The doctoral thesis is focused on reliability of lead-free solder SAC 305. Knowledge in the field of fatigue models used in determining the lifetime of solder joints are observed in this thesis. Also such methods of predicting reliability as numerically-analytical methods or reliability experimental tests are mentioned. Practical results of reliability measurement are presented. Experimental data served as the foundation for determining empirical coefficients for the fatigue model based on deformation induced by creep of the solder, which was implemented in the ANSYS environment. Results from different methods were compared and conclusions discussing the suitability of the presented prediction methods are formulated.

AR-Glas wird in Form von Multifilamentgarn zur Verstärkung in textilbewehrtem Beton eingesetzt. Während des Herstellungsprozesses wird auf die AR-Glasfilamente die Schlichte aufgebracht, deren chemische Zusammensetzung maßgeblich die Qualität der Filament-Matrix-Grenzschicht bestimmt, sowie die chemische Beständigkeit im alkalischen Milieu gewährleistet. Zur Beurteilung der chemischen Beständigkeit in alkalischer Umgebung werden beschleunigte Alterungsversuche in wässrigen, alkalischen Lösungen durchgeführt. Die Reaktion von Hydroxid-Ionen mit dem Si-O-Si-Gruppen des Glasnetzwerkes führt zur Ausbildung hydratisierter Oberflächen und gelösten Silikaten. Das Ausmaß der Glaskorrosion ist von der chemischen Zusammensetzung der Glasfaser, der Schlichte bzw. Beschichtung und der alkalischen Lösung sowie von Zeit und Temperatur abhängig. Die beschleunigte Alterung von verschiedenen AR-Glasfasern in NaOH-Lösung sowie Zementlösung zeigt, dass sich der Korrosionsmechanismus aufgrund der vorhandenen Calcium-Ionen unterscheidet. Die Filamentbruchspannung wird anhand der Weibull-Verteilungsfunktion analysiert. Das mechanische Verhalten hängt deutlich von der chemischen Zusammensetzung der Alterungslösung ab, was zu unterschiedlichen Parametern der Weibull-Verteilungsfunktion sowie vermengten Verteilungen führen kann. Die Alterung in NaOH-Lösung führt zur Ausbildung einer korrodierten Schicht an der Filamentoberfläche. In Ca-haltigen Zementlösungen kommt es dagegen zu einer lokal begrenzten Korrosion. Für die Beurteilung verschiedener Polymerbeschichtungen werden Betonverbunde bei unterschiedlichen Temperaturen und Umgebungsfeuchten gelagert, wodurch geeignete Alterungsbedingungen evaluiert werden und den Vergleich der chemischen Beständigkeit unterschiedlicher Beschichtungen ermöglichen. / Rovings made of AR-glass are used in textile reinforced concrete. During the manufacturing process the sizing is applied on the AR-glass filaments. The chemical constitution of the sizing determines the quality of the filament-matrix-interface but also the chemical durability of the glass filaments in alkaline environment. The durability is evaluated by accelerated ageing tests in aqueous, alkaline solutions. In alkaline solutions, the reaction of hydroxyl ions with Si-O-Si-groups of the glass network leads to the formation of hydrated surfaces and dissolved silicate. The rate of this corrosion depends on the chemical constitution of the fibre and the alkaline solution as well as on time and temperature. The investigation of the ageing of glass fibres with different chemical constitutions in NaOH and cement solutions shows that the corrosion mechanism changes due to the inhibiting effect of calcium ions. The strength distributions have been evaluated using a Weibull distribution function. The mechanical behaviour strongly depends on the chemistry of the solution and determines the parameters of the Weibull distribution function in terms of either single or mixed distributions. The corrosion in NaOH solution leads to a strong dissolution of the outer layer of the glass fibres, whereas during aging in cement solution at the same pH-value a limited, local attack was revealed. The evaluation of polymer coatings is realised by the ageing of concrete composites at different temperatures and humidities to deduce adequate ageing conditions for the comparison of different coatings.

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.

