Dissertations / Theses on the topic 'Weibull distribution function'

In recent years, studying soft errors has become an issue of greater importance. There have been many methods developed that estimate the Soft Error Rate. Those methods are either deterministic or statistical. The proposed deterministic model aims to improve Soft Error Rate estimation by accurately approximating the generated pulse and all subsequent pulses. The generated pulse is approximated by a piecewise function consisting of two Weibull cumulative distribution functions. This method is an improvement over existing methods as it offers high accuracy while requiring less pre-characterization. The proposed algorithm reduces pre-characterization by allowing the beta Weibull parameter to be calculated during runtime using gate parameters such as the gate delay.

A surge function is a mathematical function of the form f(x)=axpe-bx. We simplify the surge function by holding p constant at 1 and investigate the simplified form as a potential model to represent the full peak of a stream discharge hydrograph. The previously studied Weibull and gamma distributions are included for comparison. We develop an analysis algorithm which produces the best-fit parameters for every peak for each model function, and we process the data with a MATLAB script that uses spectral analysis to filter year-long, 15-minute, stream-discharge data sets. The filtering is necessary to locate the concave-upward inflection points used to separate the data set into its constituent, individual peaks. The Levenberg-Marquardt algorithm is used to iteratively estimate the unknown parameters for each version of the modeled peak by minimizing the sum of squares of residuals. The results allow goodness-of-fit comparisons between the three model functions, as well as a comparison of peaks at the same gage through the year of record. Application of these methods to five rivers from three distinct hydrologic regions shows that the simple surge function is a special case of the gamma distribution, which is known to be useful as a modeling function for a full-peak hydrograph. The study also confirms that the Weibull distribution produces good fits to 15-minute hydrograph data.

No presente trabalho, e proposto um modelo de regressão utilizando a distribuição gama generalizada exponenciada (GGE) para dados censurados, esta nova distribuição e uma extensão da distribuição gama generalizada. A distribuição GGE (CORDEIRO et al., 2009) que tem quatro parâmetros pode modelar dados de sobrevivência quando a função de risco tem forma crescente, decrescente, forma de U e unimodal. Neste trabalho apresenta-se uma expansão natural da distribuição GGE para dados censurados, esta distribuição desperta o interesse pelo fato de representar uma família paramétrica que possui como casos particulares outras distribuições amplamente utilizadas na analise de dados de tempo de vida, como as distribuições gama generalizada (STACY, 1962), Weibull, Weibull exponenciada (MUDHOLKAR et al., 1995, 1996), exponencial exponenciada (GUPTA; KUNDU, 1999, 2001), Rayleigh generalizada (KUNDU; RAKAB, 2005), dentre outras, e mostra-se útil na discriminação entre alguns modelos probabilísticos alternativos. Considerando dados censurados, e abordado o método de máxima verossimilhança para estimar os parâmetros do modelo proposto. Outra proposta deste trabalho e introduzir um modelo de regressão log-gama generalizado exponenciado com efeito aleatório. Por fim, são apresentadas três aplicações para ilustrar a distribuição proposta.
In the present study, we propose a regression model using the exponentiated generalized gama (EGG) distribution for censored data, this new distribution is an extension of the generalized gama distribution. The EGG distribution (CORDEIRO et al., 2009) that has four parameters it can model survival data when the risk function is increasing, decreasing, form of U and unimodal-shaped. In this work comes to a natural expansion of the EGG distribution for censored data, is awake distribution the interest for the fact of representing a parametric family that has, as particular cases, other distributions which are broadly used in lifetime data analysis, as the generalized gama (STACY, 1962), Weibull, exponentiated Weibull (MUDHOLKAR et al., 1995, 1996), exponentiated exponential (GUPTA; KUNDU, 1999, 2001), generalized Rayleigh (KUNDU; RAKAB, 2005), among others, and it is shown useful in the discrimination among some models alternative probabilistics. Considering censored data, the maximum likelihood estimator is considered for the proposed model parameters. Another proposal of this work was to introduce a log-exponentiated generalized gamma regression model with random eect. Finally, three applications were presented to illustrate the proposed distribution.

