Regular fractional factorial designs with minimum aberration and maximum estimation capacity

Ching‐Shui Cheng · Rahul Mukerjee

70 citations0/0 files storedThe Annals of Statistics

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Optimal Experimental Design Methods Advanced Combinatorial Mathematics Advanced Statistical Methods and Models

Abstract

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.

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References

2000The 2 k-p Fractional Factorial Designs Part I 1980Minimum Aberration 2 k-p Designs 1993A Catalogue of Two-Level and Three-Level Fractional Factorial Designs with Small Runs 1961The 2k—pFractional Factorial Designs Part II.1996Characterization of minimum aberration $2\sp {n-k}$ designs in terms of their complementary designs 1984Constructing Tables of Minimum AberrationPn–mDesigns 1996$2\sp {n-l}$ designs with weak minimum aberration 1992Some Results on $2^{n - k}$ Fractional Factorial Designs and Search for Minimum Aberration Designs

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