In this thesis, we develop some inferential results for one-shot device testing data analysis. These extend and generalize existing methods in the literature. First, a competing-risk model is introduced for one-shot testing data under accelerated life-tests. One-shot devices are products which will be destroyed immediately after use. Therefore, we can observe only a binary status as data, success or failure, of such products instead of its lifetime. Many one-shot devices contain multiple components and failure of any one of them will lead to the failure of the device. Failed devices are inspected to identify the specific cause of failure. Since the exact lifetime is not observed, EM algorithm becomes a natural tool to obtain the maximum likelihood estimates of the model parameters. Here, we develop the EM algorithm for competing exponential and Weibull cases. Second, a semi-parametric approach is developed for simple one-shot device testing data. Semi-parametric estimation is a model that consists of parametric and non-parametric components. For this purpose, we only assume the hazards at different stress levels are proportional to each other, but no distributional assumption is made on the lifetimes. This provides a greater flexibility in model fitting and enables us to examine the relationship between the reliability of devices and the stress factors. Third, Bayesian inference is developed for one-shot device testing data under exponential distribution and Weibull distribution with non-constant shape parameters for competing risks. Bayesian framework provides statistical inference from another perspective. It assumes the model parameters to be random and then improves the inference by incorporating expert's experience as prior information. This method is shown to be very useful if we have limited failure observation wherein the maximum likelihood estimator may not exist. The thesis proceeds as follows. In Chapter 2, we assume the one-shot devices to have two components with lifetimes having exponential distributions with multiple stress factors. We then develop an EM algorithm for developing likelihood inference for the model parameters as well as some useful reliability characteristics. In Chapter 3, we generalize to the situation when lifetimes follow a Weibull distribution with non-constant shape parameters. In Chapter 4, we propose a semi-parametric model for simple one-shot device test data based on proportional hazards model and develop associated inferential results. In Chapter 5, we consider the competing risk model with exponential lifetimes and develop inference by adopting the Bayesian approach. In Chapter 6, we generalize these results on Bayesian inference to the situation when the lifetimes have a Weibull distribution. Finally, we provide some concluding remarks and indicate some future research directions in Chapter 7. / Thesis / Doctor of Philosophy (PhD)

En fiabilité et en analyse de survie, les distributions qui ont une fonction de hasard unimodale ne sont pas nombreuses, qu'on peut citer: Gaussienne inverse ,log-normale, log-logistique, de Birnbaum-Saunders, de Weibull exponentielle et de Weibullgénéralisée. Dans cette thèse, nous développons les tests modifiés du Chi-deux pour ces distributions tout en comparant la distribution Gaussienne inverse avec les autres. Ensuite nousconstruisons le modèle AFT basé sur la distribution Gaussienne inverse et les systèmes redondants basés sur les distributions de fonction de hasard unimodale. / In reliability and survival analysis, distributions that have a unimodalor $\cap-$shape hazard rate function are not too many, they include: the inverse Gaussian,log-normal, log-logistic, Birnbaum-Saunders, exponential Weibull and power generalized Weibulldistributions. In this thesis, we develop the modified Chi-squared tests for these distributions,and we give a comparative study between the inverse Gaussian distribution and the otherdistributions, then we realize simulations. We also construct the AFT model based on the inverseGaussian distribution and redundant systems based on distributions having a unimodal hazard ratefunction.

In the case of soil chemical analyses, frequency distributions for some elements show a dissymmetrical aspect, with a very marked spread to the right or to the left. A high frequency of extreme values is also observed and a possible mixture of several distributions, due to the presence of various soil types within a single geographical unit, is encountered. Then, for the outliers detection and the establishment of detection limits, an original outliers detection procedure has been developed; it allows estimating extreme quantiles above and under which observations are considered as outliers. The estimation of these detection limits is based on the right and the left of the distribution tails. A first estimation is realised for each elementary geographical unit to determine an appropriate truncation level. Then, a spatial classification allows creating adjoining homogeneous groups of geographical units to estimate robust limit values based on an optimal number of observations. / Dans le cas des analyses chimiques de sols, les distributions de fréquences des résultats présentent, pour certains éléments étudiés, un caractère très dissymétrique avec un étalement très marqué à droite ou à gauche. Une fréquence importante de valeurs extrêmes est également observée et un mélange éventuel de plusieurs distributions au sein dune même entité géographique, lié à la présence de divers types de sols, peut être rencontré. Dès lors, pour la détection des valeurs aberrantes et la fixation des limites de détection, une méthode originale, permettant destimer des quantiles extrêmes au-dessus et en dessous desquelles les observations sont considérées comme aberrantes, a été élaborée. Lestimation des limites de détection est établie de manière distincte à partir des queues des distributions droite et gauche. Une première estimation par entité géographique élémentaire est réalisée afin de déterminer un niveau de troncature adéquat. Une classification spatiale permet ensuite de créer des groupes dentités homogènes contiguës, de manière à estimer des valeurs limites robustes basées sur un nombre dobservations optimal.

