Orientador: Josmar Mazucheli / Resumo: Na análise de séries climatológicas, a metodologia conhecida como “análise de frequências” inicia-se, após a verificação da validade de algumas suposições, pela escolha e ajuste de uma distribuição de probabilidade. A etapa mais importante desta análise é a escolha ou seleção da distribuição de probabilidade que melhor descreva o verdadeiro comportamento da variável em estudo. Uma vez adotada uma distribuição de probabilidade que esteja bem ajustada, segundo um ou vários critérios, é de interesse, por exemplo, estimar a probabilidade de que eventos de certa magnitude sejam igualados ou excedidos em T anos. O inverso desta probabilidade é chamado de período de retorno, sendo esta uma medida de extrema importância na avaliação de riscos associados a fenômenos climatológicos. Em princípio, qualquer distribuição de probabilidade com suporte nos números reais positivos pode ser utilizada na descrição do comportamento de séries fluviométricas, pluviométricas, eólicas, entre outras. Em se tratando de séries pluviométricas, formadas, por exemplo, pelas pluviosidades diárias, decendiais, mensais, trimestrais e anuais, as distribuições Gama e Weibull são as mais utilizadas. Nos últimos anos, a partir de métodos específicos, uma infinidade de novas distribuições vêm sendo propostas para a análise de observações contínuas e estritamente positivas, cujas aplicações, em sua grande maioria, restringem-se a dados de sobrevivência e confiabilidade. Nesta dissertação de Mestrado, foram avaliad... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In the climatological series analysis, a methodology known as “frequency analysis” begins, after the validity of some assumptions, by choice and adjustment of a probability distribution. The most important step of this analysis is the choice or selection of probability distribution that best describes the true behavior of the variable under study. Once a probability distribution, that is well adjusted according to one or several criteria, is adopted, it is of interest, for example, to estimate a probability of events of a certain magnitude that are matched or exceeded in T years. The opposite of this probability is called a return period, which is a measure of extreme importance in the evaluation of risks associated with climatological phenomena. In principle, any probability distribution supported by positive real numbers can be used to describe the behavior of fluviometric, pluviometric and wind series, among others. When it comes to the case of rainfall series, formed, for example, by daily, decendial, monthly, quarterly and annual rainfall, the Gamma and Weibull Distributions are more used. In recent years, from specific methods, a plethora of new distributions are being proposed for an analysis of continuous and strictly positive observations, which applications, for the most part, are restricted to survival and reliability data. In this Master’s dissertation, the performances of the Odd Weibull, Marshall-Olkin Weibull, Exponentiated Weibull and Transmutated Weibull Dist... (Complete abstract click electronic access below) / Mestre

