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Optimum two level fractional factorial plans for model identification and discrimination

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  • Ghosh, Subir
  • Tian, Ying

Abstract

Model identification and discrimination are two major statistical challenges. In this paper we consider a set of models for factorial experiments with the parameters representing the general mean, main effects, and only k out of all two-factor interactions. We consider the class of all fractional factorial plans with the same number of runs having the ability to identify all the models in , i.e., the full estimation capacity. The fractional factorial plans in with the full estimation capacity for k[greater-or-equal, slanted]2 are able to discriminate between models in for u[less-than-or-equals, slant]k*, where k*=(k/2) when k is even, k*=((k-1)/2) when k is odd. We obtain fractional factorial plans in satisfying the six optimality criterion functions AD, AT, AMCR, GD, GT, and GMCR for 2m factorial experiments when m=4 and 5. Both single stage and multi-stage (hierarchical) designs are given. Some results on estimation capacity of a fractional factorial plan for identifying models in are also given. Our designs D4.1 and D10 stand out in their performances relative to the designs given in Li and Nachtsheim [Model-robust factorial designs, Technometrics 42(4) (2000) 345-352.] for m=4 and 5 with respect to the criterion functions AD, AT, AMCR, GD, GT, and GMCR. Our design D4.2 stands out in its performance relative the Li-Nachtsheim design for m=4 with respect to the four criterion functions AT, AMCR, GT, and GMCR. However, the Li-Nachtsheim design for m=4 stands out in its performance relative to our design D4.2 with respect to the criterion functions AD and GD. Our design D14 does have the full estimation capacity for k=5 but the twelve run Li-Nachtsheim design does not have the full estimation capacity for k=5.

Suggested Citation

  • Ghosh, Subir & Tian, Ying, 2006. "Optimum two level fractional factorial plans for model identification and discrimination," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1437-1450, July.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1437-1450
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    References listed on IDEAS

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    1. 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.
    2. Atanu Biswas, 2002. "An efficient design for model discrimination and parameter estimation in linear models," Biometrika, Biometrika Trust, vol. 89(3), pages 709-718, August.
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