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Data · dataset · 2014

Graphical Aids for the Analysis of Two-Level Nonregular Designs

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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.

Description

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.

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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.

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Mathematics

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