## The Annals of Statistics

### Clear two-factor interactions and minimum aberration

#### Abstract

Wu and Hamada recommend selecting resolution IV designs with the maximum number of clear two-factor interactions (2FIs), called MaxC2 designs. In this paper, 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 in 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.

#### Article information

Source
Ann. Statist., Volume 30, Number 5 (2002), 1496-1511.

Dates
First available in Project Euclid: 28 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1035844985

Digital Object Identifier
doi:10.1214/aos/1035844985

Mathematical Reviews number (MathSciNet)
MR1936328

Zentralblatt MATH identifier
1015.62083

Subjects
Primary: 62K15: Factorial designs

#### Citation

Wu, Huaiqing; Wu, C. F. J. Clear two-factor interactions and minimum aberration. Ann. Statist. 30 (2002), no. 5, 1496--1511. doi:10.1214/aos/1035844985. https://projecteuclid.org/euclid.aos/1035844985

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• 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