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Choice of optimal initial designs in sequential experiments

Author

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  • Peng-Fei Li
  • Min-Qian Liu
  • Run-Chu Zhang

Abstract

Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment into two parts with equal size to obtain some information about the process, especially for the case not considering the blocking factor. In this paper, the definition of combined-optimal design is extended to the case when blocking factor is significant, and this new class of designs is called blocked combined-optimal designs. Some general results are obtained which relate 2 k − p III initial designs with their complementary designs when [InlineMediaObject not available: see fulltext.], where n=2 k − p . By applying these results, we are able to characterize 2 k − p III combined-optimal designs or blocked combined-optimal designs in terms of their complementary designs. It is also proved that both 2 k − p III combined-optimal and blocked combined-optimal designs are not minimum aberration designs when [InlineMediaObject not available: see fulltext.] and n−1−k > 2. And some combined-optimal and blocked combined-optimal designs with 16 and 32 runs are constructed for illustration. Copyright Springer-Verlag 2005

Suggested Citation

  • Peng-Fei Li & Min-Qian Liu & Run-Chu Zhang, 2005. "Choice of optimal initial designs in sequential experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 127-135, April.
    • Handle: RePEc:spr:metrik:v:61:y:2005:i:2:p:127-135
    DOI: 10.1007/s001840400327
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    Citations

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    Cited by:

    1. A. M. Elsawah, 2018. "Choice of optimal second stage designs in two-stage experiments," Computational Statistics, Springer, vol. 33(2), pages 933-965, June.
    2. Zujun Ou & Hongyi Li, 2021. "A new foldover strategy and optimal foldover plans for three-level design," Statistical Papers, Springer, vol. 62(5), pages 2433-2451, October.
    3. Elsawah, A.M. & Qin, Hong, 2015. "Lee discrepancy on symmetric three-level combined designs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 273-280.
    4. Tu, Min & Huang, Hui & Liu, Ze-Hua & Chen, Huan-Xin & Ren, Cheng-Qin & Chen, Guo-Jie & Hu, Yan, 2017. "Factor analysis and optimization of operational parameters in a liquid desiccant air-conditioning system," Energy, Elsevier, vol. 139(C), pages 767-781.
    5. Zujun Ou & Hong Qin, 2019. "Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy," Statistical Papers, Springer, vol. 60(5), pages 1699-1716, October.
    6. Peng-Fei Li & Min-Qian Liu & Run-Chu Zhang, 2007. "2 m 4 1 designs with minimum aberration or weak minimum aberration," Statistical Papers, Springer, vol. 48(2), pages 235-248, April.

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