Made available in DSpace on 2016-06-02T20:06:06Z (GMT). No. of bitstreams: 1 4331.pdf: 1908865 bytes, checksum: d564b46a6111fdca6f7cc9f4d5596637 (MD5) Previous issue date: 2009-03-18 / Universidade Federal de Minas Gerais / The Weibull distribuition is a common initial choice for modeling data with monotone hazard rates. However, such distribution fails to provide a reasonable parametric _t when the hazard function is unimodal or bathtub-shaped. In this context, Cooray (2006) proposed a generalization of the Weibull family by considering the distributions of the odds of Weibull and inverse Weibull families, referred as the odd Weibull family which is not just useful for modeling unimodal and bathtub-shaped hazards, but it is also convenient for testing goodness-of-_t of Weibull and inverse Weibull as submodels. In this project we have systematically studied the odd Weibull family along with its properties, showing motivations for its utilization, inserting covariates in the model, pointing out some troubles associated with the maximum likelihood estimation and proposing interval estimation and hypothesis test construction methodologies for the model parameters. We have also compared resampling results with asymptotic ones. Coverage probability from proposed con_dence intervals and size and power of considered hypothesis tests were both analyzed as well via Monte Carlo simulation. Furthermore, we have proposed a Bayesian estimation methodology for the model parameters based in Monte Carlo Markov Chain (MCMC) simulation techniques. / A distribuição Weibull é uma escolha inicial freqüente para modelagem de dados com taxas de risco monótonas. Entretanto, esta distribuição não fornece um ajuste paramétrico razoável quando as funções de risco assumem um formato unimodal ou em forma de banheira. Neste contexto, Cooray (2006) propôs uma generalização da família Weibull considerando a distribuição da razão de chances das famílias Weibull e Weibull inversa, referida como família Weibull de razão de chances. Esta família não é apenas conveniente para modelar taxas de risco unimodal e banheira, mas também é adequada para testar a adequabilidade do ajuste das famílias Weibull e Weibull inversa como submodelos. Neste trabalho, estudamos sistematicamente a família Weibull de razão de chances e suas propriedades, apontando as motivações para o seu uso, inserindo covariáveis no modelo, veri_cando as di_culdades referentes ao problema da estimação de máxima verossimilhança dos parâmetros do modelo e propondo metodologia de estimação intervalar e construção de testes de hipóteses para os parâmetros do modelo. Comparamos os resultados obtidos por meio dos métodos de reamostragem com os resultados obtidos via teoria assintótica. Tanto a probabilidade de cobertura dos intervalos de con_ança propostos quanto o tamanho e poder dos testes de hipóteses considerados foram estudados via simulação de Monte Carlo. Além disso, propusemos uma metodologia Bayesiana de estimação para os parâmetros do modelo baseados em técnicas de simulação de Monte Carlo via Cadeias de Markov.

Ce travail de thèse porte sur les outils statistiques pour l'évaluation des maxima de charges de sloshing dans les cuves de méthaniers. Selon les caractéristiques du navire, son chargement et les conditions de navigation, un ballotement hydrodynamique est observé à l'intérieur des cuves, phénomène communément appelé sloshing. La détermination des charges qui s'appliquent à la structure est basée sur des mesures de pression d'impact au moyen d'essais sur maquette. Les maxima de pression par impact, extraits des mesures, sont étudiés. La durée d'un essai est équivalente à 5 heures au réel et insuffisante pour déterminer des maxima de pression associés à de grandes périodes de retour (40 ans). Un modèle probabiliste est nécessaire pour extrapoler les maxima de pression. Le modèle usuel est une loi de Weibull. Comme ce sont les valeurs extrêmes des échantillons qui nous intéressent, les ajustements sont aussi effectués par les lois des valeurs extrêmes et de Pareto généralisées via les méthodes de maximum par bloc et d'excès au-dessus d'un seuil.L'originalité du travail repose sur l'emploi d'un système alternatif, plus pertinent pour la capture des maxima de pression et d'une quantité de 480 heures de mesures disponible pour les mêmes conditions d'essai. Cela fournit une distribution de référence pour les maxima de pression et nous permet d'évaluer la pertinence des modèles sélectionnés. Nous insistons sur l'importance d'évaluer la qualité des ajustements par des tests statistiques et de quantifier les incertitudes sur les estimations obtenues. La méthodologie fournie a été implémentée dans un logiciel nommé Stat_R qui facilite la manipulation et le traitement des résultats. / This thesis focuses on statistical tools for the assessment of maxima sloshing loads in LNG tanks. According to ship features, tank cargo and sailing conditions, a sloshing phenomenon is observed inside LNG tanks. The determination of sloshing loads supported by the tank structure is derived from impact pressure measurements performed on a test rig. Pressure maxima per impact, extracted from test measurements, are investigated. Test duration is equivalent to 5 hours in full scale. This duration is not sufficient to determine pressure maxima associated with high return periods (40 years). It is necessary to use a probabilistic model in order to extrapolate pressure maxima. Usually, a Weibull model is used. As we focus on extreme values from samples, fittings are also performed with the generalized extreme value distribution and the generalized Pareto distribution using block maximum method and peaks over threshold method.The originality of this work is based on the use of an alternate measurement system which is more relevant than usual measurement system to get pressure maxima and a 480 hours measured data available for same test conditions. This provides a reference distribution for pressure maxima which is used to assess the relevance of the selected probabilistic models. Particular attention is paid to the assessment of fittings quality using statistical tests and to the quantification of uncertainties on estimated values.The provided methodology has been implemented in a software called Stat_R which makes the manipulation and the treatment of results easier.

