Date of Award

Summer 8-6-2018

Degree Type

Dissertation-Restricted

Degree Name

Ph.D.

Degree Program

Engineering and Applied Science

Department

Mathematics

Major Professor

Tumulesh Solanky

Second Advisor

Linxiong Li

Third Advisor

Vesselin P Jilkov

Fourth Advisor

Huimin Chen

Fifth Advisor

Jairo Santanilla

Abstract

ANOVA analysis is a classic tool for multiple comparisons and has been widely used in numerous disciplines due to its simplicity and convenience. The ANOVA procedure is designed to test if a number of different populations are all different. This is followed by usual multiple comparison tests to rank the populations. However, the probability of selecting the best population via ANOVA procedure does not guarantee the probability to be larger than some desired prespecified level. This lack of desirability of the ANOVA procedure was overcome by researchers in early 1950's by designing experiments with the goal of selecting the best population. In this dissertation, a single-stage procedure is introduced to partition k treatments into "good" and "bad" groups with respect to a control population assuming some key parameters are known. Next, the proposed partition procedure is genaralized for the case when the parameters are unknown and a purely-sequential procedure and a two-stage procedure are derived. Theoretical asymptotic properties, such as first order and second order properties, of the proposed procedures are derived to document the efficiency of the proposed procedures. These theoretical properties are studied via Monte Carlo simulations to document the performance of the procedures for small and moderate sample sizes.

Rights

The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.

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