Simmons, Gregory Lawrence (1997) Properties of some minimum run resolution IV designs. Research Master thesis, Victoria University of Technology.

Abstract

The regular resolution TV fractional factorial designs described in the have many desirable properties; main effect estimates are uncorrelated and are unbiased by two-factor interactions, whilst estimates of the two-factor interaction effects are limited to the identification of a significant orthogonal aliased string. An augmenting experiment is required to identify which interactions in the string are significant and which are inert. In addition to the regular class of fractional designs there exist a series of minimum run non-regular resolution IV designs. These non-regular designs can be further divided into orthogonal and non-orthogonal designs. To examine n factors these designs require 2n runs and are generated from minimum run resolution III designs via the Box and Wilson foldover thereom. These designs usually result in a saving of runs when compared with the corresponding regular fractional designs. Orthogonal designs provide uncorrelated main effect estimates. However, the two-factor interaction effects are usually confounded in an complex manner. Non-orthogonal designs provide correlated main effect estimates and also exhibit complex confounding in the two-factor interaction subspace. This thesis examines a number of minimum run resolution IV non-regular designs and determines whether it is possible to search for and estimate a small number of two-factor interactions without the need of augmenting trials. The orthogonal designs considered are the foldover designs generated from the 12,20 and 24 factor Plackett and Burman designs, whilst the non-orthogonal designs considered are the foldover designs generated from the Yang 6 and 14 factor designs and the Raghavarao 13 factor design. Unlike the regular factorial designs, some of these non-regular designs provide estimates of a small number of two-factor interactions without the addition of augmenting trials. In particular the 20 and 24 factor Plackett and Burman foldover designs are shown to be resolution V in every set of 5 factors and to allow the search and estimation of up to two two-factor interactions. The foldovers of the Yang and Raghavarao designs allow the search and estimation of up to one two-factor interaction. As the number of interactions considered gets larger, the search and estimation cannot be done for some values of the interaction effects. In these cases a number of models are equally likely. In situations such as this augmenting trials are discussed, and a technique is devised to deal with the design of augmenting trials. This thesis is also concerned with the analysis of these non-regular designs and two methods are presented to analyse search designs which are illustrated through the examination of some simulated experiments.

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