Abstract
An optimal design should minimize the confounding among factor effects, especially the lower-order effects, such as main effects and two-factor interaction effects. Based on the aliased component-number pattern, general minimum lower-order confounding (GMC) criterion can provide the confounding information among factors of designs in a more elaborate and explicit manner. In this paper, we extend GMC theory to s-level regular designs, where s is a prime or prime power. For an \(s^{n-m}\) design D with \(N=s^{n-m}\) runs, the confounding of design D is given by complementary set. Further, according to the factor number n, we discuss two cases: (i) \(N/s<n\le (N-1)/(s-1)\), and (ii) \((N/s+1)/2<n\le N/s\). We not only provide the lower-order confounding information among component effects of D, but also obtain three necessary conditions for design D to have GMC.
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Acknowledgments
This work was partially supported by Scientific Research Program of the Higher Education Institution of XinJiang Grant XJEDU2012S01 and the Doctoral Program of XinJiang University Grant BS130106, the National Natural Science Foundation of China Grants 11271312, 11101074 and 41261087.
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Li, Z., Teng, Z., Zhang, T. et al. Analysis on \(s^{n-m}\) designs with general minimum lower-order confounding. AStA Adv Stat Anal 100, 207–222 (2016). https://doi.org/10.1007/s10182-015-0259-3
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DOI: https://doi.org/10.1007/s10182-015-0259-3
Keywords
- s-level design
- Component effect hierarchy principle
- Aliased component-number pattern
- General minimum lower-order confounding
- GMC design
- Complementary set