The Annals of Statistics

Minimum $G_2$-aberration for nonregular fractional factorial designs

Lih-Yuan Deng and Boxin Tang

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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.

Article information

Ann. Statist., Volume 27, Number 6 (1999), 1914-1926.

First available in Project Euclid: 4 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K15: Factorial designs
Secondary: 62K05: Optimal designs

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


Tang, Boxin; Deng, Lih-Yuan. Minimum $G_2$-aberration for nonregular fractional factorial designs. Ann. Statist. 27 (1999), no. 6, 1914--1926. doi:10.1214/aos/1017939244.

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