Statistica Sinica 12(2002), 991-1000

GENERALIZED MINIMUM ABERRATION

AND DESIGN EFFICIENCY

FOR NONREGULAR FRACTIONAL FACTORIAL DESIGNS

Ching-Shui Cheng$^1$, Lih-Yuan Deng$^2$ and Boxin Tang$^2$

$^1$University of California and $^2$University of Memphis

Abstract: Tang and Deng (1999) proposed a generalized minimum aberration criterion (GMA) as a natural extension of the minimum aberration criterion (MA) from regular to nonregular designs. While MA was defined for regular designs only, GMA applies to both regular and nonregular designs. In this paper, we investigate the relationship between GMA and some model-dependent efficiency criteria, and show that GMA is supported by these criteria. An extensive evaluation of designs with 20 runs and 5 factors shows that the GMA criterion can be used to classify and rank-order these designs. Empirical studies also demonstrate that the GMA ranking is consistent with those obtained by using other model-dependent efficiency criteria.

Key words and phrases: Df-criterion, estimation capacity, regular design, supersaturated design.