Statistica Sinica 19 (2009), 1787-1802

GENERAL MINIMUM LOWER ORDER CONFOUNDING

IN BLOCK DESIGNS USING COMPLEMENTARY SETS

Runchu Zhang$^{1, 2}$ and Rahul Mukerjee$^{3}$

$^1$Nankai University, $^2$Northeast Normal University

and $^3$Indian Institute of Management Calcutta

Abstract: We consider regular fractions of $s$-level factorials arranged in block designs. Optimal designs are explored under the criterion of general minimum lower order confounding which aims, in an elaborate manner, at keeping the lower order factorial effects unaliased with one another and unconfounded with blocks. A finite projective geometric formulation, that identifies the alias sets with the points and the blocking system with a flat of the geometry, forms the mathematical basis of our approach. Theoretical results and tables are obtained in terms of complementary sets and an idea of double complementation is found to be useful in some situations.

Key words and phrases: Alias set, double complementation, effect hierarchy principle, flat, projective geometry, wordlength pattern.