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Clear two-factor interactions and minimum aberration. (English) Zbl 1015.62083
Summary: C.F.J. Wu and M. Hamada [Experiments: Planning, analysis and parameter design optimization. (2000; Zbl 0964.62065)] recommend selecting resolution IV designs with the maximum number of clear two-factor interactions (2FIs), called MaxC2 designs. We develop a method by using graphical representations, combinatorial and group-theoretic arguments to prove if a given design is a MaxC2 design. In particular, we show that all known minimum aberration designs with resolution IV are MaxC2 designs (except in six cases) and that the second \(2^{9-4}\), \(2^{13-7}\), \(2^{16-10}\) and \(2^{17-11}\) designs given by Wu and Hamada are MaxC2 designs. The method also enables us to identify new MaxC2 designs that are too large to be verified by computer search.

62K15 Factorial statistical designs
05C90 Applications of graph theory
Full Text: DOI
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[11] AMES, IOWA 50011-1210 E-MAIL: isuhwu@iastate.edu DEPARTMENT OF STATISTICS UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN 48109-1285 E-MAIL: jeffwu@umich.edu
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