Abstract
Motivated by the effect hierarchy principle, Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect number pattern (AENP) for regular fractional factorial designs and based on the new pattern proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal \(2^{n-m}\) designs. Zhang et al. (Stat Sinica 18:1689–1705, 2008) proved that most existing criteria can be obtained by functions of the AENP. In this paper we propose a simple method for the calculation of AENP. The method is much easier than before since the calculation only makes use of the design matrix. All 128-run GMC designs with the number of factors ranging from 8 to 32 are provided for practical use.
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Acknowledgments
The authors would like to thank the Editor and one anonymous referee for their valuable comments and constructive suggestions that lead to a significant improvement of the paper. Yang is supported by the Fundamental Research Funds for the Central Universities 65011361 and the NNSF of China Grants 11101224, 11271205 and 11271355.
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Appendix
Appendix
See “Appendix” Table 1.
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Wei, JL., Yang, JF. On simplifying the calculations leading to designs with general minimum lower-order confounding. Metrika 76, 723–732 (2013). https://doi.org/10.1007/s00184-013-0442-z
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DOI: https://doi.org/10.1007/s00184-013-0442-z