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Pyatrin, D. K., O. V. Kozhokhina, G. Y. Marinchenko, L. V. Blahaia, Д. К. Пятрін, О. В. Кожохіна, Г. Є. Марінченко, and Л. В. Благая. "Weibull distribution avionics application." Thesis, National aviation university, 2021. https://er.nau.edu.ua/handle/NAU/50499.
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1. Reliability of avionics systems. Textbook/Gribov V.M., Kozhokhina O.V., Marinchenko H.Y., Strelnikov V.P., - K.: Aliant, 2021, - 264p.
2. Weibull W. A statistical distribution function of wide application. ASME paper 51-A-6, Nov 1951.
3. Sherwin D J and Lees F P. An investigation of the application of failure data analysis to decision making in the maintenance of process plant. Proc Instn Mech Engrs, Vol 194, No 29, 1980.The paper deals with the weibull distribution in avionics application. During the operation of aircraft, the events that determine the transition of the product to different technical states occur randomly. Intervals of time of stay of a product in this or that condition have casual values of duration. The Weibull distribution is a fairly flexible function that can well align a variety of failure statistics and can be a model for the reliability of both electronic and mechanical products. The Weibull distribution successfully can be used in reliability engineering and failure analysis.
У тезах розглядається розподіл Вейбулла в застосуванні до авіоніки. Під час експлуатації літальних апаратів події, що визначають перехід виробу в різні технічні стани, відбуваються випадковим чином. Інтервали часу перебування виробу в тому чи іншому стані мають випадкові значення тривалості. Розподіл Вейбулла — це досить гнучка функція, яка може добре узгоджувати різноманітні статистичні дані про відмови та може бути взірцем надійності як електронних, так і механічних виробів. Розподіл Вейбулла може бути використаний в прогнозуванні надійності авіоніки та аналізі відмов.
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Hansen, Mary Jo. "Probability of Discrete Failures, Weibull Distribution." DigitalCommons@USU, 1989. https://digitalcommons.usu.edu/etd/7023.
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The intent of this research and these is to describe the development of a series of charts and tables that provide the individual and cumulative probabilities of failure applying to the Weibull statistical distribution. The mathematical relationships are developed and the computer programs are described for deterministic and Monte Carlo models that compute and verify the results. Charts and tables reflecting the probabilities of failure for a selected set of parameters of the Weibull distribution functions are provided.
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Nielsen, Mark A. "Parameter Estimation for the Two-Parameter Weibull Distribution." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2509.
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The Weibull distribution, an extreme value distribution, is frequently used to model survival, reliability, wind speed, and other data. One reason for this is its flexibility; it can mimic various distributions like the exponential or normal. The two-parameter Weibull has a shape (γ) and scale (β) parameter. Parameter estimation has been an ongoing search to find efficient, unbiased, and minimal variance estimators. Through data analysis and simulation studies, the following three methods of estimation will be discussed and compared: maximum likelihood estimation (MLE), method of moments estimation (MME), and median rank regression (MRR). The analysis of wind speed data from the TW Daniels Experimental Forest are used for this study to test the performance and flexibility of the Weibull distribution.
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Han, Yi Carpenter Mark. "Location-scale bivariate Weibull distributions for bivariate lifetime modeling." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2006%20Spring/master's/HAN_YI_21.pdf.
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Crumer, Angela Maria. "Comparison between Weibull and Cox proportional hazards models." Kansas State University, 2011. http://hdl.handle.net/2097/8787.
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Master of ScienceDepartment 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.
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Rodrigues, Cristiane. "Distribuições em série de potências modificadas inflacionadas e distribuição Weibull binominal negativa." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-28062011-095106/.
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Neste trabalho, alguns resultados, tais como, função geradora de momentos, relações de recorrência para os momentos e alguns teoremas da classe de distribuições em séries de potencias modificadas (MPSD) proposta por Gupta (1974) e da classe de distribuições em séries de potências modificadas inflacionadas (IMPSD) tanto em um ponto diferente de zero como no ponto zero são apresentados. Uma aplicação do Modelo Poisson padrão, do modelo binomial negativo padrão e dos modelos inflacionados de zeros para dados de contagem, ZIP e ZINB, utilizando-se as técnicas dos MLGs, foi realizada para dois conjuntos de dados reais juntamente com o gráfico normal de probabilidade com envelopes simulados. Também foi proposta a distribuição Weibull binomial negativa (WNB) que é bastante flexível em análise de dados positivos e foram estudadas algumas de suas propriedades matemáticas. Esta é uma importante alternativa para os modelos Weibull e Weibull geométrica, sub-modelos da WNB. A demostração de que a densidade da distribuição Weibull binomial negativa pode ser expressa como uma mistura de densidades Weibull é apresentada. Fornecem-se, também, seus momentos, função geradora de momentos, gráficos da assimetria e curtose, expressoes expl´citas para os desvios médios, curvas de Bonferroni e Lorenz, função quantílica, confiabilidade e entropia, a densidade da estat´stica de ordem e expressões explícita para os momentos da estatística de ordem. O método de máxima verossimilhança é usado para estimar os parametros do modelo. A matriz de informação esperada ´e derivada. A utilidade da distribuição WNB está ilustrada na an´alise de dois conjuntos de dados reais.In this paper, some result such as moments generating function, recurrence relations for moments and some theorems of the class of modified power series distributions (MPSD) proposed by Gupta (1974) and of the class of inflated modified power series distributions (IMPSD) both at a different point of zero as the zero point are presented. The standard Poisson model, the standard negative binomial model and zero inflated models for count data, ZIP and ZINB, using the techniques of the GLMs, were used to analyse two real data sets together with the normal plot with simulated envelopes. The new distribution Weibull negative binomial (WNB) was proposed. Some mathematical properties of the WNB distribution which is quite flexible in analyzing positive data were studied. It is an important alternative model to the Weibull, and Weibull geometric distributions as they are sub-models of WNB. We demonstrate that the WNB density can be expressed as a mixture of Weibull densities. We provide their moments, moment generating function, plots of the skewness and kurtosis, explicit expressions for the mean deviations, Bonferroni and Lorenz curves, quantile function, reliability and entropy, the density of order statistics and explicit expressions for the moments of order statistics. The method of maximum likelihood is used for estimating the model parameters. The expected information matrix is derived. The usefulness of the new distribution is illustrated in two analysis of real data sets.
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Reis, Thaís Carolina Santos dos. "Extensões da Distribuição Weibull Aplicadas na Análise de Séries Climatológicas /." Presidente Prudente, 2017. http://hdl.handle.net/11449/152391.
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Orientador: Josmar MazucheliResumo: 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
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Carrasco, Jalmar Manuel Farfán. "Modelo de regressão log-Weibull modificado e a nova distribuição Weibull modificada generalizada." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-29022008-151018/.
