Graphical Aids for the Analysis of Two-Level Nonregular Designs

Abstract

The complex alias pattern between main effects and two-factor interactions for two-level nonregular designs has been considered a problem when analyzing these designs. If only a few two-factor interactions are active, however, the pattern induced into the estimated main effects contrasts from the active interactions may be very structured. This is, in particular, true for the 12-run and the 20-run Plackett–Burman (PB) designs, probably the two most important designs for physical experimentation. This article presents a graphical method for the analysis of nonregular two-level designs. The method consists of two steps. The first step is called contrast plots interpretation and is directed toward revealing the cause for the pattern observed in contrast plots. The second step is called alias reduction and aims at simplifying the interpretation of the contrast plots by reducing the aliasing caused by effects that, with a high degree of certainty, may be considered active. The method is tested on the 12-run PB design both with simulated and real data and on the 20-run PB design for one particular case with real data. Supplementary materials (MINITAB codes for performing calculations and plots) are available online.