The Annals of Statistics

A complementary design theory for doubling

Hongquan Xu and Ching-Shui Cheng

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Chen and Cheng [Ann. Statist. 34 (2006) 546–558] discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for 9N/32≤n≤5N/16, all minimum aberration designs with N runs and n factors are projections of the maximal design with 5N/16 factors which is constructed by repeatedly doubling the 25−1 design defined by I=ABCDE. This paper develops a general complementary design theory for doubling. For any design obtained by repeated doubling, general identities are established to link the wordlength patterns of each pair of complementary projection designs. A rule is developed for choosing minimum aberration projection designs from the maximal design with 5N/16 factors. It is further shown that for 17N/64≤n≤5N/16, all minimum aberration designs with N runs and n factors are projections of the maximal design with N runs and 5N/16 factors.

Article information

Ann. Statist., Volume 36, Number 1 (2008), 445-457.

First available in Project Euclid: 1 February 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K15: Factorial designs

Maximal design minimum aberration Pless power moment identity wordlength pattern


Xu, Hongquan; Cheng, Ching-Shui. A complementary design theory for doubling. Ann. Statist. 36 (2008), no. 1, 445--457. doi:10.1214/009005360700000712.

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