Correlation-Based r -plot for Evaluating Supersaturated Designs

Abstract

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 design matrix. Hence, we need a means 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.

Graphical methods for evaluating covering arrays

“…This approach is only sensible if we believe in effect sparsity, which suggests that many of the factors will not be active, but we do not know a priori which these will be. Jang et al suggested correlation‐based r‐plot for evaluating supersaturated designs. This r‐plot is a checker plot in which off‐diagonal panels consist of boxes to show | r ij | = | corr ( c i , c j )|, which is the absolute value of the correlation coefficient between the ( i , j )th pair of design columns c i and c j .…”

Selecting the Best Wild Card Entries in a Covering Array

“…Jang et al investigated the property of supersaturated design for comparative purposes. They checked the imbalance of number of levels for each column of arrays and called this a property of balance as orthogonality of strength 1.…”