κεφάλαιο. Νέα αποτελέσματα της διατριβής αυτής δημοσιεύονται στις εργασίες των Dafnis et al. (2007), Dafnis and Philippou (2010), Dafnis et al. (2010a), Dafnis et al. (2010b) και Dafnis et al. (2010c). / In the present Ph.D. thesis we extend and generalize well-known runs' distributions. For this purpose, we study exact distributions of simple patterns using the Markov chain embedding technique. Both binomial-type and waiting-time random variables are treated. In Chapter 1, we review known results on distributions of runs presented over the last decades. In Chapter 2, we study distributions of simple patterns, which extend and generalize distributions of runs. The trials are considered to be independent. This assumption is replaced by the more general one of first order dependence. Under this new framework, waiting time distributions are studied in chapter 3. In Chapter 4, we first review the research on consecutive systems in Reliability Theory. Then, we introduce and study two new systems which are generalizations of consecutive systems extensively studied in literature. Finally, in Chapter 5, a well-known restricted occupancy problem, applicable to the Theory of Runs and often met in Chapter 1, is generalized. New results of the thesis are published in the papers of Dafnis et al. (2007), Dafnis and Philippou (2010), Dafnis et al. (2010a), Dafnis et al. (2010b) and Dafnis et al. (2010c).