JSM 2011 Online Program

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Abstract Details

Activity Number: 128
Type: Contributed
Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
Sponsor: International Chinese Statistical Association
Abstract - #300765
Title: A Theory of General Minimum Lower-Order Confounding for Factorial Designs
Author(s): Runchu Zhang*+
Companies: Nankai University/Northeast Normal University
Address: School of Mathematical Sciences, Tianjin, 300071, China
Keywords: Clear effect ; Confounding ; Blocked design ; Factorial design ; Minimum aberration ; Split-plot design
Abstract:

This talk presents a theory of general minimum lower order confounding (GMC) for fractional factorial designs proposed by Zhang, Li, Zhao and Ai(2008) and its recent developments. A characterization of GMC criterion to s-level case was given; Some essential properties of existing criteria (MA, MEC and CE) were discovered by GMC theory; All the $2^{n-m}$ GMC designs with $N/4+1 \le n\le N-1$ have been obtained, where $N$ is run number and $n$ factor number. The GMC criteria for blocked factorial designs were established, including B-GMC and B$^1$-GMC for single block variable case and B$^2$-GMC for multi block variable case; All the B$^1$-GMC $2^{n-m}:2^r$ designs with $5N/16+1\le n\le N-1$ have been obtained, where $r$ is block factor number; The GMC theory was extended to the case of split-plot designs; The factor aliased effect-umber pattern (F-AENP) was introduced for arranging factors. The works are included in ZLZA(2008), Zhang and Mukerjee(2009a,b), Hu and Zhang(2010), Li,Zhao and Zhang(2010), Zhang and Cheng(2010), Cheng and Zhang(2010),Zhao et al(2010), Zhang,Li and Wei(2010), Wei et al(2010),Zhang,Wei and Li(2010), and Zhou,Balakrishnan and Zhang(2010).


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