Some results on constructing general minimum lower order confounding $$2^{n-m}$$ 2 n - m designs for $$n\le 2^{n-m-2}$$ n ≤ 2 n - m - 2

Bing Guo, Qi Zhou and Runchu Zhang ()

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 6, 732 pages

Abstract: Zhang et al. (Stat Sinica 18:1689–1705, 2008 ) introduced an aliased effect-number pattern for two-level regular designs and proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal designs. All the GMC $$2^{n-m}$$ 2 n - m designs with $$N/4+1\le n\le N-1$$ N / 4 + 1 ≤ n ≤ N - 1 were constructed by Li et al. (Stat Sinica 21:1571–1589, 2011 ), Zhang and Cheng (J Stat Plan Inference 140:1719–1730, 2010 ) and Cheng and Zhang (J Stat Plan Inference 140:2384–2394, 2010 ), where $$N=2^{n-m}$$ N = 2 n - m is run number and $$n$$ n is factor number. In this paper, we first study some further properties of GMC design, then we construct all the GMC $$2^{n-m}$$ 2 n - m designs respectively with the three parameter cases of $$n\le N-1$$ n ≤ N - 1 : (i) $$m\le 4$$ m ≤ 4 , (ii) $$m\ge 5$$ m ≥ 5 and $$n=(2^m-1)u+r$$ n = ( 2 m - 1 ) u + r for $$u>0$$ u > 0 and $$r=0,1,2$$ r = 0 , 1 , 2 , and (iii) $$m\ge 5$$ m ≥ 5 and $$n=(2^m-1)u+r$$ n = ( 2 m - 1 ) u + r for $$u\ge 0$$ u ≥ 0 and $$r=2^m-3,2^m-2$$ r = 2 m - 3 , 2 m - 2 . Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Aliased effect-number pattern; Fractional factorial design; General minimum lower-order confounding; Minimum aberration; Resolution; Wordlength pattern (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00184-013-0461-9

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