Evaluation on alias relations between main effect and interaction in Plackett Burman design (N=20) and its application to guide assignments

Abstract

Plackett Burman designs, that is one of the fractional factorial designs, have a property that the columns to be assigned the main effects are mutually orthogonal. Plackett Burman designs have been used in screening experiments for identifying active main effects out of candidate factors frequently. The screened results are not always correct due to the experimental errors and the alias relations between main effects and two-factor interactions. While several previous researches has been discussed the alias relations in Plackett Burman designs, not many researches has been focusing on the alias relations between main effect and interaction in N=20 as a structured manner. In fact, although Hamada and Wu (1992) enumerated large combinations of correlations, this study has organized the structure manner into a clear and unique table as table4. We demonstrated the alias relations in a systematic manner as a form of 0.6-triplet, indicating that the correlation coefficient between estimates of main effect and two-factor interaction is equal to 0.6. Furthermore, a new rule to describe appearance of 0.6 triplet is demonstrated as an application of BIBD. We also propose a new assignment method in N=20 Plackett Burman designs that avoids 0.6-triplets. The assignment method is confirmed that it has better property comparing to the conventional approach.