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Neste trabalho propomos um modelo de regress~ao utilizando a distribuição Weibull modificado, esta distribuição pode ser usada para modelar dados de sobrevivência quando a de função de risco tem forma de U ou banheira. Assumindo dados censurados, é considerado os estimadores de máxima verossimilhança e Jackknife para os parâmetros do modelo proposto. Foram derivadas as matrizes apropriadas para avaliar influiência local sobre os parâmetros estimados considerando diferentes peturbações e também é apresen- tada alguma medidas de influência global. Para diferentes parâmetros fixados, tamanhos de amostra e porcentagem de censuras, varia simulações foram feitas para avaliar a distribuição empírica do resíduo deviance modificado e comparado coma distribuição normal padrão. Esses estudos sugerem que a distribuição empírica do resíduo devianve modificado para o modelo de regressão log-Weibull modificado com dados censurados aproxima-se de uma dis- tribuição normal padrão. Finalmente analisamos um conjunto de dados utilizando o modelo de regressão log-Weibull modificado. Uma nova distribuição de quatro parâmetros é definida para modelar dados de tempo de vida. Algumas propriedades da distribuição é discutida, assim como ilustramos com exemplos a aplicação dessa nova distribuição. Palavras-chaves: Modelo de regressão; Distribuição Weibull modificada; Distribuição weibull modificada generalizada; Análise de sensibilidade; Dados censurados; Análise de resíduoIn this paperwork are proposed a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider a classic and Jackknife estimator for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under diferent perturbation schemes and we also present some ways to perform global influence. Besides, for diferent parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the deviance modified residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extend for a martingale-type residual in log-modifiedWeibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the deviance modified residual are performed to select an appropriate model. A new four-parameter distribution is introduced. Various properties the new distribution are discussed. Illustrative examples based on real data are also given.
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Watkins, Adam Christopher. "RADIATION INDUCED TRANSIENT PULSE PROPAGATION USING THE WEIBULL DISTRIBUTION FUNCTION." OpenSIUC, 2012. https://opensiuc.lib.siu.edu/theses/811.
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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.
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Abeyratne, Anura T. "Comparison of k-Weibull populations under random censoring /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9737910.
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Barajas, Freddy Hernandez. "Modelos multiníveis Weibull com efeitos aleatórios." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-07052013-203915/.
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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
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Negash, Efrem Ocubamicael. "Risk and admissibility for a Weibull class of distributions." Thesis, Stellenbosch : Stellenbosch University, 2004. http://hdl.handle.net/10019.1/50086.
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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.
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Pietroluongo, Márcia. "Estudo de uma inequivalência terapêutica entre duas suspensões de carbamazepina e desenvolvimento de método de dissolução biorrelevante." reponame:Repositório Institucional da FIOCRUZ, 2005. https://www.arca.fiocruz.br/handle/icict/8541.
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Previous issue date: 2005Fundação 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.
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Barbosa, HÃlio de Paula. "Use of harmony search to fit Weibull distribution in wind energy applications." Universidade Federal do CearÃ, 2016. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=16017.
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CoordenaÃÃo de AperfeiÃoamento de NÃvel SuperiorThe wind resource assessment is a key step in the development of wind power generation projects. Minimizing errors in this step brings significant reliability gains for the whole project. In this study we sought a reduction in the errors associated with the adjustment of the Weibull distribution with respect to data collected by an improvement of this setting. With this purpose, it was applied the optimization algorithm of Harmonic Search (HS) to find the Weibull distribution parameters with the best fit. The HS was used to find the Weibull distribution parameters for two sets of data from the Sistema de OrganizaÃÃo de Dados Ambientais (SONDA) of the cities of Petrolina-PE and SÃo Martinho da Serra-RS. The parameters of the HS were selected by two methods, one being a result of the novel combination of two other already presented in the literature. We therefore compared the errors for each one to determine which method provides better optimization. For evaluating the quality setting, the root mean square error (RMSE) and the correlation coefficient were used. The HS-PA method uses a selection of random parameters but, results showed more stable than the IHS. It was found for the IHS method one RMSE = 0.006418 for Petrolina and RMSE = 0.008303 for SÃo Martinho da Serra. The HS-PA method presented a RMSE = 0.006419 for Petrolina and RMSE = 0.008303 for SÃo Martinho da Serra. The RMSE values for the traditional methods applied to the same data set, there were two or more times greater than those found by employing the Harmonic search.
A anÃlise de recurso eÃlico à uma etapa fundamental no desenvolvimento de projetos de geraÃÃo de energia eÃlica. A minimizaÃÃo dos erros nesta etapa traz ganhos significativos de confiabilidade para o projeto como um todo. Neste trabalho foi buscada uma diminuiÃÃo dos erros associados ao ajuste da distribuiÃÃo de Weibull em relaÃÃo aos dados coletados atravÃs de uma melhora deste ajuste. Visando tal intento, foi aplicado o algoritmo de otimizaÃÃo da Busca HarmÃnica (HS) para encontrar os parÃmetros da distribuiÃÃo de Weibull com o melhor ajuste. A HS foi utilizada para encontrar os parÃmetros da distribuiÃÃo de Weibull para dois conjuntos de dados provenientes do Sistema de OrganizaÃÃo de Dados ambientais (SONDA) das cidades de Petrolina-PE e SÃo Martinho da Serra-RS. Os parÃmetros da HS foram selecionados atravÃs de duas metodologias, sendo uma delas inovadora por resultar da combinaÃÃo de outras duas jà apresentadas anteriormente em literatura. Foram, portanto, comparados os erros referentes a cada uma para determinar qual mÃtodo fornecia uma melhor otimizaÃÃo. Para a avaliaÃÃo da qualidade do ajuste, foram utilizados o erro mÃdio quadrÃtico (RMSE) e o coeficiente de correlaÃÃo. O mÃtodo HS-PA, embora utilize uma seleÃÃo de parÃmetros aleatÃria, apresentou resultados mais estÃveis do que o IHS. Foi encontrado para o mÃtodo IHS um RMSE = 0,006418 para Petrolina e RMSE = 0,008303 para SÃo Martinho da Serra. O mÃtodo HS-PA apresentou um RMSE = 0,006419 para Petrolina e RMSE = 0,008303 para SÃo Martinho da Serra. Os valores de RMSE para os mÃtodos tradicionais aplicados ao mesmo conjunto de dados, foram duas ou mais vezes maiores do que os encontrados, empregando a Busca HarmÃnica.
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Krit, Meryam. "Goodness-of-fit tests in reliability : Weibull distribution and imperfect maintenance models." Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENM038/document.
