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December 1999 Theory of optimal blocking of $2^{n-m}$ designs
Hegang Chen, Ching-Shui Cheng
Ann. Statist. 27(6): 1948-1973 (December 1999). DOI: 10.1214/aos/1017939246


In this paper, we define the blocking wordlength pattern of a blocked fractional factorial design by combining the wordlength patterns of treatment-defining words and block-defining words. The concept of minimum aberration can be defined in terms of the blocking wordlength pattern and provides a good measure of the estimation capacity of a blocked fractional factorial design. By blending techniques of coding theory and finite projective geometry, we obtain combinatorial identities that govern the relationship between the blocking wordlength pattern of a blocked $2^{n-m}$ design and the split wordlength pattern of its blocked residual design. Based on these identities, we establish general rules for identifying minimum aberration blocked $2^{n-m}$ designs in terms of their blocked residual designs. Using these rules, we study the structures of some blocked $2^{n-m}$ designs with minimum aberration.


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Hegang Chen. Ching-Shui Cheng. "Theory of optimal blocking of $2^{n-m}$ designs." Ann. Statist. 27 (6) 1948 - 1973, December 1999.


Published: December 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0961.62066
MathSciNet: MR1765624
Digital Object Identifier: 10.1214/aos/1017939246

Primary: 62K15
Secondary: 62K05

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 6 • December 1999
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