published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

The purpose of this study was to investigate the medical records of 900 maintenance personnel employed in an aircraft manufacturing plant, and determine if the accident rate followed a Poisson distribution as well as the extent to which it did. It was assumed that the closer the data conformed to the Poisson curve, the more likely it would be that the variance in accident rates was due to "pure chance factors." The investigation of data in this study was expected to reveal information concerning the relative importance of the various injury sources, the conditions, processes or activities that produce injuries, extent of recurrence of each kind of injury or accident in each type of activity or operation, repeaters, which could be utilized in preventing recurrence.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Thèse de doctorat : Mathématiques appliquées : Evry-Val d'Essonne : 2008. / Titre provenant de l'écran-titre.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 100-104). Also available in print.

Thesis (Ph. D.)--Ohio State University, 2007. / Full text release at OhioLINK's ETD Center delayed at author's request

abstract: There has been much research involving simultaneous monitoring of several correlated quality characteristics that rely on the assumptions of multivariate normality and independence. In real world applications, these assumptions are not always met, particularly when small counts are of interest. In general, the use of normal approximation to the Poisson distribution seems to be justified when the Poisson means are large enough. A new two-sided Multivariate Poisson Exponentially Weighted Moving Average (MPEWMA) control chart is proposed, and the control limits are directly derived from the multivariate Poisson distribution. The MPEWMA and the conventional Multivariate Exponentially Weighted Moving Average (MEWMA) charts are evaluated by using the multivariate Poisson framework. The MPEWMA chart outperforms the MEWMA with the normal-theory limits in terms of the in-control average run lengths. An extension study of the two-sided MPEWMA to a one-sided version is performed; this is useful for detecting an increase in the count means. The results of comparison with the one-sided MEWMA chart are quite similar to the two-sided case. The implementation of the MPEWMA scheme for multiple count data is illustrated, with step by step guidelines and several examples. In addition, the method is compared to other model-based control charts that are used to monitor the residual values such as the regression adjustment. The MPEWMA scheme shows better performance on detecting the mean shift in count data when positive correlation exists among all variables. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010

The statistical inferences about the parameters of Binomial-Poisson hierarchy model are discussed. Based on the estimators of paired observations we consider the other two cases with extra observations on both the first and second layer of the model. The MLEs of lambda and p are derived and it is also proved the MLE lambda is also the UMVUE of lambda. By using multivariate central limit theory and large sample theory, both the estimators based on extra observations on the first and second layer are obtained respectively. The performances of the estimators are compared numerically based on extensive Monte Carlo simulation. Simulation studies indicate that the performance of the estimators is more efficient than those only based on paired observations. Inference about the confidence interval for p is presented for both cases. The efficiency of the estimators is compared with condition given that same number of extra observations is provided.

