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Chen, Hegang; Cheng, Ching-Shui

Theory of optimal blocking of \(2^{n-m}\) designs. (English) Zbl 0961.62066

Ann. Stat. 27, No. 6, 1948-1973 (1999).
Summary: 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.

Cited in 1 Review
Cited in 43 Documents

MSC:

62K15 Factorial statistical designs
62K05 Optimal statistical designs
05B25 Combinatorial aspects of finite geometries
62B10 Statistical aspects of information-theoretic topics

Keywords:

fractional factorial design; linear code; MacWilliams identities; resolution; weight distribution; finite projective geometry; wordlength pattern
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References:

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[17] MINNEAPOLIS, MINNESOTA 55454-1015 BERKELEY, CALIFORNIA 94720-3860 E-MAIL: chen h@epi.umn.edu E-MAIL: cheng@stat.berkeley.edu
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