2-LEVEL FACTORIAL-DESIGNS FOR MAIN EFFECTS AND SELECTED 2-FACTOR INTERACTIONS

From a Practical viewpoint the first decision to be made in the construction of a design of a two-level factorial experiment is the choice of the parameters of interest. It is convenient to represent such a choice by considering an undirected graph g with n vertices and e edges. The vertices and edges of g are used respectively to identify the main effects of n two-level factors and the e two-factor interactions Of interest. The parameters identified by g together with the general mean are taken to be the parameters of interest. A design d of the 2n factorial will be called a g-design if and only if d is saturated and is capable of providing an unbiased estimator of the parameters of interest relative to the orthogonal polynomial model. In this paper (i) a g-design is constructed for each graph g and certain features of g-designs are noted, (ii) some D-optimality results for g-designs within the class of all g-designs are obtained.