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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

Abstract

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.

Suggested Citation

  • Li, Peng-Fei & Liu, Min-Qian & Zhang, Run-Chu, 2004. "Some theory and the construction of mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 105-116, August.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:1:p:105-116
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    References listed on IDEAS

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    1. Yamada, Shu & Lin, Dennis K. J., 1999. "Three-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 31-39, October.
    2. 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.
    3. Shu Yamada & Dennis Lin, 2002. "Construction of mixed-level supersaturated design," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 56(3), pages 205-214, December.
    4. Kai-Tai Fang & Dennis K. J. Lin & Min-Qian Liu, 2003. "Optimal mixed-level supersaturated design," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 279-291, December.
    5. Fred J. Hickernell, 2002. "Uniform designs limit aliasing," Biometrika, Biometrika Trust, vol. 89(4), pages 893-904, December.
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    Cited by:

    1. Chen, Jie & Liu, Min-Qian, 2008. "Optimal mixed-level supersaturated design with general number of runs," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2496-2502, October.
    2. Gupta, V.K. & Singh, Poonam & Kole, Basudev & Parsad, Rajender, 2009. "Construction of efficient unbalanced mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2359-2366, November.
    3. Liu, Min-Qian & Zhang, Li, 2009. "An algorithm for constructing mixed-level k-circulant supersaturated designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2465-2470, May.
    4. Yan Liu & Min-Qian Liu, 2012. "Construction of equidistant and weak equidistant supersaturated designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 33-53, January.

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