Applied Statistics

Since their invention in the 1920s, control charts have been popular tools for use in monitoring processes in fields as varied as manufacturing and healthcare. Most of these charts are designed to monitor a single process parameter, but recently, a number of charts and schemes for jointly monitoring the location and scale of processes which follow two-parameter distributions have been developed. These joint monitoring charts are particularly relevant for processes in which special causes may result in a simultaneous shift in the location parameter and the scale parameter. Among the available schemes for jointly monitoring location and scale parameters, the vast majority are designed for normally distributed processes for which the in-control mean and variance are known rather than estimated from data. When the process data are non-normally distributed or the process parameters are unknown, alternative control charts are needed. This dissertation presents and compares several control schemes for jointly monitoring data from Laplace and shifted exponential distributions with known parameters as well as a pair of charts for monitoring data from normal distributions with unknown mean and variance. The normal theory charts are adaptations of two existing procedures for the known parameter case, Razmy's (2005) Distance chart and Chen and Cheng's (1998) Max chart, while the Laplace and shifted exponential charts are designed using an appropriate statistic for each parameter, such as the maximum likelihood estimators. iii DEDICATION This dissertation is dedicated to my closest family members who encouraged me throughout many years of formal education: my parents, Bob and Barbara McMillan; my brother, Robert McMillan; my husband, Will McCracken; and my daughter, Anna McCracken. iv ACKNOWLEDGEMENTS I am pleased to have the opportunity to thank those who helped me during the dissertation development process. I would first like to thank the chairman of my doctoral committee, Dr. Subhabrata Chakraborti, for his continuing guidance. I learned a tremendous amount from him, both during the courses he taught and during the many hours I spent in his office discussing details of this dissertation and my various papers and conference presentations. I would also like to thank the other faculty members who served on my committee: Dr.

In attempting to find the most practical and efficient nonparametric rank test in the two-sample problem of testing for equality of populations, it is submitted that correlation coefficients might be useful. As a measure of the strength of the linear relationship between comparable test statistics, the correlation helps to determine how the tests distinguish between rank orders in the null distribution. This paper gives expressions for the correlations between Gastwirth's percentile-modified Tp+_B~ tests, the Wilcoxon test, Barton-David test, Mood test and Savage tests, and indicates how they could be used in choosing which test to employ in practice, including optimal selection of p and r in the percentilemodified tests.

In attempting to find the most practical and efficient nonparametric rank test in the two-sample problem of testing for equality of populations, it is submitted that correlation coefficients might be useful. As a measure of the strength of the linear relationship between comparable test statistics, the correlation helps to determine how the tests distinguish between rank orders in the null distribution. This paper gives expressions for the correlations between Gastwirth's percentile-modified Tp+_B~ tests, the Wilcoxon test, Barton-David test, Mood test and Savage tests, and indicates how they could be used in choosing which test to employ in practice, including optimal selection of p and r in the percentilemodified tests.

Tlze U.S. I'irgilz Islands' tozrrism indztstry remainsstatic rvlzile the indzrstry in tlze Caribbearz lzas beet: growing. Tlze depreciation of tlze U.S. dollar will attract larger rzumbers of Canadiarzs and Ezlropeans as uvell as C'.S. visitors to otlzer areas of tlze Caribbean for beach holidays, but it nzay rzot help tlze U.S. Virgin Islarzders wzless go\*errzment and private industry developmerit erzcowages visitors to come and sta? in lzotels it.lzile also 1i elcomirzg cruiseship passengers.

On a multiple-choice test in which each item has k alternative responses, the test taker is permitted to choose any subset which he believes contains the one correct answer. A scoring system is devised that depends on the size of the subset and on whether or not the correct answer is eliminated. The mean and variance of the score per item are obtained. Methods are derived for determining the total number of items that should be included on the test so that the average score on all items can be regarded as a good measure of the subject's knowledge. Efficiency comparisons between conventional and the subset selection scoring procedures are made. The analogous problem of r > 1 correct answers for each item (with r fixed and known) is also considered.