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Some results on generalized minimum aberration for symmetrical fractional factorial designs

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  • Qin, Hong
  • Chen, Yin-Bao

Abstract

Generalized minimum aberration of fractional factorial designs has popularly been discussed. Recently, Lu et al. (Technical Report-324, 2002) proposed a so-called nearest balance criterion, which extends the V-criterion studied by Tang (Biometrika, 88 (2001) 401) for two-level designs to multi-level designs, to evaluate fractional factorials. In this paper, that generalized minimum aberration coincides with nearest balance for symmetrical factorials is reported, which is a generalization of the related results in Tang (2001). Our results not only further provide a projection interpretation of generalized minimum aberration in terms of level combinations but they also give a theoretical justification of the nearest balance criterion. A lower bound of generalized word length pattern for symmetrical factorials is also obtained.

Suggested Citation

  • Qin, Hong & Chen, Yin-Bao, 2004. "Some results on generalized minimum aberration for symmetrical fractional factorial designs," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 51-57, January.
  • Handle: RePEc:eee:stapro:v:66:y:2004:i:1:p:51-57
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    References listed on IDEAS

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    1. Kai-Tai Fang & Gen-Nian Ge & Min-Qian Liu & Hong Qin, 2003. "Construction of minimum generalized aberration designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 57(1), pages 37-50, February.
    2. C.‐S. Cheng & D. M. Steinberg & D. X. Sun, 1999. "Minimum aberration and model robustness for two‐level fractional factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 85-93.
    3. Chen, Hegang, 1998. "Some projective properties of fractional factorial designs," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 185-188, September.
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    Cited by:

    1. Zhang, Shangli & Qin, Hong, 2006. "Minimum projection uniformity criterion and its application," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 634-640, March.

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