In dieser Arbeit werden die Folgen der Calvo-Annahme in dynamischen makroökonomischen Modellen untersucht. Dafür wird die Calvo-Annahme unter Anwendung des Konzepts der statistischen Hazardfunktion verallgemeinert. Ich untersuche zwei mögliche Anwendungen dieses Ansatzes innerhalb von DSGE-Modellen. Im ersten Artikel zeige ich, dass der Zugewinn an Handhabbarkeit, der aus der Calvo-Annahme für Neu-Keynesianische Modelle folgt, mit unerwünschten Folgen in Bezug auf die Inflationsdynamiken einher geht. Der zweite Artikel schätzt die aggregierte Hazardfunktion unter Verwendung des theoretischen Rahmens des ersten Artikels. Es zeigt sich, dass die Annahme einer konstanten Hazardfunktion, die aus der Calvo-Annahme folgt, von den Daten eindeutig abgelehnt wird. Im dritten Artikel analysiere ich die Implikationen der empirisch geschätzten Hazardfunktion für die Persistenz von Inflation und die Geldpolitik. Die Untersuchungen zeigen, dass mittels der empirisch plausiblen aggregierten Hazardfunktion Zeitreihen simuliert werden können, die mit der Persistenz der inflatorischen Lücke im US Verbraucherpreisindex konsistent sind. Anhand dieser Ergebnisse komme ich zu dem Schluss, dass die Hazardfunktion eine entscheidende Rolle für die dynamischen Eigenschaften von Inflation spielt. Der letzte Artikel wendet den selben Modellierungsansatz auf ein Real-Business-Cycle Model mit rigidem Arbeitsmarkt an. Unter Verwendung eines allgemeineren stochastischen Anpassungsprozess stelle ich fest, dass die Arbeitsmarktdynamiken von einem Parameter beinflusst werden, der das Monotonieverhalten der Hazardfunktion bestimmt. Insbesondere steigt die Volatilität des Beschäftigungsniveaus, wohingegen dessen Persistenz mit zunehmendem Parameterwert abnimmt.
The Calvo assumption (Calvo, 1983) is widely used in the macroeconomic literature to model market frictions that limit the ability of economic agents to re-optimize their control variables. In spite of its virtues, the Calvo assumption also implies singular adjustment behavior at the firm level as well as a restrictive aggregation mechanism for the whole economy. In this study, I examine implications of the Calvo assumption for macroeconomic dynamics. To do so, I extend the Calvo assumption to a more general case based on the concept of the statistical hazard function. Two applications of this approach are studied in the DSGE framework. In the first essay, I apply this approach to a New Keynesian model, and demonstrate that tractability gained from the Calvo pricing assumption is costly in terms of inflation dynamics. The second essay estimates aggregate price reset hazard function using the theoretical framework constructed in the first essay, and shows that the constant hazard function implied by the Calvo assumption is strongly rejected by the aggregate data. In the third essay, I further explore implications of the empirically based hazard function for inflation persistence and monetary policy. I find that the empirically plausible aggregate price reset hazard function can generate simulated data that are consistent with inflation gap persistence found in the US CPI data. Based on these results, I conclude that the price reset hazard function plays a crucial role for generating inflation dynamics. The last essay applies the same modeling approach to a RBC model with employment rigidity. I find that, when introducing a more general stochastic adjustment process, the employment dynamics vary with a parameter, which determines the monotonic property of the hazard function. In particular, the volatility of employment is increasing, but the persistence is decreasing in the value of the parameter.

In alkalischen Lösungen führt die Reaktion von Hydroxylionen mit den Si-O-Si-Bindungen des Glasnetzwerks zur Bildung hydratisierter Oberflächen und gelöstem Silikat. Der Grad der Korrosion bzw. der Alterung der Glasfaser ist abhängig von der chemischen Zusammensetzung des Glases und Korrosionslösung sowie von Zeit und Temperatur. Die Untersuchung von Glasfasern verschiedener chemischer Zusammensetzung in NaOH- sowie Zementlösungen zeigte, dass die inhibierende Wirkung von Ca-Ionen zu einem veränderten Korrosionsmechanismus führt. Dies konnte anhand der mechanischen Eigenschaften der Glasfasern sowie rasterelektronenmikroskopischen Untersuchungen gezeigt werden. Während die Korrosion in NaOH-Lösung zu einer ausgeprägten Umwandlung der gesamten äußeren Glasfaserschicht in Reaktionsprodukte führte, zeigten Glasfasern in Zementlösung bei gleichem pH-Wert einen stark lokal begrenzten, punktförmigen Angriff. Daraus resultieren unterschiedliche mechanische Eigenschaften der Glasfasern in Abhängigkeit von der gewählten Korrosionslösung.

