A THEORY ON CONSTRUCTING 2(n-m) DESIGNS WITH GENERAL MINIMUM LOWER ORDER CONFOUNDING

作者：Li, Pengfei^*; Zhao, Shengli; Zhang, Runchu

来源：Statistica Sinica, 2011, 21(4): 1571-1589.

DOI：10.5705/ss.2008.336

• Aliased effect-number pattern
• effect hierarchy principle
• fractional factorial design
• minimum aberration
• resolution
• wordlength pattern
• Yates order

When designing an experiment, it is important to choose a design that is optimal under model uncertainty. The general minimum lower-order confounding (GMC) criterion can be used to control aliasing among lower-order factorial effects. A characterization of GMC via complementary sets was considered in Zhang and Mukerjee (2009a); however, the problem of constructing GMC designs is only partially solved. We provide a solution for two-level factorial designs with n factors and N = 2(n-m) runs subject to a restriction on (n, N): 5N/16 1 <= n <= N - 1. The construction is quite simple: every GMC design, up to isomorphism, consists of the last n columns of the saturated 2((N-1)-(N-1-n+m)) design with Yates order. In addition, we prove that GMC designs differ from minimum aberration designs when (n, N) satisfies either of the following conditions: (i) 5N/16 + 1 <= n <= N/2 - 4, or (ii) n >= N/2, 4 <= n 2(r) N <= 2(r-1) -4 with r >= 4.

• 出版日期2011-10
• 单位东北师范大学; 曲阜师范大学; 南开大学