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Ce travail porte sur les tests d'adéquation en fiabilité, à la fois pour les systèmes non réparables et les systèmes réparables. Les tests d'adéquation sont des outils efficaces pour vérifier la pertinence d'un modèle pour un jeu de données. Pour les systèmes non réparables, la loi exponentielle et la loi de Weibull sont les lois de durée de vie les plus utilisées en fiabilité. Une comparaison exhaustive des tests d'adéquation pour la loi exponentielle est présentée pour des données complètes et censurées, suivie par des recommandations d'utilisation de ces tests. La loi de Weibull à deux paramètres permet de modéliser des taux de hasard décroissants et croissants contrairement à la loi exponentielle qui suppose un taux de hasard constant. Cependant, il existe moins de tests d'adéquation à la loi de Weibull dans la littérature. Une revue exhaustive des tests existant est effectuée et deux familles de tests exacts sont preésentées. La première famille est la famille des tests basés sur la vraisemblance et la deuxième est la famille des tests basés sur la transformée de Laplace. Des propriétés asymptotiques des nouvelles statistiques de tests sont établies. Une comparaison complète des tests d'adéquation pour la loi de Weibull est effectuée. Des recommandations sur les tests les plus puissants sont données en fonction des caractéristiques du jeu de donnés testé. Pour les systèmes réparables, de nouveaux tests d'adéquation sont développés pour des modèles de maintenance imparfaite avec à la fois des maintenances correctives et des maintenances préventives déterministes. Ces tests sont exacts et peuvent être appliqués à des petits jeux de données. Finalement, des applications à de vrais jeux de données issus de l'industrie sont effectuées pour des systèmes réparables et des systèmes non réparablesThis work deals with goodness-of-fit (GOF) tests in reliability for both non repairable and repairable systems. GOF tests are efficient techniques to check the relevance of a model for a given data set. For non repairable systems, the Exponential and Weibull distributions are the most used lifetimes distributions in reliability. A comprehensive comparison study of the GOF tests for the Exponential distribution is presented for complete and censored samples followed by recommendations about the use of the tests. The two-parameter Weibull distribution allows decreasing and increasing failure rates unlike the Exponential distribution that makes the assumption of a constant hazard rate. Yet, there exist less GOF tests in the literature for the Weibull distribution. A comprehensive review of the existing GOF tests is done and two new families of exact GOF tests are introduced. The first family is the likelihood based GOF tests and the second is the family of tests based on the Laplace transform. Theoretical asymptotic properties of some new tests statistics are established. A comprehensive comparison study of the GOF tests for the Weibull distribution is done. Recommendations about the most powerful tests are given depending on the characteristics of the tested data sets. For repairable systems, new GOF tests are developed for imperfect maintenance models when both corrective maintenance and deterministic preventive maintenance are performed. These tests are exact and can be applied to small data sets. Finally, illustrative applications to real data sets from industry are carried out for repairable and non repairable systems
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Reis, Thaís Carolina Santos dos [UNESP]. "Extensões da Distribuição Weibull Aplicadas na Análise de Séries Climatológicas." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/152391.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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 avaliadas as performances das distribuições Odd Weibull, Marshall-Olkin Weibull, Weibull exponenciada e Weibull transmutada como alternativas para as distribuições Gama e Weibull na análise de séries pluviométricas históricas, obtidas de 33 estações meteorológicas do Brasil. Concluiu-se que em um contexto geral a distribuição Weibull foi a mais adequada na descrição da variável “precipitação acumulada mensalmente”, contudo, analisando-se pontualmente cada uma das 33 séries, em nove delas uma das extensões foi classificada como a mais adequada na descrição da variável em questão. Diante disso, tal estudo proporcionou a inserção de algumas das recentes extensões da distribuição Weibull na análise de dados climatológicos.
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 Distributions were evaluated as alternatives for the Gamma and Weibull Distributions in the analysis of historical rainfall series, obtained from 33 meteorological stations in Brazil. It was reasoned that in a general context the Weibull Distribution was published in the description of the variable “monthly cumulative precipitation”, however, analyzing each of the 33 series punctually, in nine of them one of the extensions was classified as the most suitable in the description of the variable in question. Thus, such study provided an insight into some of the recent extensions of the Weibull Distribution in the analysis of climatological data.
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Kim, Hyun-Joo. "Model selection criteria based on Kullback information measures for Weibull, logistic, and nonlinear regression frameworks /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9988677.
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FERREIRA, Ricardo José. "Development of a mixed model using generalized renewal processes and the weibull distribution." Universidade Federal Rural de Pernambuco, 2016. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7248.
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In order to analyze interventions in repairable systems, the literature contains several methodologies aiming to model the behavior of times between interventions. Such interventions can be modeled by Point Stochastic Processes in order to analyze the probabilistic behavior of times between events. Specifically, the Generalized Renewal Processes allow the study of times between interventions by measuring the quality of each intervention and the response of the system to these interventions — this is done by using the concept of virtual age. In such concept it is possible to apply two kinds of Kijima models (Type I and II). Therefore, this work presents a model capable of study the quality of interventions using up of a mix between the two Kijima models where it is possible to capture the performance on each of these interventions proportionally. Specifically, a new approach to virtual age of Kijima models is presented as well as mathematical properties of the Generalized Renewal Process using the Weibull distribution probability. Finally, the applicability of the model is checked in real data from some problems found in the literature.
Para analisar intervenções em sistemas reparáveis, a literatura apresenta diversas metodologias visando modelar o comportamento de tempos entre intervenções. Tais intervenções podem ser modeladas por Processos Estocásticos Pontuais visando analisar o comportamento probabilístico dos tempos entre eventos. Especificamente, os Processos de Renovação Generalizados permitem o estudo de tempos entre intervenções medindo a qualidade de impacto de cada intervenção e a resposta do sistema a tais intervenções - isto é feito utilizando o conceito de idade virtual. Em tal conceito é possível se aplicar dois tipos de modelos Kijima (tipo I e II).Sendo assim, esse trabalho apresenta um modelo capaz de estudar a qualidade de intervenções utilizando-se de uma mistura entre os dois modelos Kijima onde é possível capturar a atuação de cada um desses sobre as intervenções proporcionalmente. Especificamente, uma nova abordagem sobre a idade virtual dos modelos Kijima é apresentada, bem como propriedades matemáticas dos Processos de Renovação Generalizados utilizando a distribuição de probabilidadeWeibull. Por fim, a aplicabilidade do modelo é verificada em dados reais de alguns problemas presentes na literatura.
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GUSMÃO, Felipe Ricardo Santos de. "Uma abordagem Bayesiana para distribuição Weibull inversa generalizada." Universidade Federal Rural de Pernambuco, 2008. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/4979.
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The distribution inverse Weibull is suitable for modeling failure rates which are quite common in reliability and biological studies. In this work a new three-parameter distribution generalized inverse Weibull with decreasing and unimodal failure rate is introduced.We provide a comprehensive treatment of the mathematical properties of the generalized inverse Weibull and derive expressions for its moment generating function and the rth generalized moment. We also discuss maximum likelihood estimation and we provide formulae for the elements of the Observed information matrix, we also made an bayesian approach for this new distribution and an applied was made for a real data set for the methods classicand bayes.