This thesis compares Weibull weakest link theory with inclusion of one and all three principal stresses. Principal stresses needed for this theory were calculated with finite element method. The informational research is in the introduction of this thesis. It includes ceramic materials, Weibull weakest link theory, Gaussian quadrature over spherical surface and ceramic head of hip joint endoprothesis. Theoretical part is used for next calculations of probability of failure. The probability of failure of ceramic rod loaded by four-point bending is calculated in first calculations. This task is solved as contact in the next step. Next part of this thesis is about selection of suitable method of numerical integration. This method will be used in the calculation with all three principal stresses. The results of calculation with all three principal stresses are compared with the results of the calculation which includes only first principal stress. Firstly, this is done for cylindrical body and then used on head of hip joint endoprothesis. In the last part of this thesis, probability of fracture of head hip joint endoprothesis with shape deviation of nominal conicity is calculated.

Cure rate models, introduced by Boag (1949), are very commonly used while modelling lifetime data involving long time survivors. Applications of cure rate models can be seen in biomedical science, industrial reliability, finance, manufacturing, demography and criminology. In this thesis, cure rate models are discussed under a competing cause scenario, with the assumption of proportional odds (PO) lifetime distributions for the susceptibles, and statistical inferential methods are then developed based on right-censored data. In Chapter 2, a flexible cure rate model is discussed by assuming the number of competing causes for the event of interest following the Conway-Maxwell (COM) Poisson distribution, and their corresponding lifetimes of non-cured or susceptible individuals can be described by PO model. This provides a natural extension of the work of Gu et al. (2011) who had considered a geometric number of competing causes. Under right censoring, maximum likelihood estimators (MLEs) are obtained by the use of expectation-maximization (EM) algorithm. An extensive Monte Carlo simulation study is carried out for various scenarios, and model discrimination between some well-known cure models like geometric, Poisson and Bernoulli is also examined. The goodness-of-fit and model diagnostics of the model are also discussed. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. Next, in Chapter 3, the destructive cure rate models, introduced by Rodrigues et al. (2011), are discussed under the PO assumption. Here, the initial number of competing causes is modelled by a weighted Poisson distribution with special focus on exponentially weighted Poisson, length-biased Poisson and negative binomial distributions. Then, a damage distribution is introduced for the number of initial causes which do not get destroyed. An EM-type algorithm for computing the MLEs is developed. An extensive simulation study is carried out for various scenarios, and model discrimination between the three weighted Poisson distributions is also examined. All the models and methods of estimation are evaluated through a simulation study. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. In Chapter 4, frailty cure rate models are discussed under a gamma frailty wherein the initial number of competing causes is described by a Conway-Maxwell (COM) Poisson distribution in which the lifetimes of non-cured individuals can be described by PO model. The detailed steps of the EM algorithm are then developed for this model and an extensive simulation study is carried out to evaluate the performance of the proposed model and the estimation method. A cutaneous melanoma dataset as well as a simulated data are used for illustrative purposes. Finally, Chapter 5 outlines the work carried out in the thesis and also suggests some problems of further research interest. / Thesis / Doctor of Philosophy (PhD)