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Some theory and the construction of mixed-level supersaturated designs


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  • Li, Peng-Fei
  • Liu, Min-Qian
  • Zhang, Run-Chu
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    Supersaturated design is a form of fractional factorial design and has recently received much interest because of its potential in factor screening experiments. This paper mainly concerns the existing criteria for mixed-level designs, i.e. the [chi]2(D) criterion (for design D) proposed by Yamada and Matsui (J. Statist. Plann. Inference 104 (2002) 459), the E(fNOD) criterion proposed by Fang et al. (Metrika 58 (2003b) 279) and the minimum moment aberration (MMA) proposed by Xu (Statist. Sinica 13 (2003) 691). A lower bound of [chi]2(D) is obtained along with the sufficient and necessary condition for achieving it. The connections between [chi]2(D) and other criteria are discussed. Especially, it is shown that [chi]2(D) and the second power moment K2(D) are in fact equivalent to each other and hence the two criteria, [chi]2(D) and MMA, share the same optimal supersaturated designs, which can be constructed from saturated orthogonal arrays and other supersaturated designs.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 69 (2004)
    Issue (Month): 1 (August)
    Pages: 105-116

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    Handle: RePEc:eee:stapro:v:69:y:2004:i:1:p:105-116

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    Keywords: Factorial design Orthogonal array Minimum moment aberration Supersaturated design U-type design;


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    1. Kai-Tai Fang & Dennis K. J. Lin & Min-Qian Liu, 2003. "Optimal mixed-level supersaturated design," Metrika, Springer, Springer, vol. 58(3), pages 279-291, December.
    2. Yamada, Shu & Lin, Dennis K. J., 1999. "Three-level supersaturated designs," Statistics & Probability Letters, Elsevier, Elsevier, vol. 45(1), pages 31-39, October.
    3. Fred J. Hickernell, 2002. "Uniform designs limit aliasing," Biometrika, Biometrika Trust, Biometrika Trust, vol. 89(4), pages 893-904, December.
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    Cited by:
    1. Gupta, V.K. & Singh, Poonam & Kole, Basudev & Parsad, Rajender, 2009. "Construction of efficient unbalanced mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(22), pages 2359-2366, November.
    2. Chen, Jie & Liu, Min-Qian, 2008. "Optimal mixed-level supersaturated design with general number of runs," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(15), pages 2496-2502, October.
    3. Yan Liu & Min-Qian Liu, 2012. "Construction of equidistant and weak equidistant supersaturated designs," Metrika, Springer, Springer, vol. 75(1), pages 33-53, January.


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