A distribuição Weibull inversa tem a habilidade de modelar funções de risco com forma unimodal que são bastante comuns em estudos biológicos e de confiabilidade. Uma nova distribuição Weibull inversa generalizada tri-paramétrica com taxa de falha decrescente e unimodal é proposta. Um compreensivo tratamento das propriedades matemáticas de Weibull inversa generalizada é provido e foi encontrado expressões para suas funções geradoras de momentos e o r-ésimo momento generalizado foi determinado. Também discutimos a estimação de máxima verossimilhança e as fórmulas para os elementos da matriz de informação observada. Uma abordagem bayesiana para esta nova distribuição foi proposta e exemplificada, modelando um conjunto de dados agrários pelos métodos clássico e bayesiano.
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BARROS, Patrícia Silva Nascimento. "Classes de distribuições Weibull generalizada: teorias e aplicações." Universidade Federal Rural de Pernambuco, 2015. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/5240.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The Weibull distribution is very popular to model survival data. Many modi cations of the Weibull distribution have been proposed in recent years. Inspired by the notion of generalized gamma-generated family of distribution of Zografos e Balakrishnan, the Generalized Weibull Distributions Class is proposed. A comprehensive treatment of the mathematical properties of some new distribution is provided, expressions giving for the distribution function, density function, hazard function, moment generating function, characteristic function, mean, variance, skewness and kurtosis. Real data sets were modeled showing best ts, according the chosen criteria, were obtained by the new models. Thus for the Generalized Weibull Distributions Class, in spite of having more parameters to be estimated, the algorithms were able to best adjust the survival analysis data.
A distribuição Weibull é muito popular para modelar dados de sobrevida. Muitas modificações da distribuição Weibull foram propostas nos últimos anos. Inspirado pela noção da família gama-generalizada de distribuições de Zografos e Balakrishnan, é proposta, a classe de distribuições Weibull generalizada. Um tratamento compreensivo das propriedades matem áticas de algumas novas distribuições é feita, sendo encontradas as expressões para a função de distribuição, função densidade, função de risco, função geradora de momentos, função característica, m édia, variância, assimetria e curtose. Ajustou-se os novos modelos para conjuntos de dados reais veri cando, pelos critérios de escolha, que os melhores ajustes foram obtidos pelos novos modelos. Dessa forma a classe de distribuições Weibull Generalizada mesmo tendo mais parâmetros a serem estimados, os algoritmos foram capazes de ajustar os dados de análise de sobrevivência.
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Salem, J. A. "Generalized reliability methodology applied to brittle anisotropic single crystals /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/7049.
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Jiang, Siyuan. "Mixed Weibull distributions in reliability engineering: Statistical models for the lifetime of units with multiple modes of failure." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185481.
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The finite mixed Weibull distribution is an appropriate distribution in modeling the lifetime of the units having more than one possible failure cause. Due to the lack of a systematic statistical procedure of fitting the distribution to a data set, it has not been widely used in lifetime data analyses. Many areas on this subject have been studied in this research. The following are the findings and contributions. Through a change of variable, 5 parameters in a two Weibull mixture can be reduced to 3. A parameter'vector (p₁, η, β) defines a family of two-Weibull mixtures which have common characteristics. Numerous probability plots are investigated on Weibull probability paper (WPP). For a given p₁ the η-β plane is partitioned into seven regions which are labeled by A through F and S. The Region S represents the two Weibull mixtures whose cdf curves are very close to a straight line. The Regions A through F represent six typical shapes of the cdf curves on WPP, respectively. The two-Weibull mixtures in one region have similar characteristics. Three important features of the two-Weibull mixture with well separated subpopulations are proved. Two existing methods for the graphical estimation of the parameters are discussed, and one is recommended over the other. The EM algorithm is successfully applied to solve the MLE for mixed Weibull distributions when m, the number of subpopulations in a mixture is known. The algorithms for complete, censored, grouped and suspended samples with non-postmortem and postmortem failures are developed accordingly. The developed algorithms are powerful, efficient and they are insensitive to the initial guesses. Extensive Monte Carlo simulations are performed. The distributions of the MLE of the parameters and of the reliability of a two Weibull mixture are studied. The MLEs of the parameters are sensitive to the degree of separation of the two subpopulation pdfs, but the MLE of the reliability is not. The generalized likelihood ratio (GLR) test is used to determine m. Under H₀: m=1 and H₁: m=m₁>1, ζ, the GLR is independent of the parameters in the distribution of H₀. The distributions of ζ or -21n(ζ) with n=50, 100 and 150 are obtained through Monte Carlo simulations. Compared with the chi-square distribution, they fall in between x²(4) and x²(6), and they are very close to x²(5). A FORTRAN computer program is developed to conduct simulation of the GLR test for 1 ≤ m₀ < m₁ ≤ 5.
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Jiang, Tao. "Information Approach for Change Point Detection of Weibull Models with Applications." Bowling Green State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1434382384.
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Olteanu, Denisa Anca. "Cumulative Sum Control Charts for Censored Reliability Data." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/26665.
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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.
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Chen, Dongming. "Interval estimation and point estimation for the location parameter of the three-parameter Weibull distribution." FIU Digital Commons, 2005. http://digitalcommons.fiu.edu/etd/2130.
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Employing the approach proposed by Z. Chen for constructing an exact confidence interval for the location parameter, this study has investigated the exact confidence intervals, confidence limits and point estimators for the location parameter μ of the three-parameter Weibull distributions. Statistical simulation was carried out for different selections of i, j and k with specified confidence level and sample size. The critical values (ωα/2 and ω1-α/2 have been found using Mote-Carlo simulation. The optimization of the combination of i, j and k has been discussed. The point estimator for the location parameter of the three-parameter Weibull distributions is explored.
It is observed that the critical values do not depend on the parameters. Simulation results show that the optimization of i, j and k is i=1, k-n and j=[n+2/3]. Compared with the commonly used MLE method, the described method provides a simpler, more accurate and more efficient way to estimate the location parameter of the three-parameter Weibull distributions. The described method yields very good statistical inferences for the location parameter of the three-parameter Weibull distributions.
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Ramaisa, Motlalepula. "Inferring congestion from delay and loss characteristics using parameters of the three-parameter Weibull distribution." Diss., Pretoria : [s.n.], 2005. http://upetd.up.ac.za/thesis/available/etd-08282007-112036.
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Liu, Xi. "Bayesian Designing and Analysis of Simple Step-Stress Accelerated Life Test with Weibull Lifetime Distribution." Ohio University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1283365980.
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Zhang, Yuping, and mikewood@deakin edu au. "The Tensile behaviour of non-uniform fibres and fibrous composites." Deakin University. School of Engineering and Technology, 2001. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051017.143549.
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This work investigates the tensile behaviour of non-uniform fibres and fibrous composites. Wool fibres are used as an example of non-uniform fibres because they're physical, morphological and geometrical properties vary greatly not only between fibres but also within a fibre. The focus of this work is on the effect of both between-fibre and within-fibre diameter variations on fibre tensile behaviour. In addition, fit to the Weibull distribution by the non-brittle and non-uniform visco-elastic wool fibres is examined, and the Weibull model is developed further for non-uniform fibres with diameter variation along the fibre length. A novel model fibre composite is introduced to facilitate the investigation into the tensile behaviour of fibre-reinforced composites.