Made available in DSpace on 2014-10-07T19:33:50Z (GMT). No. of bitstreams: 2 license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) 129.pdf: 673904 bytes, checksum: c8e6282bf283d81a9d5c15d7a9f4243a (MD5) Previous issue date: 2005 / Fundação Oswaldo Cruz. Instituto Nacional de Controle de Qualidade em Saúde. Rio de Janeiro, RJ, Brasil. / Um caso de inequivalência terapêutica entre duas suspensões de carbamazepina foi estudado com o objetivo de explicar sua ocorrência com base em diferenças prováveis das matérias-primas e da velocidade de dissolução in vitro, cujo método não se encontra nas farmacopéias. Não se encontraram diferençassignificativas na tensão superficial dos dois produtos ou no coeficiente de dissolução intrínseca das duas substâncias, embora os espectros de calorimetria diferencial de varredura tenham revelado uma fração ligeiramente aumentada do polimorfo beta, omais solúvel, na carbamazepina utilizada no produto referência. A análise de tamanho de partícula revelou uma área superficial significativamente aumentadapara o produto referência, o que explica sua maior velocidade de dissolução. Um método de dissolução farmacopéico foi proposto, com base em resultadosencontrados utilizando-se 900 mL de água como meio de dissolução, com o método n 2 a 50 rpm e 1 ml de amostra de suspensão a 2 por cento. O ensaio realizado nessascondições mostrou poder discriminador satisfatório, aumentado ainda mais pela utilização de solução de NaCl 15 por cento como meio de dissolução, o que permitebloquear o efeito solubilizador do tensoativo presente nas formulações dos dois produtos. Outrossim, a aplicação de um modelo de Weibull aos resultados, por meiodo programa de regressão não linear COMSTAT (UCL, Bruxelas) permitiu determinar parâmetros de forma e escala da curva que se mostraram muito úteispara extrapolação de valores de tempo dissolvido, particularmente no caso de cinéticas de dissolução ultra-rápidas, como no caso estudado, de suspensões farmacêuticas(AU). / A therapeutical non-equivalence case between two carbamazepine pediatric suspensions was investigated for suspected differences either in carbamazepine raw materials used or in vitro dissolution rate, for which compendia methods do no exist. There were not significant differences in surface tension between the products neither in intrinsic dissolution coefficients between the correspondent carbamazepine substances, while DSC results show a slightly increased fraction of the more soluble beta polymorph carbamazepine used in the reference product. The increased dissolution rate for the last one may be more realistically explained by a higher surface area, from Malvern Size particle distribuition result. A dissolution procedure using paddle method 50 rpm and 900 mL of water is suggested, for the minimum possible sample 1 mL of 2% carbamazepine suspension normally collectable. Though not yet totally performed in sink conditions, the method showed a good discriminating power, still more if NaCl 15% in water as medium is used, to block the effect of surfactant present in both the formulations. Moreover, dissolution results fitted by Weibull function with the aid of a non linear program Comstat (Sidec, Brussels), based on a Steepest Descent algorithm, allowed to calculated U (form of the curve) and Td (time) parameters that are very useful in the general case of ultra fast dissolution kinetcs, like suspension-formulated drug products, not only to compare several curves but mainly to extrapolate percent dissolved times not obtained in experimental data, making essier the establishment of compendia specifications.

Reliability experiments provide important information regarding the life of a product, including how various factors may affect product life. Current analyses of reliability data usually assume a completely randomized design. However, reliability experiments frequently contain subsampling which is a restriction on randomization. A typical experiment involves applying treatments to test stands, with several items placed on each test stand. In addition, raw materials used in experiments are often produced in batches. In some cases one batch may not be large enough to provide materials for the entire experiment and more than one batch must be used. These batches lead to a design involving blocks. This dissertation proposes two methods for analyzing reliability experiments with random blocks and subsampling. The first method is a two-stage method which can be implemented in software used by most practitioners, but has some limitations. Therefore, a more rigorous nonlinear mixed model method is proposed. / Ph. D.

Electrical and electronic device insulation systems experience multiple stresses while in service. Insulation design engineers usually make attempts to study the behavior of insulation under multiple stresses to keep the size and weight of the electrical insulation at a minimum. In this thesis, magnet wire insulation properties under multiple stresses are studied. Magnet wires are used for insulation in transformers, flyback transformers, solenoids, sensors, motors, adjustable speed drives etc. The magnet wire insulation under study in this work is micrometers thick, yet they are expected to provide high breakdown strength, good windability, and resistance to moisture. Accelerated life tests are performed on two different AWG 43 magnet wires. Combined Weibull Electrical-Thermal life models and Electrical-Thermal-Frequency life models were successfully verified in this work. The statistical information like lifetime characteristics, probability of failures, and lifetime percentiles determined for the two different magnet wire insulation is helpful for a better understanding of their insulation properties.

