Statistica Sinica 9(1999), 1071-1082

GENERALIZED RESOLUTION AND MINIMUM ABERRATION

CRITERIA FOR PLACKETT-BURMAN AND

OTHER NONREGULAR FACTORIAL DESIGNS

Lih-Yuan Deng$^*$ and Boxin Tang$^{*\dagger}$

$^*$University of Memphis and $^\dagger$University of Western Ontario

Abstract: Resolution has been the most widely used criterion for comparing regular fractional factorials since it was introduced in 1961 by Box and Hunter. In this paper, we examine how a generalized resolution criterion can be defined and used for assessing nonregular fractional factorials, notably Plackett-Burman designs. Our generalization is intended to capture projection properties, complementing that of Webb (1964) whose concept of resolution concerns the estimability of lower order effects under the assumption that higher order effects are negligible. Our generalized resolution provides a fruitful criterion for ranking different designs while Webb's resolution is mainly useful as a classification rule. An additional advantage of our approach is that the idea leads to a natural generalization of minimum aberration. Examples are given to illustrate the usefulness of the new criteria.

Key words and phrases: Confounding, estimability, fractional factorial, Hadamard matrix, orthogonality, projection property, word length pattern.