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An algorithm for constructing mixed-level k-circulant supersaturated designs

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  • Liu, Min-Qian
  • Zhang, Li

Abstract

Supersaturated design (SSD) has received much interest because of its potential in factor screening experiments. Recently, Chen and Liu [Chen, J., Liu, M.Q., 2008a. Optimal mixed-level k-circulant supersaturated designs. J. Statist. Plann. Inference 138, 4151-4157] explored the construction of E(fNOD)-optimal mixed-level SSDs using k-cyclic generators. As an extension, this paper further studies how to construct optimal mixed-level k-circulant SSDs under the [chi]2(D) criterion. A sufficient condition under which the generator vector produces a [chi]2(D)-optimal SSD is obtained, and some other properties of the resulting SSDs are investigated. Note that, the construction of optimal mixed-level k-circulant SSDs under the [chi]2(D) criterion is much more complicated than that under . Hence, an algorithm for finding generators of (nearly) [chi]2(D)-optimal designs is provided, and many (nearly) [chi]2(D)-optimal mixed-level SSDs are then constructed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2465-2470
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Nguyen, Nam-Ky & Liu, Min-Qian, 2008. "An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5269-5276, August.
    4. 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.
    5. S. Georgiou & C. Koukouvinos, 2006. "Multi-level k-circulant Supersaturated Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 209-220, October.
    6. 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.
    7. Koukouvinos, C. & Mantas, P., 2005. "Construction of some E(fNOD) optimal mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 312-321, October.
    8. Yamada, Shu & Matsui, Michiyo & Matsui, Tomomi & Lin, Dennis K.J. & Takahashi, Takenori, 2006. "A general construction method for mixed-level supersaturated design," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 254-265, January.
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    Cited by:

    1. 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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