Diameter distributions of juvenile loblolly pine (Pinus taeda L.) with different planting densities were characterized utilizing a two-parameter Weibull distribution. Trend analysis was employed to describe the effects of planting density, age, relative spacing, and rectangularity on the estimated diameter distributions for juvenile loblolly pine. A reparameterization of the two-parameter Weibull distribution was sought to reduce the dispersion of the estimated shape parameter. Methods that quantify the amount of inter-tree spatial dependency in a particular stand were applied. Empirical semivariograms were derived for each plot over all ages to enable spatial trend recognition. Moran's I and Geary's C coefficients were estimated for ground-line diameters from ages 2 to 5, and for breast height diameters from ages 5 to 11. Though there was no discernable trend in the presence of significant spatial autocorrelation with planting density, an initial negative trend with age was present, but leveled off by age 5. A conditional autoregressive model was utilized to evaluate the amount of spatial influence stems in a stand have on one another. The occurrence of significant spatial influences was positively associated with age through age 8, the trend then leveled off; no recognizable trend was detected with planting density. These indices help to describe stand dynamics that are influenced by the spatial distribution of stems. Models to predict the parameters of the two-parameter Weibull distribution were developed to aid in forecasting and simulation of juvenile loblolly pine. Simulations were conducted where a spatial dependency was imposed on the diameters within a stand. The spatial structure simulation enables accurate representations of stem characteristics when simulating forest stands that include spatially-explicit information. / Ph. D.

Companies routinely perform life tests for their products. Typically, these tests involve running a set of products until the units fail. Most often, the data are censored according to different censoring schemes, depending on the particulars of the test. On occasion, tests are stopped at a predetermined time and the units that are yet to fail are suspended. In other instances, the data are collected through periodic inspection and only upper and lower bounds on the lifetimes are recorded. Reliability professionals use a number of non-normal distributions to model the resulting lifetime data with the Weibull distribution being the most frequently used. If one is interested in monitoring the quality and reliability characteristics of such processes, one needs to account for the challenges imposed by the nature of the data. We propose likelihood ratio based cumulative sum (CUSUM) control charts for censored lifetime data with non-normal distributions. We illustrate the development and implementation of the charts, and we evaluate their properties through simulation studies. We address the problem of interval censoring, and we construct a CUSUM chart for censored ordered categorical data, which we illustrate by a case study at Becton Dickinson (BD). We also address the problem of monitoring both of the parameters of the Weibull distribution for processes with right-censored data. / Ph. D.

Approved for public release; distribution in unlimited. / Budget limitations have reduced the number of military components available for testing, and time constraints have reduced the amount of time available for actual testing resulting in many items still operating at the end of test cycles. These two factors produce small test populations (small sample size) with "heavily" censored data. The assumption of "normal approximation" for estimates based on these small sample sizes reduces the accuracy of confidence bounds of the probability plots and the associated quantities. This creates a problem in acquisition analysis because the confidence in the probability estimates influences the number of spare parts required to support a mission or deployment or determines the length of warranty ensuring proper operation of systems. This thesis develops a method that simulates small samples with censored data and examines the error of the Fisher-Matrix (FM) and the Likelihood Ratio Bounds (LRB) confidence methods of two test populations (size 10 and 20) with three, five, seven and nine observed failures for the Weibull distribution. This thesis includes a Monte Carlo simulation code written in S-Plus that can be modified by the user to meet their particular needs for any sampling and censoring scheme. To illustrate the approach, the thesis includes a catalog of corrected confidence bounds for the Weibull distribution, which can be used by acquisition analysts to adjust their confidence bounds and obtain a more accurate representation for warranty and reliability work. / Civilian, Department of the Air Force

Master of Science / Department of Statistics / James J. Higgins / The time for an event to take place in an individual is called a survival time. Examples include the time that an individual survives after being diagnosed with a terminal illness or the time that an electronic component functions before failing. A popular parametric model for this type of data is the Weibull model, which is a flexible model that allows for the inclusion of covariates of the survival times. If distributional assumptions are not met or cannot be verified, researchers may turn to the semi-parametric Cox proportional hazards model. This model also allows for the inclusion of covariates of survival times but with less restrictive assumptions. This report compares estimates of the slope of the covariate in the proportional hazards model using the parametric Weibull model and the semi-parametric Cox proportional hazards model to estimate the slope. Properties of these models are discussed in Chapter 1. Numerical examples and a comparison of the mean square errors of the estimates of the slope of the covariate for various sample sizes and for uncensored and censored data are discussed in Chapter 2. When the shape parameter is known, the Weibull model far out performs the Cox proportional hazards model, but when the shape parameter is unknown, the Cox proportional hazards model and the Weibull model give comparable results.

