Three-level equivalent-estimation split-plot designs based on subset and supplementary difference set designs

Abstract

In many industrial experiments, complete randomization of the runs is impossible as, often, they involve factors whose levels are hard or costly to change. In such cases, the split-plot design is a cost-efficient alternative that reduces the number of independent settings of the hard-to-change factors. In general, the use of generalized least squares is required for model estimation based on data from split-plot designs. However, the ordinary least squares estimator is equivalent to the generalized least squares estimator for some split-plot designs, including some second-order split-plot response surface designs. These designs are called equivalent-estimation designs. An important consequence of the equivalence is that basic experimental design software can be used for model estimation. This article introduces two new families of equivalent-estimation split-plot designs, one based on subset designs and another based on supplementary difference set designs. The resulting designs complement existing catalogs of equivalent-estimation designs and allow for a more flexible choice of the number of hard-to-change factors, the number of easy-to-change factors, the number and size of whole plots, and the total sample size. It is shown that many of the newly proposed designs possess good predictive properties when compared to D-optimal split-plot designs.

Keywords:

• Generalized least squares
• OLS-GLS equivalence
• ordinary least squares
• response surface design
• split-plot design
• subset design
• supplementary difference set design