This work first confirms that for processed wool, its coefficient of variation in break force can be predicted from that of minimum fibre diameters, and the prediction is better for longer fibres. This implies that even for processed wool, fibre breakage is closely associated with the occurrence of thin sections along a fibre, and damage to fibres during processing is not the main cause of fibre breakage.
The effect of along-fibre diameter variation on fibre tensile behaviour of scoured wool and mohair is examined next. Only wet wool samples were examined in the past. The extensions of individual segments of single non-uniform fibres are measured at different strain levels. An important finding is the maximum extension (%) (Normally at the thinnest section) equals the average fibre extension (%) plus the diameter variation (CV %) among the fibre segments. This relationship has not been reported before. During a tensile test, it is only the average fibre extension that is measured.
The third part of this work is on the applicability of Weibull distribution to the strength of non-uniform visco-elastic wool fibres. Little work has been done for wool fibres in this area, even though the Weibull model has been widely applied to many brittle fibres. An improved Weibull model incorporating within-fibre diameter variations has been developed for non-uniform fibres. This model predicts the gauge length effect more accurately than the conventional Weibull model.
In studies of fibre-reinforced composites, ideal composite specimens are usually prepared and used in the experiments. Sample preparation has been a tedious process. A novel fibre reinforced composite is developed and used in this work to investigate the tensile behaviour of fibre-reinforced composites. The results obtained from the novel composite specimen are consistent with that obtained from the normal specimens.
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Hartley, Michael A. "A simulation study of the error induced in one-shine reliability confidence bounds for the Weiball distribution using a small sample size with heavily censored data /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2004. http://library.nps.navy.mil/uhtbin/hyperion/04Dec%5FHartley.pdf.
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Magalh?es, Felipe Henrique Alves. "Testes em modelos weibull na forma estendida de Marshall-Olkin." Universidade Federal do Rio Grande do Norte, 2011. http://repositorio.ufrn.br:8080/jspui/handle/123456789/18639.
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Previous issue date: 2011-12-28Universidade Federal do Rio Grande do Norte
In survival analysis, the response is usually the time until the occurrence of an event of interest, called failure time. The main characteristic of survival data is the presence of censoring which is a partial observation of response. Associated with this information, some models occupy an important position by properly fit several practical situations, among which we can mention the Weibull model. Marshall-Olkin extended form distributions other a basic generalization that enables greater exibility in adjusting lifetime data. This paper presents a simulation study that compares the gradient test and the likelihood ratio test using the Marshall-Olkin extended form Weibull distribution. As a result, there is only a small advantage for the likelihood ratio test
Em an?lise de sobreviv?ncia, a vari?vel resposta e, geralmente, o tempo at? a ocorr?ncia de um evento de interesse, denominado tempo de falha, e a principal caracter?stica de dados de sobreviv?ncia e a presen?a de censura, que ? a observa??o parcial da resposta. Associados a essas informa??es, alguns modelos ocupam uma posi??o de destaque por sua comprovada adequa??o a v?rias situa??es pr?ticas, entre os quais ? poss?vel citar o modelo Weibull. Distribui??es na forma estendida de Marshall-Olkin oferecem uma generaliza??o de distribui??es b?sicas que permitem uma flexibilidade maior no ajuste de dados de tempo de vida. Este trabalho apresenta um estudo de simula??o que compara duas estat?sticas de teste, a da Raz?o de Verossimilhan?as e a Gradiente, utilizando a distribui??o Weibull em sua forma estendida de Marshall-Olkin. Como resultado, verifica-se apenas uma pequena vantagem para estat?stica da Raz?o de Verossimilhancas
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Yiqi, Bao. "Estimação e diagnóstico na disribuição Weibull-Binomial-Negativa em análise de sobrevivência." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-26072012-095418/.
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Neste trabalho propomos a distribuição Weibull-Binomial-Negativa (WBN) considerando uma estrutura de ativação latente para explicar a ocorrência do evento de interesse, em que o número de causas competitivas é modelado pela distribuição Binomial Negativa, e os tempos não observados devido às causas seguem a distribuição Weibull. Em geral, as causas competitivas podem ter diferentes mecanismos de ativação, sendo assim os casos de primeira ativação, última ativação e ativação aleatória foram considerados no estudo. Desse modo o modelo proposto inclui uma ampla distribuição, tais como Weibull-Geométrico (WG) e Exponencial-Poisson Complementar (EPC), introduzidas por Barreto-Souza et al. (2011) e G. et al. (2011), respectivamente. Baseando-nos na mesma estrutura, consideramos o modelo de regressão locação-escala baseado na distribuição proposta (WBN) e o modelo para dados de sobrevivência com fração de cura. Os principais objetivos deste trabalho é estudar as propriedades matemáticas dos modelos propostos e desenvolver procedimentos de inferências desde uma perspectiva clássica e Bayesiana. Além disso, as medidas de diagnóstico Bayesiana baseadas na \'psi\'-divergência (Peng & Dey, 1995; Weiss, 1996), que inclui como caso particular a medida de divergência Kullback-Leibler (K-L), foram consideradas para detectar observações influentesIn this work we propose the Weibull-Negative-Binomial (WNB) considering a latent activation structure to explain the occurrence of an event of interest, where the number of competing causes are modeled by the Negative Binomial distribution and the no observed time due to the causes following the Weibull distribution. In general, the competitive causes may have different activation mechanisms, cases of first, last and random activation were considered in the study. Thus, the proposed model includes a wide distribution such as Weibull-Geometric distribution (WG) and Exponential-Poisson complementary (EPC) introduced by (Barreto-Souza et al., 2011) and (G. et al., 2011) respectively. Based on the same structure, we propose a location-scale regression model based on the proposed distribution (WNB) and the model for survival data with cure fraction. The main objectives of this work is to study the mathematical properties of the proposed models and develop procedures inferences from a classical and Bayesian perspective. Moreover, the Bayesian diagnostic measures based on the \'psi\'-divergence (Peng & Dey, 1995; Weiss, 1996), which includes Kullback-Leibler (K-L) divergence measure as a particular case, were considered to detect influential observations
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Lee, Gunhee. "Noninformative priors for some models useful in reliability and survival analysis /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9720544.
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Lin, Min. "Correlation of Bivariate Frailty Models and a New Marginal Weibull Distribution for Correlated Bivariate Survival Data." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1307321226.
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Kuhlhoff, Igor Ribeiro. "Method for application of weibull distribution to the reliability calculation of functional safety for industrial machinery." reponame:Repositório Institucional da UFSC, 2014. https://repositorio.ufsc.br/xmlui/handle/123456789/132745.
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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.
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Polavarapu, Indira. "Optimal design of an accelerated degradation experiment with reciprocal Weibull degradation rate." [Tampa, Fla.] : University of South Florida, 2004. http://purl.fcla.edu/fcla/etd/SFE0000503.