A resistência à ruptura de materiais frágeis como o concreto de granulometria fina é fortemente dependente de sua heterogeneidade, do tamanho da amostra e da heterogeneidade das tensões. A partir de uma abordagem probabilista, fundamentada no modelo de Weibull, este trabalho trata da influência de tais efeitos sobre a resistência à tração de painéis compósitos formados por concreto de granulometria fina e telas soldadas. Desde que as armaduras se mantenham em regime elástico, mostra-se que o modelo de Weibull de dois parâmetros pode ser empregado com sucesso na previsão da ruptura dos painéis compósitos em estudo. Os parâmetros foram então identificados com medidas de ensaios de flexão em três e em quatro pontos de barras de concreto de granulometria fina de dois tamanhos diferentes. A utilização do modelo de Weibull confirmou, por outro lado, a validade da teoria de misturas como ferramenta para estimar as resistências de rupturas locais correspondentes a diferentes níveis de formação de fissuras
The rupture strength of brittle materials such as the microconcrete is strongly dependent on the microstructural heterogeneity, the sample size and the stress heterogeneity. Using a probabilistic approach, based on the Weibull distribution, this work deals with the influence of such effects on the tensile strength of composite panels formed by microconcrete and welded wire grids. Provide the reinforcements behaves in elastic regime, it is shown that the model of Weibull of two parameters can be used with success to predict the failure of the composite panels studied. The parameters were then identified from measurements of flexural tests in three and in four points of two different sizes of microconcrete samples. The feasibility of the Weibull model validates, as well, the rule of mixture as a satisfactory tool to estimate local failure strengths of related to different levels of cracking

