Blocked regular fractional factorial designs with minimum aberration

Hongquan Xu

31 citations0/0 files storedThe Annals of Statistics

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Optimal Experimental Design Methods Advanced Combinatorial Mathematics Statistical Methods and Applications

Abstract

This paper considers the construction of minimum aberration (MA) blocked factorial designs. Based on coding theory, the concept of minimum moment aberration due to Xu [Statist. Sinica 13 (2003) 691–708] for unblocked designs is extended to blocked designs. The coding theory approach studies designs in a row-wise fashion and therefore links blocked designs with nonregular and supersaturated designs. A lower bound on blocked wordlength pattern is established. It is shown that a blocked design has MA if it originates from an unblocked MA design and achieves the lower bound. It is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros. Sufficient conditions are given for constructing MA blocked designs from unblocked MA designs. The theory is then applied to construct MA blocked designs for all 32 runs, 64 runs up to 32 factors, and all 81 runs with respect to four combined wordlength patterns.

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References

1980Minimum Aberration 2 k-p Designs 1961The 2 k-p Fractional Factorial Designs Part I 1993A Catalogue of Two-Level and Three-Level Fractional Factorial Designs with Small Runs 2001Minimum moment aberration for nonregular designs and supersaturated designs 1999Theory of optimal blocking of $2^{n-m}$ designs 1997Fractional Resolution and Minimum Aberration in Blocked 2 n-k Designs 2001A General Method of Constructing E(s2)-Optimal Supersaturated Designs 1992Some Results on $2^{n - k}$ Fractional Factorial Designs and Search for Minimum Aberration Designs

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