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Statistica Sinica 5(1995), 235-250



J. C. Wang and C. F. Jeff Wu

Western Michigan University and University of Michigan

Abstract: Box and Hunter (1961) made an important observation that any fractional factorial design of resolution R has the property that when projected onto any R-1 factors it becomes a full factorial design. This has a significant implication for statistical analysis. We observe that the Plackett-Burman and related designs have a hidden projection property with an analogous implication for the analysis. Because of complex aliasing, these designs have traditionally been used for screening main effects only. The hidden projection property suggests that complex aliasing actually allows some interactions to be entertained and estimated without making additional runs and provides an explanation for the success of an analysis strategy due to Hamada and Wu (1992). We give a detailed study of the hidden projection property for 12-run and 20-run designs with two levels and an 18-run design with three levels.

Key words and phrases: Fractional factorial design, Plackett-Burman design, Hada- mard matrix, orthogonal array, resolution, projective rationale, hidden projection, interaction, D efficiency, Ds efficiency.

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