The Weibull distribution is a popular and widely used distribution in reliability and in lifetime data analysis. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. Many modifications of the Weibull distribution have achieved the above purpose. On the other hand, the number of parameters has increased, the forms of the survival and hazard functions have become more complicated and the estimation problems have risen. This thesis provides an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution, which could serve as an important reference and encourage further modifications of the Weibull distribution. Four different modifications of the Weibull distribution are proposed to address some of the above problems using different techniques. First model, with five parameters, is constructed by considering a two-component serial system with one component following a Weibull distribution and another following a modified Weibull distribution. A new method has been proposed to reduce the number of parameters of the new modified Weibull distribution from five to three parameters to simplify the distribution and address the estimation problems. The reduced version has the same desirable properties of the original distribution in spite of having two less parameters. It can be an alternative distribution for all modifications of the Weibull distribution with bathtub shaped hazard rate functions. To deal with unimodal shaped hazard rates, the third model with four parameters, named as the exponentiated reduced modified Weibull distribution is introduced. This model is flexible, has a nice physical interpretation and has the ability to capture monotonically increasing, unimodal and bathtub shaped hazard rates. It is a generalization of the reduced modified Weibull distribution. The proposed distribution gives the best fit comparing to other modifications of the Weibull distribution including those having similar properties. A three-parameter discrete distribution is introduced based on the reduced distribution. It is one of only three discrete distributions allowing for bathtub shaped hazard rate functions. Four real data sets have applied to this distribution. The new distribution is shown to outperform at least three other models including the ones allowing for bathtub shaped hazard rate functions. The new models show flexibility and can be used to model different kinds of real data sets better than other modified versions of Weibull distribution including those having the same number of parameters. The mathematical properties and statistical inferences of the new models are studied. Based on a simulation study the performances of the MLEs of each model are assessed with respect to sample size n. We find no evidence that the generalized modified Weibull distribution can provide a better fit than the exponentiated Weibull distributionfor data sets exhibiting the modified unimodal hazard function.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2014.
Made available in DSpace on 2015-05-12T04:03:06Z (GMT). No. of bitstreams: 1 333353.pdf: 5233518 bytes, checksum: 599b6c026148a94e45d4b00a33f14b78 (MD5) Previous issue date: 2014
O desenvolvimento de sistemas elétricos e eletrônicos permitiu a massificação do uso de dispositivos eletrônicos programáveis para comando e controle de operações de sistemas técnicos. Tais dispositivos possibilitaram o desenvolvimento de sistemas técnicos mais complexos, porém, devido a essa elevada complexidade, observou-se um aumento de acidentes causados por falhas inerentes ao controle de tais sistemas. Para se reduzir esses acidentes, foram criadas normas técnicas para sistemas de controle, cuja aplicação seja relevante a segurança, o que deu origem a segurança funcional. Segurança funcional refere-se à segurança que é mantida atráves do correto funcionamento de um sistema técnico. Diferentes segmentos industriais tem aplicado o conceito de segurança funcional, para criar máquinas e sistemas mais seguros. No setor de construção de máquinas, o uso de funções de segurança reduz o número de acidentes de trabalho, ao evitar que operadores, mantenedores e pessoas ao redor fiquem expostas aos perigos inerente das máquinas. As normas técnicos impõe requisitos quantitativos e qualitativos sobre os sistemas de controle de segurança. A norma técnica internacional IEC 61508 definiu um framework para quantificação de segurança funcional. Para cada setor industrial, normas específicas foram baseadas baseadas na IEC 61508. Esse framework é bem adequado para componentes elétricos e eletrônicos. Porém, na área de maquinário industrial, sistemas de controle são realizados não somente com tais componentes, mas também por componentes mecânicos, pneumáticos e hidráulicos, os quais apresentam um comportamento diferente de falha. Tais componentes são considerados pela norma técnica internacional ISO 13849. No entanto, os métodos de quantificação desta norma contém fortes limitações e não são completamente compreendidos pelos usuários. Este trabalho dedica-se ao estudo da norma