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Tang, Boxin; Deng, Lih-Yuan

Minimum \(G_2\)-aberration for nonregular fractional factorial designs. (English) Zbl 0967.62055

Ann. Stat. 27, No. 6, 1914-1926 (1999).
Summary: We [Stat. Sin. 9, No. 4, 1071-1082 (1999; Zbl 0942.62084)] 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 of B. Tang and C.F.J. Wu [Ann. Stat. 24, No. 6, 2549-2559 (1996; Zbl 0867.62068)] which characterize a minimum aberration (regular) \(2^{m-k}\) design through its complementary design.

Cited in 3 Reviews
Cited in 123 Documents

MSC:

62K15 Factorial statistical designs
62K05 Optimal statistical designs

Keywords:

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

Citations:

Zbl 0942.62084; Zbl 0867.62068
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References:

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