Incorporating Cost and Optimizing Central Composite Designs for Split - Plot Response Surface Methodology Experiments

Complete randomization in many industrial and agricultural experiments is frequently impractical due to constraints in time, cost or existence of one or more hard-to-change factors. In these situations, restrictions on randomization lead to split-plot designs (SPD), allowing certain factor levels to be randomly applied to the whole plot units and remaining factor levels randomly to the subplot units. Separate random errors in whole plot units and in subplot units are due to the two randomizations in the experiment. The resulting compound symmetric error structure affects not only estimation and inference, but also the choice of design. In this paper, we first consider looking at the prediction properties of split-plot designs, expanding the comparison between designs beyond just looking at parameter estimation properties, and we present the 3-dimensional variance dispersion graphs (3-D VDGs) as a tool for evaluating the prediction capability of splitplot designs and for developing design strategies. A popular design for second-order models is the central composite design (CCD). By studying the distribution of the scaled prediction variance (SPV) in the 3-D VDGs, we demonstrate that the Gand Vefficiencies of standard CCDs can be improved upon by changing the factorial levels of the CCD. 2.1 Split-Plot Designs Many industrial experiments involve two types of factors, some with levels hard or costly to change and others with levels that are relatively easy to change. Typical examples of hard-to-change factors include humidity, pressure and temperature. When hard-to-change factors exist, it is in the practitioner’s best interest to minimize the number of times the