técnica internacional de segurança funcional no setor de construção de máquinas industriais, a ISO 13849. O foco do estudo é a quantificação de falhas físicas de componentes. Falhas físicas sao quantificadas através de indicadores probabilísticos, sendo objeto de estudo da engenharia de confiabilidade. No primeiro capítulo, desenvolve-se o conceito de segurança funcional. O conceito é explorado como um todo, como uma ferramenta de redução de riscos, e posteriormente como esse conceito é aplicado no setor de construção de máquinas. O apêndice A complementa o capítulo 1 com a estrutura legal no que diz respeito à segurança de máquinas na Europa, definido pela Diretiva Europeia de Máquinas, da qual a norma técnica ISO 13849 faz parte. Ainda no capítulo 1 são identificadas as principais linhas de pesquisa, e o objetivo do trabalho é enunciado. Este trabalho, feito em parceria com a Bosch Rexroth, tem como objetivo o desenvolvimento de um método que possibilite a quatificação de índices de confiabilidade para segurança funcional utilizando distribuição de Weibull. No segundo capítulo, conceitos básicos para a compreensão do trabalho são apresentados. Os primeiros conceitos relacionam-se com conceitos da engenharia de confiabilidade, com o objetivo de esclarecer conceitos como probabilidade, confiabilidade, probabilidade de falha e construir o conceito do índice utilizado pela ISO 13849, a frequência média de falhas perigosas por hora, PFH. O apêndice B complementa esse capítulo, com uma explicação intuitiva do que é medido através do PFH. Neste capítulo também é apresentada a distribuição de Weibull, bem como métodos de cálculo de PFH. Os parâmetros para cálculo do PFH segundo a ISO 13849 são apresentados e explicados. No terceiro capítulo é apresentado como se é calculado o PFH através de simulação a eventos discretos. Um método para cálculo do PFH considerando distribuição de Weibull, para estruturas simples e estruturas redundantes, correspondendo às categorias B, 1, 3 e 4 da norma técnica ISO 13849. O apêndices C desenvolve a equação para determinaão do número mínimo de simulações para se alcançar o resultado desejado, e o apêndice D desenvolve as equações utilizadas pelo método proposto para estruturas redundantes com falha de componentes seguindo a distribuição de Weibull. Os resultados para os casos de comparação com a ISO 13849 são apresentados no apêndice E. No quarto capítulo é apresentado um exemplo de aplicação do método proposto em uma máquina hidráulica simples do Laboratório de Sistemas Hidráulicos e Pneumáticos (LASHIP), da Universidade Federal de Santa Catarina (UFSC). A determinação do PFH e subsequentemente do PL é realizada através do procedimento dado pela norma e pelo método proposto. Utilizando-se o método proposto, foi possível calcular PFH para intervalos de utilização diferente do considerado pela ISO 13849, bem como reconhecer o efeito do desgaste do componente, caracterizado pela distribuição de Weibull. No quinto capítulo é apresentado uma visão geral de como integrar o cálculo de PFH com distribuição de Weibull com o processo de desenvolvimento de uma máquina, baseado em experiência com a Bosch Rexroth. No capítulo de conclusão é analisado o potencial de se realizar análises mais realistas, e as limitações do método proposto, sendo adequado apenas para máquinas o subsistemas produzidos em série, devido ao requerimento de dados de campo para extrair os parâmetros da distribuição de Weibull para cada componente. Analisa-se também como que a pesquisa desenvolvida se encaixa na linha de pesquisa explicitada no primeiro capítulo, e qual a relevância para o cenário brasileiro. Adicionalmente, sugestões para trabalhos futuros são feitas.
Abstract : The IEC 61508 standard series defined a framework for quantification of functional safety. For each particular industry sector, specific standards are being developed based on it. This framework is well suited for electrical and electronic components. However, in the field of machinery, control systems are realized not only by such components, but also by mechanical, pneumatic and hydraulic components, which exhibit a different failure behavior. Such components are considered by the ISO 13849 standard. However, quantification methods of this standard are still not quite well understood by the users, and have strong limitations. This work presents a study an alternative method of how to calculate the average frequency of dangerous failures (PFH), required by ISO 13849 in order to achieve a Performance Level (PL). This alternative method includes modeling safety functions as Reliability Block Diagram and evaluation of PFH using the software BlockSim, through Discrete Event Simulation. Modeling hypothesis and limitations are discussed. The proposed method enables calculation of the standard s cases, as well as consideration of different failure distributions, of which Weibull distribution is considered. A study case considering Weibull distributed failures is presented. Applicability of the method is also discussed.