Thesis (MSc)--Stellenbosch University, 2004. / ENGLISH ABSTRACT: The Bayesian approach to decision-making is considered in this thesis for reliability/survival models pertaining to a Weibull class of distributions. A generalised right censored sampling scheme has been assumed and implemented. The Jeffreys' prior for the inverse mean lifetime and the survival function of the exponential model were derived. The consequent posterior distributions of these two parameters were obtained using this non-informative prior. In addition to the Jeffreys' prior, the natural conjugate prior was considered as a prior for the parameter of the exponential model and the consequent posterior distribution was derived. In many reliability problems, overestimating a certain parameter of interest is more detrimental than underestimating it and hence, the LINEX loss function was used to estimate the parameters and their consequent risk measures. Moreover, the same analogous derivations have been carried out relative to the commonly-used symmetrical squared error loss function. The risk function, the posterior risk and the integrated risk of the estimators were obtained and are regarded in this thesis as the risk measures. The performance of the estimators have been compared relative to these risk measures. For the Jeffreys' prior under the squared error loss function, the comparison resulted in crossing-over risk functions and hence, none of these estimators are completely admissible. However, relative to the LINEX loss function, it was found that a correct Bayesian estimator outperforms an incorrectly chosen alternative. On the other hand for the conjugate prior, crossing-over of the risk functions of the estimators were evident as a result. In comparing the performance of the Bayesian estimators, whenever closed-form expressions of the risk measures do not exist, numerical techniques such as Monte Carlo procedures were used. In similar fashion were the posterior risks and integrated risks used in the performance compansons. The Weibull pdf, with its scale and shape parameter, was also considered as a reliability model. The Jeffreys' prior and the consequent posterior distribution of the scale parameter of the Weibull model have also been derived when the shape parameter is known. In this case, the estimation process of the scale parameter is analogous to the exponential model. For the case when both parameters of the Weibull model are unknown, the Jeffreys' and the reference priors have been derived and the computational difficulty of the posterior analysis has been outlined. The Jeffreys' prior for the survival function of the Weibull model has also been derived, when the shape parameter is known. In all cases, two forms of the scalar estimation error have been t:. used to compare as much risk measures as possible. The performance of the estimators were compared for acceptability in a decision-making framework. This can be seen as a type of procedure that addresses robustness of an estimator relative to a chosen loss function. / AFRIKAANSE OPSOMMING: Die Bayes-benadering tot besluitneming is in hierdie tesis beskou vir betroubaarheids- / oorlewingsmodelle wat behoort tot 'n Weibull klas van verdelings. 'n Veralgemene regs gesensoreerde steekproefnemingsplan is aanvaar en geïmplementeer. Die Jeffreyse prior vir die inverse van die gemiddelde leeftyd en die oorlewingsfunksie is afgelei vir die eksponensiële model. Die gevolglike aposteriori-verdeling van hierdie twee parameters is afgelei, indien hierdie nie-inligtingge-wende apriori gebruik word. Addisioneel tot die Jeffreyse prior, is die natuurlike toegevoegde prior beskou vir die parameter van die eksponensiële model en ooreenstemmende aposteriori-verdeling is afgelei. In baie betroubaarheidsprobleme het die oorberaming van 'n parameter meer ernstige nagevolge as die onderberaming daarvan en omgekeerd en gevolglik is die LINEX verliesfunksie gebruik om die parameters te beraam tesame met ooreenstemmende risiko maatstawwe. Soortgelyke afleidings is gedoen vir hierdie algemene simmetriese kwadratiese verliesfunksie. Die risiko funksie, die aposteriori-risiko en die integreerde risiko van die beramers is verkry en word in hierdie tesis beskou as die risiko maatstawwe. Die gedrag van die beramers is vergelyk relatief tot hierdie risiko maatstawwe. Die vergelyking vir die Jeffreyse prior onder kwadratiese verliesfunksie het op oorkruisbare risiko funksies uitgevloei en gevolglik is geeneen van hierdie beramers volkome toelaatbaar nie. Relatief tot die LINEX verliesfunksie is egter gevind dat die korrekte Bayes-beramer beter vaar as die alternatiewe beramer. Aan die ander kant is gevind dat oorkruisbare risiko funksies van die beramers verkry word vir die toegevoegde apriori-verdeling. Met hierdie gedragsvergelykings van die beramers word numeriese tegnieke toegepas, soos die Monte Carlo prosedures, indien die maatstawwe nie in geslote vorm gevind kan word nie. Op soortgelyke wyse is die aposteriori-risiko en die integreerde risiko's gebruik in die gedragsvergelykings. Die Weibull waarskynlikheidsverdeling, met skaal- en vormingsparameter, is ook beskou as 'n betroubaarheidsmodel. Die Jeffreyse prior en die gevolglike aposteriori-verdeling van die skaalparameter van die Weibull model is afgelei, indien die vormingsparameter bekend is. In hierdie geval is die beramingsproses van die skaalparameter analoog aan die afleidings van die eksponensiële model. Indien beide parameters van die Weibull modelonbekend is, is die Jeffreyse prior en die verwysingsprior afgelei en is daarop gewys wat die berekeningskomplikasies is van 'n aposteriori-analise. Die Jeffreyse prior vir die oorlewingsfunksie van die Weibull model is ook afgelei, indien die vormingsparameter bekend is. In al die gevalle is twee vorms van die skalaar beramingsfoute gebruik in die vergelykings, sodat soveel as moontlik risiko maatstawwe vergelyk kan word. Die gedrag van die beramers is vergelyk vir aanvaarbaarheid binne die besluitnemingsraamwerk. Hierdie kan gesien word as 'n prosedure om die robuustheid van 'n beramer relatief tot 'n gekose verliesfunksie aan te spreek.

