D-Optimal Split-Plot Designs With Given Numbers and Sizes of Whole Plots

Abstract

The design of split-plot experiments has received considerable attention during the last few years. The goal of this article is to provide an efficient algorithm to compute D-optimal split-plot designs with given numbers of whole plots and given whole-plot sizes. The algorithm is evaluated and applied to a protein extraction experiment. In addition, it is shown that two-level factorial and fractional factorial designs are D-optimal for estimating first-order response surface models for specific numbers and sizes of whole plots.

KEY WORDS :

• 2^m and 2^m−f designs
• Correlated observations
• D-optimal design
• Equivalence of ordinary least squares and generalized least squares
• Hard-to-change factors
• Protein extraction experiment
• Split-plot experiment.