A stochastic model for the dynamics of a limit order book is evaluated and tested on empirical data. Arrival of limit, market and cancellation orders are described in terms of a Markovian queuing system with exponentially distributed occurrences. In this model, several key quantities can be analytically calculated, such as the distribution of times between price moves, price volatility and the probability of an upward price move, all conditional on the state of the order book. We show that the exponential distribution poorly fits the occurrences of order book events and further show that little resemblance exists between the analytical formulas in this model and the empirical data. The log-normal and Weibull distribution are suggested as replacements as they appear to fit the empirical data better.

Made available in DSpace on 2016-06-02T20:04:51Z (GMT). No. of bitstreams: 1 3028.pdf: 7339557 bytes, checksum: 16711c2271b754604bfa0b0fba30290b (MD5) Previous issue date: 2010-03-04
In this work, we introduce a Bayesian Analysis for survival multivariate data in the presence of a covariate vector and censored observations. Different frailties or latent variables are considered to capture the correlation among the survival times for the same individual. We also introduce a Bayesian analysis for some of the most popular bivariate exponential distributions introduced in the literature. A Bayesian analysis is also introduced for the Block & Basu bivariate exponential distribution using Markov Chain Monte Carlo (MCMC) methods and considering lifetimes in presence of covariates and censored data. In another topic, we introduce a Bayesian Analysis for bivariate lifetime data in the presence of covariates and censoring data assuming different bivariate Weibull distributions derived from some existing copula functions. A great computational simplification to simulate samples for the joint posterior distribution is obtained using the WinBUGS software. Numerical illustrations are introduced considering real data sets considering every proposed methodology.
Nesta tese introduzimos uma an´alise Bayesiana para dados de sobreviv encia multivariados, na presen¸ca de um vetor de covari´aveis e observa¸c oes censuradas. Diferentes fragilidades ou vari´aveis latentes s ao consideradas para capturar a correla¸c ao existente entre os tempos de sobreviv encia, para o mesmo indiv´ıduo. Tamb´em apresentamos uma an´alise Bayesiana para algumas das mais populares distribui¸c oes exponenciais bivariadas introduzidas na literatura. Uma an´alise Bayesiana tamb´em ´e introduzida para a distribui¸c ao exponencial bivariada de Block & Basu, usando m´etodos MCMC (Monte Carlo em Cadeias de Markov) e considerando os tempos de sobreviv encia na presen¸ca de covari´aveis e dados censurados. Em outro t´opico, introduzimos uma an´alise Bayesiana para dados de sobreviv encia bivariados na presen¸ca de covari´aveis e observa¸c oes censuradas, assumindo diferentes distribui¸c oes bivariadas Weibull derivadas de algumas fun¸c oes c´opulas existentes. Uma grande simplifica¸c ao computacional para simular amostras da distribui¸c ao a posteriori conjunta de interesse ´e obtida usando o software WinBUGS. Ilustra¸c oes num´ericas s ao introduzidas considerando conjunto de dados reais, para cada uma das metodologias propostas.

