Comprehensive description of main effects and interactions in Plackett Burman design

Plackett Burman designs are used to estimate main effects because the columns assigned main effects are mutually orthogonal. However, correlations between estimates of a main effect column and a two-factor interaction column are not orthogonal in general. There are variations in the magnitude of correlation depending on the size of Plackett Burman design. For example, correlation coefficients between a main effect and a two-factor interaction are either 0 or ±0.33 in Plackett Burman design N=12. However, most of them are ±0.2 and some of them are 0.6 in Plackett Burman design N=20. When a correlation coefficient between main effects and two-factor interactions is significantly large, analysis results may be depart from the true status. Therefore, in this study, we comprehensively describe correlation coefficients between a main effect and a two-factor interaction for all designs proposed by the Plackett and Burman designs such that N=8,...,100. In addition, for designs that have large correlation coefficients, they are classified according to how to construct a design table and examined in detail. We describe certain rules in combination of a main effect and a two-factor interaction with large correlation coefficient. We also show how to construct designs that avoids large correlation based on the rules.