Computer Construction of “D-Optimal” First-Order Designs

Abstract

This paper presents the results of a study in which the computer algorithm DETMAX was used for the purpose of constructing n-run “D-optimal” designs over a cubic region of interest for the first-order model E(y) = β₀ + β₀ x ₁ + … + β _p x _p . These results suggest some general “rules” (actually conjectures) for the construction of such designs. For p ≤ 9, all but 12 combinations of n and p are covered by these “rules;” the 12 exceptions are discussed separately. The resolution IV designs obtained by folding over these “D-optimal” first-order designs are also discussed and are shown to compare favorably with designs previously published.

KEY WORDS:

• Computer-Aided Design
• D-optimal
• First-Order Model
• Non-Orthogonal Designs
• Resolution III
• Resolution IV
• Two-Level Designs