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Regular fractional factorial designs with minimum aberration and maximum estimation capacity. (English) Zbl 0927.62076
Summary: Using the approach of finite projective geometry, we make a systematic study of estimation capacity, a criterion of model robustness, under the absence of interactions involving three or more factors. Some general results, providing designs with maximum estimation capacity, are obtained.
In particular, for two-level factorials, it is seen that constructing a design with maximum estimation capacity calls for choosing points from a finite projective geometry such that the number of lines is maximized and the distribution of these lines among the chosen points is as uniform as possible. We also explore the connection with minimum aberration designs under which the sizes of the alias sets of two-factor interactions which are not aliased with main effects are the most uniform possible.

MSC:
62K15 Factorial statistical designs
05B25 Combinatorial aspects of finite geometries
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[11] DEPARTMENT OF STATISTICS JOKA, DIAMOND HARBOUR ROAD 367 EVANS HALL 3860 P.O. BOX NO. 16757, ALIPORE POST OFFICE BERKELEY, CALIFORNIA 94720-3860 CALCUTTA 700 027 E-MAIL: Cheng@stat.Berkeley.edu INDIA E-MAIL: rmuk1@hotmail.com
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