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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.

MSC:
62K15 Factorial statistical designs
05C90 Applications of graph theory
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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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