Lubrication of ceramics is a difficult and not completely solved problem. Ceramics do not respond to conventional lubricants which are designed to function by a chemical reaction with the surface. There is, accordingly, increased interest in the development of lubrication alternatives for ceramics, and in understanding the tribochemical fundamentals by which new lubrication processes can be designed and controlled. In particular, the mechanism of tribopolymerization for some addition-type monomers is thought to be initiated and controlled by triboemitted low-energy electrons. This Ph.D. dissertation presents the experimental work carried out at the Virginia Polytechnic Institute and State University for the characterization of charge intensity and energy distribution of charged-particles triboemitted from sliding contacts of ceramics. A review is presented of research work on tribochemistry and, in particular, on tribopolymerization as a lubrication mechanism. Relevant literature is also reviewed on the phenomena of exoemission, triboemission and fractoemission of charged-particles. The design, construction and development of a new instrument and data acquisition system to carry out triboemission measurements under high vacuum and for controlled load, sliding speed and retarding grid-voltage is described. The charge intensity is characterized of the particles triboemitted from two related ceramics, alumina and sapphire, and from one metallic material, i.e., aluminum, when scratched by a diamond pin. In the case of alumina, triboemitted-charge intensity also is studied by sliding contact of an alumina ball. Burst-type negatively-charged particle triboemission was observed from diamond-on-alumina, diamond-on-sapphire, and alumina-on-alumina sliding contacts. The different crystalline structure, i.e., of alumina and sapphire, does not appear to be a factor in electron triboemission. In general, large bursts of electron triboemission may appear superimposed on a constant lower level of small-burst emission. This constant level, being higher than background-noise, does not vary between different ceramic specimens, while maximum levels of triboemission-bursts differ by two orders of magnitude between different specimens. The characteristic decay-time of the triboemission bursts is found of about 100ms. Lower-level decaying post-contact emission of negatively-charged particles from ceramics is observed. Low negatively-charged triboemission was observed from diamond-on-aluminum sliding contacts. The positively-charged triboemission from these sliding material systems was also measured. Low positive-ion emission, barely above background level, was observed for the diamond-on-ceramics and alumina-on-alumina systems. The retarded-energy spectra of the negatively-charged particle triboemissions from ceramics were also obtained. Such spectra show decaying rates of triboemission for increasing minimum energy of the triboemitted particles: an important fraction of the total electron triboemission is produced in the zero to 5eVolts energy-range, with a decaying tail extending beyond the test maximum level of 48 Volts. These experimental measurements are discussed with a focus on the possible role of triboemitted charged-particles in tribopolymerization as a mechanism of ceramic lubrication. It is concluded that low-energy electrons are emitted in bursts from ceramics under sliding contact, the essential first step in the hypotheses of tribopolymerization of certain addition-type monomers, while positively-charged emission is negligible. These findings strongly support tribopolymerization results from previous research. A frequency domain analysis of the triboemission data is carried out. For the electron-triboemission outputs, a characteristic pattern is found for the experimentally estimated frequencies of occurrence of the triboemitted particles. A new probability distribution, called "Convoluted Poisson" is developed to describe this triboemission data. Good agreement is found between the probabilities of triboemitted-particle occurrence, as predicted by such distribution, and the experimental probabilities estimated from triboemission outputs. The significance of the two parameters defining this "Convoluted Poisson" distribution is explored and discussed with a focus on basic surface-change phenomena. / Ph. D.

Dados de contagem podem ser considerados, em geral, como provenientes de uma distribuição de Poisson. Neste contexto, a análise de tais dados apresenta certas dificuldades, pois não segue algumas pressuposições básicas para o ajuste de um modelo matemático. Desse modo, algumas transformações são sugeridas, mas nem sempre bons resultados são obtidos. No enfoque de Modelos Lineares Generalizados, a estatística que mede a qualidade do ajuste do modelo para os dados é chamada deviance. Porém, a distribuição da deviance é, em geral, desconhecida. No entanto, para dados com distribuição de Poisson, pode-se mostrar que a distribuição da deviance se aproxima de uma distribuição ?2, mas tal aproximação não é boa para tamanhos pequenos de amostra. Para melhorar essa aproximação, alguns fatores de correção para os dados são sugeridos, mas os resultados obtidos ainda não são satisfatórios. Assim, o objetivo deste trabalho é propor um novo fator de correção para os dados seguindo uma distribuição de Poisson, de modo a se obter uma melhora na distribuição da deviance para qualquer tamanho de amostra. Para isto, será adicionada uma constante à variável resposta e, através do valor esperado da deviance, calcula-se tal constante de modo a reduzir o erro cometido na aproximação. Para verificar a melhora na aproximação da distribuição da deviance a uma distribuição qui-quadrado, dados de uma distribuição de Poisson são simulados e o valor da deviance é calculado. QQ-plots são construídos para a comparação com a distribuição qui-quadrado. / Analysis of count data presents, in general, can be supposed coming from a Poisson distribution. The analysis of such data have some problems once the underlying distribution of them does not follow the basic assumptions to fit a model. Some tranformations can be suggested, but good results are not always obtained. In the approach of the Generalized Linear Models, the deviance is the statistics that measures the goodness of fit, but its distribution is unknown. Furthermore, considering Poisson distribution data, it is possible to approximate the distribution of the deviance for a chi-square distribution, but such approximation is not good for small sample size. In order of improve this approximation, corrections for the data are suggested, but the results are not good yet. Then, the aim of this work is to propose a new correction factor for data following a Poisson distribution in order to obtain an improvement in the distribution of the deviance for any sample size. For this, just adding a constant at the response variable and, through the expected value of the deviance, such constant is obtained in order to reduce the error in the aproximation. Simulated data from the Poisson distribution were made to calculate the deviance with and without the correction and QQ-plots were used to compare the values of the deviance with the chi-square distribution.