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Yahaya, Saleye. "Dynamique de la couche limite de surface semi-aride : approche des caractéristiques turbulentes par anemometrie a coupelles et effets des traitements de surface du sol." Paris 7, 2004. http://www.theses.fr/2004PA077181.
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Bullock, Bronson P. "Diameter Distributions of Juvenile Stands of Loblolly Pine (Pinus taeda L.) with Different Planting Densities." Diss., Virginia Tech, 2002. http://hdl.handle.net/10919/26412.
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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.
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Buhari, Muhammad. "Reliability assessment of ageing distribution cable for replacement in 'smart' distribution systems." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/reliability-assessment-of-ageing-distribution-cable-for-replacement-in-smart-distribution-systems(e253c774-b5e3-4872-9139-894e7df553f0).html.
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Majority of electricity networks have growing number of ageing elements. Critical network components, such as ageing underground cables, are very expensive to install and disruptive to replace. On the other hand, global climate changes have made connection of new low carbon technologies (LCT) into the grids increasingly necessary. These factors are contributing to the increasing complexity of the planning and management of power systems. Numerous techniques published on this subject tend to ignore the impact of LCT integration and the anchoring ꞌSmartꞌ solutions on ageing network assets, such as underground cables and transformers. This thesis presents the development procedures of an ageing underground cable reliability model (IEC-Arrhenius-Weibull model) and cable ranking models for replacement based on system wide effects and thermal loss-of-life metrics. In addition, a new concept of LCT integration and distribution network management was proposed using two optimization models. The first optimizes connection of new wind sources by minimizing the connection cost and the cost of cable thermal loss-of-lives in the planning period. In the second stage, the network is optimally reconfigured in such a way to minimize thermal-loss-of-life of ageing cable. Both optimization models are formulated as mixed integer non-linear programming (MINLP) problems applicable to radially operated medium voltage networks. To quantify the reliability benefits of the proposed approach, Sequential Monte Carlo Simulation (SMCS) procedure was formulated. Some of the main features of the SMCS procedure are the IEC-Arrhenius-Weibull model for ageing cable, optimal network reconfiguration, wind generation modelling using ARMA models and real time thermal ratings. The final outputs are reliability metrics, cable ranking lists for replacement, savings due to 'non-spend' cable thermal lives, etc. These studies have proven to be important in formulating an effective strategy for extending the lives of network cables, managing overall network reliability and planning cables replacement in power distribution networks.
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Vigas, Valdemiro Piedade. "Extensões dos modelos de sobrevivência referente a distribuição Weibull." Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/4579.
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Previous issue date: 2014-03-07Financiadora de Estudos e Projetos
In this dissertation, two models of probability distributions for the lifetimes until the occurrence of the event produced by a specific cause for elements in a population are reviewed. The first revised model is called the Weibull-Poisson (WP) which has been proposed by Louzada et al. (2011a). This model generalizes the exponential-Poisson distributions proposed by Kus (2007) and Weibull. The second, called long-term model, has been proposed by several authors and it considers that the population is not homogeneous in relation to the risk of event occurence by the cause studied. The population has a sub-population that consists of elements who are not liable do die by the specific cause in study. These elements are considered as immune or cured. In relation to the elements who are at risk the minimum value of time of the event accurance is observed. In the review of WP the expressions of the survival function, quantile function, probability density function, and of the hazard function, as well the expression of the non-central moments of order k and the distribution of order statistics are detailed. From this review we propose, in an original way, studies of the simulation to analyze the paramenters of frequentist properties of maximum likelihood estimators for this distribution. And also we also present results related to the inference about the parameters of this distribution, both in the case in which the data set consists of complete observations of lifetimes, and also in the case in which it may contain censored observations. Furthermore, we present in this paper, in an original way a regression model in a form of location and scale when T has WP distribution. Another original contribution of this dissertation is to propose the distribution of long-term Weibull-Poisson (LWP). Besides studying the LWP in the situation in which the covariates are included in the analysis. We also described the functions that characterize this distribution (distribution function, quantile function, probability density function and the hazard function). Moreover we describe the expression of the moment of order k, and the density function of a statistical order. A study by simulation viii of this distribution is made through maximum likelihood estimators. Applications to real data set illustrate the applicability of the two considered models.
Nesta dissertação são revistos dois modelos de distribuições de probabilidade para os tempos de vida até a ocorrência do evento provocado por uma causa específica para elementos em uma população. O primeiro modelo revisto é o denominado Weibull-Poisson (WP) que foi proposto por Louzada et al. (2011a), esse modelo generaliza as distribuições exponencial Poisson proposta por Kus (2007) e Weibull. O segundo, denominado modelo de longa duração, foi proposto por vários autores e considera que a população não é homogênea em relação ao risco de ocorrência do evento pela causa em estudo. A população possui uma sub-população constituída de elementos que não estão sujeitos ao evento pela causa especifica em estudo, sendo considerados como imunes ou curados. Em relação à parcela dos elementos que estão em risco observa-se o valor mínimo dos tempos da ocorrência do evento. Na revisão sobre a WP são detalhadas as expressões da função de sobrevivência, da função quantil, da função densidade de probabilidade e da função de risco, bem como a expressão dos momentos não centrais de ordem k e a distribuição de estatísticas de ordem. A partir desta revisão, é proposta de forma original, estudos de simulação com o objetivo de analisar as propriedades frequentistas dos estimadores de máxima verossimilhança dos parâmetros desta distribuição. E apresenta-se resultados relativos à inferência sobre os parâmetros desta distribuição, tanto no caso em que o conjunto de dados consta de observações completas de tempos de vida, como no caso em que ele possa conter observações censuradas. Alem disso, apresentamos de forma original neste trabalho um modelo de regressão na forma de locação e escala quando T tem distribuição WP. Outra contribuição original dessa dissertação é propor a distribuição de longa duração Weibull-Poisson (LWP), alem de estudar a LWP na situação em que as covariáveis são incluídas na análise. Realizou-se também a descrição das funções que caracterizam essa distribuição (função distribuição, função quantil, função densidade de probabilidade e função de risco). Assim como a descrição da expressão do momento de ordem k e da função densidade da estatística de ordem. É feito um estudo por simulação desta distribuição via máxima verossimilhança. Aplicações à conjuntos de dados reais ilustram a utilidade dos dois modelos considerados.
