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Minimum projection uniformity criterion and its application

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  • Zhang, Shangli
  • Qin, Hong

Abstract

Based on a so-called uniformity pattern, Fang and Qin [2005. Uniformity pattern and related criteria for two-level factorials. Sci. China Ser. A 48, 1-11] proposed the minimum projection uniformity criterion to assess and compare two-level factorials. In present paper, we study applications of minimum projection uniformity criterion in aberration designs, orthogonal arrays and supersaturated designs. Relationship among minimum projection uniformity, generalized minimum aberration [Ma, C. X., Fang, K. T., 2001. A note on generalized aberration factorial designs. Metrika 53, 85-93; Xu, H., Wu, C. F. J., 2001. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist. 29, 549-560], V-criterion [Tang, B., 2001. Theory of J-characteristics for fractional factorial designs and projection justification of minimum G2-aberration. Biometrika 88, 401-407], nearest balance criterion [Fang, K. T., Lu, X., Winker, P., 2003. Lower bounds for centered and wrap-around L2-discrepancies and construction of uniform designs by threshold accepting. J. Complexity 19, 692-711] and E(s2) criterion [Booth, K. H. V., Cox, D. R., 1962. Some systematic supersaturated designs. Technometrics 4, 489-495] is made explicit. Noting that minimum projection uniformity criterion is related to uniform designs, our results should raise the hope of improving the connection between uniform design theory and factorial design theory.

Suggested Citation

  • Zhang, Shangli & Qin, Hong, 2006. "Minimum projection uniformity criterion and its application," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 634-640, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:6:p:634-640
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    References listed on IDEAS

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    1. 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.
    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.
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    Citations

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    Cited by:

    1. Ou, Zujun & Qin, Hong, 2010. "Some applications of indicator function in two-level factorial designs," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 19-25, January.
    2. Kang Wang & Zujun Ou & Jiaqi Liu & Hongyi Li, 2021. "Uniformity pattern of q-level factorials under mixture discrepancy," Statistical Papers, Springer, vol. 62(4), pages 1777-1793, August.
    3. H. Evangelaras & S. D. Georgiou, 2021. "Projection properties of two-level supersaturated designs constructed from Hadamard designs using Lin’s method," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1095-1108, November.
    4. Narayanaswamy Balakrishnan & Hong Qin & Kashinath Chatterjee, 2016. "Generalized projection discrepancy and its applications in experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 19-35, January.
    5. Qiming Bai & Hongyi Li & Xingyou Huang & Huili Xue, 2023. "Design efficiency for minimum projection uniform designs with q levels," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 577-594, July.

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