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Biometrika 1996 83(4):950-955; doi:10.1093/biomet/83.4.950
© 1996 by Biometrika Trust
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MISCELLANEA

Projective properties of certain orthogonal arrays

GEORGE BOX and JOHN TYSSEDAL

Center for Quality and Productivity Improvement, University of Wisconsin-Madison Madison, Wisconsin 53705, U.S.A.
Division of Mathematical Sciences, University of Trondheim N-7034 Trondheim, Norway

A question of importance in factor screening is when a two-level orthogonal design for a multifactor experiment can be projected into lower dimension, typically P = 2 or 3. New results relate to the projectivity P of saturated designs in which n – 1 factors are tested in n runs. It is shown that: a design obtained by ‘doubling’ an n x n orthogonal array is always of projectivity P = 2; a two-level cyclic design is either a factorial array, and hence has P = 2, or it has P = 3; a two-level orthogonal design with 4m runs, m odd, has P = 3. In particular these results allow the designs derived by Plackett & Burman (1946) to be categorised in terms of these projective properties.

Key Words: Design projectivity • Design resolution • Factor screening • Fractional factorial design • Orthogonal array • Plackett-Burman design


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