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Carneiro, Tatiane Carolyne. "Characterization of Potential Wind Generation EolioelÃtrica For Purposes: A Case Study For Maracanaà (CE), ParnaÃba (PI) and Petrolina (PE)." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12256.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgicoIn recent years wind energy is becoming increasingly competitive on the world stage, making their participation in the electricity generation matrix presents a strong growth expectation. This dissertation initially presents an analysis of the behavior of wind at three locations in Northeast Brazil (Maracanau-CE, Petrolina-PE e Parnaiba-PI). In a second step, statistical analyzes are researched to the most appropriate behavior patterns of the observed wind resource in the three localities. In conclusion, the impact of the statistical analyzes used in the production of electricity from wind turbines is identified. In this study,historicaldata of speed and direction of wind collectedare used, during periods of: February 2012 to January 2013, to Maracanau; August 2012 to July 2013, for Parnaiba; and May 2012 to March 2013, for Petrolina. The Weibull distribution is applied to approximate the histograms of wind speed using different horizons of applications (annual, semiannual) and four different numerical methods (Empirical, Momentum, Energy Pattern Factor and Equivalent Energy) for estimation of the form and scale parameters. In addition to evaluating the application of Weibull, other frequency distributions (Normal, Gamma and Log-Normal)are analyzed, in order to obtain the best possible fit. In a last step, with the aid of RETScreen program,annual production of electricity, delivered to the grid from wind turbines,is calculated. The optimum wind speed occurred in Parnaiba (10 and 11 m / s), followed by Petrolina (8 and 9 m / s). Among all different numerical methods that was evaluated, the Equivalent Energy method presented the best performance, unlike the Energy Pattern Factor method, that presented the worst. The Weibull distribution showed good potential for setting wind data in Maracanau and Parnaiba, both located along the coastline. However, based on the wind data recorded, in Petrolina, which is located further inland, the performance was inferior. Among all the different frequency distributions that were verified, only normal distribution had an fit as good as Weibull distribution. Based on the annual electricity production estimation, Parnaiba is the city that has the best potential for energy production.
Nos Ãltimos anos a energia eÃlica tem se tornando cada vez mais competitiva no cenÃrio mundial, fazendo com que sua participaÃÃo na matriz elÃtrica apresente uma forte expectativa de crescimento. A presente dissertaÃÃo apresenta inicialmente uma anÃlise do comportamento do vento em trÃs localidades no Nordeste do Brasil (Maracanaà (CE), Petrolina (PE) e ParnaÃba (PI)); numa segunda etapa, sÃo pesquisadas anÃlises estatÃsticas mais adequadas aos padrÃes de comportamento do recurso eÃlico observado nas trÃs localidades e, concluindo, à identificado o impacto das anÃlises estatÃsticas utilizadas na produÃÃo de eletricidade de aerogeradores. Neste estudo sÃo utilizados dados histÃricos de velocidade e direÃÃo do vento coletados durante os perÃodos de: fevereiro de 2012 - janeiro de 2013 para MaracanaÃ, Agosto de 2012 - Julho de 2013 para ParnaÃba, maio de 2012 - marÃo 2013 para Petrolina. A distribuiÃÃo de frequÃncia de Weibull à aplicada para aproximar os histogramas de velocidade do vento, utilizando diferentes horizontes de aplicaÃÃes (anual, semestral) e quatro diferentes mÃtodos numÃricos (EmpÃrico, Momento, Fator PadrÃo de Energia e Energia Equivalente) para a estimaÃÃo dos parÃmetros de forma e escala. AlÃm de avaliar a aplicaÃÃo de Weibull, sÃo analisadas outras distribuiÃÃes de frequÃncia (Normal, Gama e Log-Normal) objetivando obter o melhor ajuste possÃvel. Numa Ãltima etapa, com o auxÃlio do programa RETScreen,à calculada a produÃÃo de eletricidade anual entregue à rede a partir de aerogeradores. Os melhores valores de velocidade do vento ocorreram em ParnaÃba (10 e 11 m/s), seguido de Petrolina (8 e 9 m/s). Dos diferentes mÃtodos numÃricos avaliados, o mÃtodo de energia equivalente apresentou o melhor desempenho e o mÃtodo fator de padrÃo de energia foi o mÃtodo com o pior desempenho. A distribuiÃÃo de Weibull demonstrou bom potencial para o ajuste de dados de vento em Maracanaà e ParnaÃba, ambas localizadas ao longo do litoral. No entanto, em Petrolina, que està situada mais para o interior, foi verificado um desempenho limitado a partir dos dados de vento registrados. Das diferentes distribuiÃÃes de frequÃncias testadas, apenas a distribuiÃÃo normal apresenta um ajuste aproximado ao que Weibull permite desenvolver. Com base nas estimaÃÃes da produÃÃo de eletricidade anual, ParnaÃba à a cidade que apresenta o melhor potencial para o aproveitamento eolioelÃtrico.
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Denecke, Liesa [Verfasser]. "Estimators and Tests based on Likelihood-Depth with Application to Weibull Distribution, Gaussian and Gumbel Copula / Liesa Denecke." Kassel : Universitätsbibliothek Kassel, 2010. http://d-nb.info/1007951192/34.
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Hartley, Michael A. "A simulation study of the error induced in one-sided reliability confidence bounds for the Weiball distribution using a small sample size with heavily censored data." Thesis, Monterey California. Naval Postgraduate School, 2004. http://hdl.handle.net/10945/1260.
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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
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Bhering, Felipe Lunardi. "Confiabilidade em sistemas coerentes: um modelo bayesiano Weibull." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-01122013-155316/.
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O principal objetivo desse trabalho é introduzir um modelo geral bayesiano Weibull hierárquico para dados censurados que estima a função de confiabilidade de cada componente para sistemas de confiabilidade coerentes. São introduzidos formas de estimação mais sólidas, sem a inserção de estimativas médias nas funções de confiabilidade (estimador plug-in). Através desse modelo, são expostos e solucionados exemplos na área de confiabilidade como sistemas em série, sistemas em paralelo, sistemas k-de-n, sistemas bridge e um estudo clínico com dados censurados intervalares. As soluções consideram que as componentes tem diferentes distribuições, e nesse caso, o sistema bridge ainda não havia solução na literatura. O modelo construído é geral e pode ser utilizado para qualquer sistema coerente e não apenas para dados da área de confiabilidade, como também na área de sobrevivência, dentre outros. Diversas simulações com componentes com diferentes proporções de censura, distintas médias, três tipos de distribuições e tamanhos de amostra foram feitas em todos os sistemas para avaliar a eficácia do modelo.The main purpose of this work is to introduce a general bayesian Weibull hierarchical model for censored data which estimates each reliability components function from coherent systems. Its introduced estimation procedures which do not consider plug-in estimators. Also, its exposed and solved with this model examples in reliability area such as series systems, parallel systems, k-out-of-n systems, bridge systems and a clinical study with interval censoring data. The problem of bridge system hadnt a solution before for the case of each component with different distribution. Actually, this model is general and can be used to analyse any kind of coherent system and censored data, not only reliability ones, but also survival data and others. Several components simulations with different censored proportions, distinct means, three kinds of distributions and sample size were made in all systems to evaluate model efficiency.
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Baseer, Mohammed Abdul. "Wind resource assessment and GIS-based site selection methodology for efficient wind power deployment." Thesis, University of Pretoria, 2017. http://hdl.handle.net/2263/61314.
