D-optimal and D-efficient equivalent-estimation second-order split-plot designs

Many industrial experiments use split-plot designs as a cost-efficient method of reducing the number of independent settings of hard-to-change factors. Generally, model estimation for split-plot designs requires the use of generalized least squares, but in some cases, ordinary least squares estimates work as well. These equivalent-estimation designs do not require estimation of the variance components in the split-plot model. Alternatively, D-optimal designs provide efficient estimation of the fixed effects of the statistical model. The relationship between these designs for a second-order response surface model is explored, and an algorithm is proposed for generating D-efficient equivalent-estimation split-plot designs.