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December 1999 Minimum $G_2$-aberration for nonregular fractional factorial designs
Lih-Yuan Deng, Boxin Tang
Ann. Statist. 27(6): 1914-1926 (December 1999). DOI: 10.1214/aos/1017939244


Deng and Tang proposed generalized resolution and minimum aberration criteria for comparing and assessing nonregular fractional factorials, of which Plackett–Burman designs are special cases.A relaxed variant of generalized aberration is proposed and studied in this paper.We show that a best design according to this criterion minimizes the contamination of nonnegligible interactions on the estimation of main effects in the order of importance given by the hierarchical assumption.The new criterion is defined through a set of $B$ values, a generalization of word length pattern. We derive some theoretical results that relate the $B$ values of a nonregular fractional factorial and those of its complementary design. Application of this theory to the construction of the best designs according to the new aberration criterion is discussed. The results in this paper generalize those in Tang and Wu, which characterize a minimum aberration (regular) $2^{m-k}$ design through its complementary design.


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Lih-Yuan Deng. Boxin Tang. "Minimum $G_2$-aberration for nonregular fractional factorial designs." Ann. Statist. 27 (6) 1914 - 1926, December 1999.


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

zbMATH: 0967.62055
MathSciNet: MR1765622
Digital Object Identifier: 10.1214/aos/1017939244

Primary: 62K15
Secondary: 62K05

Keywords: confounding , defining relation , Hadamard matrix , orthogonality , Plackett-Burman design , projection property , resolution , word length pattern

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 6 • December 1999
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