Hidden projection properties of some optimal designs

Traditionally Plackett and Burman [1946, The design of optimum multifactorial experiments. Biometrika 33, 305-325] designs have been used for screening main effects only because of their complex aliasing patterns. Recently, Wang and Wu [1995, A hidden projection property of Plackett-Burman designs. Statist. Sinica 5, 235-250] studied that these designs have certain hidden projection properties, which allow certain interactions to be entertained and estimated without making additional runs. They attributed the success of Hamada and Wu's [1992, Analysis of designed experiments with complex aliasing. J. Quality Technol. 24, 130-137] strategy for estimating two-factor interactions from Plackett-Burman-type experiments to the hidden projection property. In this paper, we have studied the hidden projection properties of a number of designs in the class of n = 1 (mod 4), n = 2 (mod 4), and n = 3 (mod 4) designs. We have also drawn non-isomorphic interaction graphs making D and D-s efficiency as the underlying criterion. (C) 1999 Elsevier Science B.V. All rights reserved.