Correlation-Based r-plot for Evaluating Supersaturated Designs

Orthogonality or near-orthogonality is an important property in the design of experiments. Supersaturated designs are natural when we wish to investigate the main effects for a large number of factors but are restricted to a small number of runs. These supersaturated designs, by definition, cannot satisfy pairwise orthogonality of all the factor columns in the designmatrix. Hence, we need ameans to evaluate the degree of near-orthogonality of different alternative supersaturated designs. It is usual to use numerical measures that condense the rich information from many pairwise column measures to assess the degree of orthogonality of given supersaturated designs, but we propose using graphical methods to better understand patterns between sets of columns and evaluate the degree of near-orthogonality to compare and select between alternative supersaturated designs. The methods are illustrated with a number of diverse examples to illustrate the information that can be extracted from the summary. Copyright © 2013 John Wiley & Sons, Ltd.