Os modelos multiníveis são uma classe de modelos úteis na análise de bases de dados com estrutura hierárquica. No presente trabalho propõem-se os modelos multiníveis com resposta Weibull, nos quais são considerados interceptos aleatórios na modelagem dos dois parâmetros da distribuição da variável resposta. Os modelos aqui propostos são flexíveis devido a que a distribuição dos interceptos aleatórios pode der escolhida entre uma das seguintes quatro distribuições: normal, log--gama, logística e Cauchy. Uma extensão dos modelos é apresentada na qual é possível incluir na parte sistemática dos dois parâmetros da distribuição da variável resposta interceptos e inclinações aleatórias com distribuição normal bivariada. A estimação dos parâmetros é realizada pelo método de máxima verossimilhança usando a quadratura de Gauss--Hermite para aproximar a função de verossimilhança. Um pacote em linguagem R foi desenvolvido especialmente para a estimação dos parâmetros, predição dos efeitos aleatórios e para a obtenção dos resíduos nos modelos propostos. Adicionalmente, por meio de um estudo de simulação foi avaliado o impacto nas estimativas dos parâmetros do modelo ao assumir incorretamente a distribuição dos interceptos aleatórios. / Multilevel models are a class of models useful in the analysis of datasets with hierarchical structure. In the present work we propose multilevel Weibull models in which random intercepts are considered to model the two parameters of the Weibull distribution. The proposed models are flexible due to random intercepts distribution can be chosen from one of the four following distributions: normal, log-gamma, logistics and Cauchy. An extension of the models is presented in which we can include, in the systematic part of the two parameters of the distribution, random intercepts and slopes with a bivariate normal distribution. The parameter estimation is performed by maximum likelihood method using the Gauss Hermite quadrature to approximate the likelihood function. A package in R language was especially developed to obtain parameter estimation, random effects predictions and residuals for the proposed models. Additionally, through a simulation study we investigated the misspecification random effect distribution on estimated parameter for the proposed model