Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 2, 362--377

Maximal Rank Minimum Aberration Blocked Regular   $2^{m-k}$}  Fractional Factorial Designs


Department of Mathematical Sciences

Washington State University

Pullman, WA 99164


SUMMARY. In this paper, an alternative method for optimally blocking regular $2^{m-k}$ fractional factorial designs in $2^p$ blocks is given.  The method given involves two stages.  The first is to find for given values of $m, k$ and $p$, those designs which maximize the total number of estimable main effects and two-factor interactions. The second is to find among those designs satisfying step one the design with the smallest ``aberration". Examples are given to compare this criterion with other criteria for blocking regular fractional factorial designs that have been suggested in this literature and a catalogue of designs satisfying the new criterion is given for designs having 16, 32, and 64 runs and various values of $m, k$ and $p$.

AMS (1991) subject classification. Primary 62K15; Secondary 62K05.

Key words and phrases. Fractional factorial design, defining contrast group, word length pattern, estimable effects.

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