Full textAbstract:
An enormous and urgent energy demand is predicted due to the growing global population, increase in power intensive industries, higher living standards, electrification of remote areas, and globalisation (transportation). Moreover, the global consciousness about the harmful effects of traditional methods of power generation on the environment. That, in turn, has created a need to strategically plan and develop renewable and sustainable energy generation systems. This study presents a wind resource assessment of seven locations proximate to the largest industrial hub in the Middle East, Jubail Industrial City, Kingdom of Saudi Arabia, and a Geographic Information System, GIS based model considering a multi-criteria wind farm site suitability approach for the entire Kingdom of Saudi Arabia and elsewhere.
The hourly mean wind speed data at 10, 50 and 90 m above the ground level (AGL) over a period of five years was used for a meteorological station at the Industrial Area (Central) of Jubail. At the remaining six sites, the meteorological data were recorded at 10 m AGL only. Five years of wind data were used for five sites and three years of data were available for the remaining one site. At the Industrial Area (East), the mean wind speeds were found to be 3.34, 4.79 and 5.35 m/s at 10, 50 and 90 m AGL, respectively. At 50 and 90 m AGL, the availability of wind speed above 3.5 m/s was more than 75%. The local wind shear exponent, calculated using measured wind speed values at three heights, was found to be 0.217. The mean wind power density values at measurement heights were 50.92, 116.03 and 168.46 W/m2, respectively. After the assessment and comparison of wind characteristics of all seven sites, the highest annual mean wind speed of 4.52 m/s was observed at Industrial Area (East) and the lowest of 2.52 m/s at the Pearl Beach with standard deviations of 2.52 and 1.1 m/s, respectively.
In general, at all sites, the highest monthly mean wind speed was observed in February/June and the lowest in September/October. The period of higher wind availability coincides with a high power demand period in the region attributable to the air conditioning load. The wind rose plots show that the prevailing wind direction for all sites was from the north-west. Weibull parameters for all sites were estimated using maximum likelihood, least-squares regression method (LSRM), and WAsP algorithm. In general, at all sites, the Weibull parameter, c, was the highest in the months of February/June and the lowest in the month of October. The most probable and maximum energy carrying wind speed was determined by all three methods. The highest value of most probable wind speed was found to be in the range of 3.2 m/s to 3.6 m/s at Industrial Area (East) and the highest value of maximum energy carrying wind speed was found to be in the range 8.6 m/s to 9.0 m/s at Industrial Area 2 (South) by three estimation methods. The correlation coefficient (R2), root mean square error (RMSE), mean bias error (MBE), and mean bias absolute error (MAE) showed that all three methods represent wind data at all sites accurately. However, the maximum likelihood method is slightly better than LSRM, followed by WAsP algorithm. The wind power output at all seven sites, from five commercially available wind turbines of rated power ranging from 1.8 to 3.3 MW, showed that Industrial Area (East) is most promising for wind farm development. At all sites, based on percentage plant capacity factor, PCF, the 1.8 MW wind turbine was found to be the most efficient. At Industrial Area (East), this wind turbine was found to have a maximum PCF of 41.8%, producing 6,589 MWh/year energy output. The second best wind turbine was 3 MW at all locations except the Al-Bahar Desalination Plant and Pearl Beach. At both of these locations, 3.3 MW was the next best option. The energy output from the 3 MW wind turbine at Industrial Area (East) was found to be 11,136 MWh/year with a PCF of 41.3%. The maximum duration of rated power output from all selected wind turbines was observed to be between 8 to 16.6% at Industrial Area 2 (South). The minimum duration of rated power output, less than 0.3% for all wind turbines, was observed at Pearl Beach. The maximum duration of zero power output of between 35 to 60% was also observed at Pearl Beach.Thesis (PhD)--University of Pretoria, 2017.
Mechanical and Aeronautical Engineering
PhD
Unrestricted
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Couto, Epaminondas de Vasconcellos. "Modelo de regressão log-gama generalizado exponenciado com dados censurados." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-16032010-112500/.
Full textAbstract:
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.
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Thomas, Gina M. "Weibull parameter estimation using genetic algorithms and a heuristic approach to cut-set analysis." Ohio : Ohio University, 1995. http://www.ohiolink.edu/etd/view.cgi?ohiou1178901727.
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Gomes, André Yoshizumi. "Família Weibull de razão de chances na presença de covariáveis." Universidade Federal de São Carlos, 2009. https://repositorio.ufscar.br/handle/ufscar/4558.
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Previous issue date: 2009-03-18Universidade 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.
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Kim, Hongman. "Statistical Modeling of Simulation Errors and Their Reduction via Response Surface Techniques." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28390.
Full textAbstract:
Errors of computational simulations in design of
a high-speed civil transport (HSCT) are investigated.
First, discretization error from a supersonic panel code,
WINGDES, is considered. Second, convergence error from
a structural optimization procedure using GENESIS is
considered along with the Rosenbrock test problem.
A grid converge study is performed to estimate
the order of the discretization error in the lift
coefficient (CL) of the HSCT calculated from WINGDES.
A response surface (RS) model using several mesh sizes
is applied to reduce the noise magnification problem
associated with the Richardson extrapolation. The RS model
is shown to be more efficient than Richardson extrapolation
via careful use of design of experiments.
A programming error caused inaccurate optimization
results for the Rosenbrock test function, while
inadequate convergence criteria of the structural
optimization produced error in wing structural weight
of the HSCT. The Weibull distribution is successfully
fit to the optimization errors of both problems.
The probabilistic model enables us to estimate average
errors without performing very accurate optimization runs
that can be expensive, by using differences between
two sets of results with different optimization control
parameters such as initial design points or convergence
criteria.
Optimization results with large errors, outliers,
produced inaccurate RS approximations. A robust regression
technique, M-estimation implemented by iteratively
reweighted least squares (IRLS), is used to identify
the outliers, which are then repaired by higher fidelity
optimizations. The IRLS procedure is applied to the
results of the Rosenbrock test problem, and wing structural
weight from the structural optimization of the HSCT.
A nonsymmetric IRLS (NIRLS), utilizing one-sidedness
of optimization errors, is more effective than IRLS in
identifying outliers. Detection and repair of the outliers
improve accuracy of the RS approximations. Finally,
configuration optimizations of the HSCT are performed
using the improved wing bending material weight RS models.Ph. D.
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Kensler, Jennifer Lin Karam. "Analysis of Reliability Experiments with Random Blocks and Subsampling." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/28415.
Full textAbstract:
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.
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Thamrin, Sri Astuti. "Bayesian survival analysis using gene expression." Thesis, Queensland University of Technology, 2013. https://eprints.qut.edu.au/62666/1/Sri_Astuti_Thamrin_Thesis.pdf.
Full textAbstract:
This thesis developed and applied Bayesian models for the analysis of survival data. The gene expression was considered as explanatory variables within the Bayesian survival model which can be considered the new contribution in the analysis of such data. The censoring factor that is inherent of survival data has also been addressed in terms of its impact on the fitting of a finite mixture of Weibull distribution with and without covariates. To investigate this, simulation study were carried out under several censoring percentages. Censoring percentage as high as 80% is acceptable here as the work involved high dimensional data. Lastly the Bayesian model averaging approach was developed to incorporate model uncertainty in the prediction of survival.