Dans le premier chapitre, la notion d'évaluation des risques sismiques est définie et les caractéristiques sismotectoniques de la région d'étude sont brièvement présentés. Un examen rigoureux des modèles stochastiques, appliqués au domaine de la sismologie est fourni. Dans le chapitre 2, différents modèles semi-Markoviens sont développés pour étudier la sismicité des îles Ioniennes centrales ainsi que le Nord de la mer Egée (Grèce). Les quantités telles que le noyau semi-Markovien et les probabilités de destination sont évaluées, en considérant que les temps de séjour suivent les distributions géométrique, discrète Weibull et Pareto. Des résultats utiles sont obtenus pour l'estimation de la sismicité. Dans le troisième chapitre un nouvel algorithme de Viterbi pour les modèles semi-Markoviens cachés est construit, dont la complexité est une fonction linéaire du nombre d'observations et une fonction quadratique du nombre d'états cachés, la plus basse existante dans la littérature. Une extension de ce nouvel algorithme est développée pour le cas où une observation dépend de l'état caché correspondant, mais aussi de l'observation précédente (cas SM1-M1). Dans le chapitre 4 les modèles semi-Markoviens cachés sont appliquées pour étudier la sismicité du Nord et du Sud de la mer Égée. La séquence d'observation est constituée des magnitudes et des positions d’un tremblement de terre et le nouvel algorithme de Viterbi est mis en œuvre afin de décoder les niveaux des tensions cachés qui sont responsables pour la sismogenèse. Les phases précurseurs (variations des tensions cachées) ont été détectées en avertissant qu’un tremblement de terre pourrait se produire. Ce résultat est vérifié pour 70 sur 88 cas (le score optimal). Les temps de séjour du processus caché étaient supposés suivre les distributions Poisson, logarithmique ou binomiale négative, tandis que les niveaux de tensions cachés ont été classés en 2, 3 ou 4 états. Les modèles de Markov caché ont également été adaptés sans présenter des résultats intéressants concernant les phases précurseurs. Dans le chapitre 5 un algorithme de Viterbi généralisé pour les modèles semi-Markoviens cachés, est construit dans le sens que les transitions au même état caché sont autorisées et peuvent également être décodées. De plus, une extension de cet algorithme généralisé dans le contexte SM1-M1 est présentée. Dans le chapitre 6 nous modifions de manière convenable le modèle Cramér-Lundberg y compris des sinistres négatifs et positifs, afin de décrire l'évolution avec le temps des changements de contraintes de Coulomb (valeurs ΔCFF) calculées pour sept épicentres (M ≥ 6) du Nord de la mer Egée. Formules pour les probabilités de ruine sont définies sous une forme générale. Corollaires sont également formulés pour la distribution exponentielle et Pareto. L'objectif est de mettre en lumière la question suivante qui pose la problématique dans la Sismologie: Au cours d'une année pourquoi un tremblement de terre s’est produit dans une position précise et pas dans une autre position, aux régions sismotectoniquement homogènes ayant valeurs ΔCFF positives. Les résultats montrent que les nouvelles formules de probabilité peuvent contribuer à répondre au problème susmentionné
In the first chapter the definition of the seismic hazard assessment is provided, the seismotectonic features of the study areas are briefly presented and the already existing mathematical models applied in the field of Seismology are thoroughly reviewed. In chapter 2, different semi-Markov models are developed for studying the seismicity of the areas of the central Ionian Islands and the North Aegean Sea (Greece). Quantities such as the kernel and the destination probabilities are evaluated, considering geometric, discrete-Weibull and Pareto distributed sojourn times. Useful results are obtained for forecasting purposes. In the third chapter a new Viterbi algorithm for hidden semi-Markov models is developed, whose complexity is a linear function of the number of observations and a quadratic function of the number of hidden states, the lowest existing in the literature. Furthermore, an extension of this new algorithm is introduced for the case that an observation depends on the corresponding hidden state but also on the previous observation (SM1-M1 case). In chapter 4, different hidden semi-Markov models (HSMMs) are applied for the study of the North and South Aegean Sea. The earthquake magnitudes and locations comprise the observation sequence and the new Viterbi algorithm is implemented in order to decode the hidden stress field associated with seismogenesis. Precursory phases (variations of the hidden stress field) were detected warning for an anticipated earthquake occurrence for 70 out of 88 cases (the optimal model’s score). The sojourn times of the hidden process were assumed to follow Poisson, logarithmic or negative binomial distributions, whereas the hidden stress levels were classified into 2, 3 or 4 states. HMMs were also adapted without presenting significant results as for the precursory phases. In chapter 5 a generalized Viterbi algorithm for HSMMs is constructed in the sense that now transitions to the same hidden state are allowed and can also be decoded. Furthermore, an extension of this generalized algorithm in the SM1-M1 context is given. In chapter 6 we modify adequately the Cramér-Lundberg model considering negative and positive claims, in order to describe the evolution in time of the Coulomb failure function changes (ΔCFF values) computed at the locations of seven strong (M ≥ 6) earthquakes of the North Aegean Sea. Ruin probability formulas are derived and proved in a general form. Corollaries are also formulated for the exponential and the Pareto distribution. The aim is to shed light to the following problem posed by the seismologists: During a specific year why did an earthquake occur at a specific location and not at another location in seismotectonically homogeneous areas with positive ΔCFF values (stress enhanced areas). The results demonstrate that the new probability formulas can contribute in answering the aforementioned question

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.

碩士
輔仁大學
數學系研究所
92
In this article , we consider the cumulative hazard function of a series system product which is composed by two independent components . We consider a nonparametric approach when there are no information about the distributions of these two independent components . We propose a direct estimator and an indirect estimator of the cumulative hazard function of the system . Then compare these two estimators via their asymptotic mean square errors . On the other hand , if the two independent components of the series are from Exponentiated Weibull distribution , we propose a direct estimator and an indirect estimator of the cumulative hazard function of the system . Again , we study the large sample behavior of these two estimators , then compare their asymptotic mean square errors .It is shown that both nonparametric approach and parametric approach lead to the same conclusion that indirect estimator is better than the direct estimator in the sense of mean square error .

No
The probability density and exceedance probability functions of the induced currents in a screened cable connecting two enclosures, resulting from the close. presence of single and multiple mobile phones working at 900 MHz, are investigated. The analysis of the problem is undertaken using the Method of Moments, but due to weak coupling, the impedance matrix was modified to reduce the memory and time requirements for the problem, to enable it to be executed multiple times. The empirical probability distribution functions (PDFs) and exceedance probabilities for the induced currents are presented. The form of the PDFs is seen to be quite well approximated by a log-normal distribution for a single source and by a Weibull distribution for multiple sources