A set of rules for constructing an admissible set of D optimal exact designs

Abstract

In the search for a D-optimal exact design using the combinatorial iterative technique introduced by Onukogu and Iwundu, 2008, all the support points that make up the experimental region are grouped into H concentric balls according to their distances from the centre. Any selection of N support points from the balls defines a class of designs N x . The technique requires the identification of best D-optimal exact design(s) within a class and moves progressively from one class to another with a higher determinant value until it reaches an optimum. Quite often, each class contains several N-point designs and a hundred per cent search is required to identify best design(s) within a class. A set of rules for selecting best design(s) within a class, alternative to one hundred per cent search is developed. The effectiveness of the rules is measured by the reduction in the number of determinant evaluations relative to a hundred per cent search