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The resolution has perhaps been the most widely used criterion for selecting regular fractional factorials since it was introduced in 1961 by Box and Hunter. In this talk, we examine how a generalized resolution criterion can be defined and used for assessing nonregular fractional factorials, notably those Plackett-Burman designs. We show that when applied to regular fractional factorials this generalized resolution reduces to the original resolution criterion, and as the latter it possesses some appealing projection properties. Furthermore, the same idea leads to a natural generalization of minimum aberration, which reduces to the usual minimum aberration criterion for regular fractional factorials. Examples are given to illustrate the usefulness of the new criteria.
In this talk, we also evaluate the generalized minimum aberration (GMA) criterion for assessing and classifying nonregular fractional factorial designs. We further develop some general theory on the confounding pattern for nonregular designs. Using the GMA criterion, we classify and then rank various designs taken from Hadmard matrices of order 12, 16, 20 and 24. |