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Choice of optimal second stage designs in two-stage experiments

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  • A. M. Elsawah

    (Zagazig University
    BNU-HKBU United International College)

Abstract

In real-life projects, in order to obtain precious information about the process, we often partition the experiment into two stages with equal size. The main purpose of this article is to study how to choose the first stage experimental designs (FSED) and the second stage experimental designs (SSED) to construct uniform or at least good approximation to uniform (GATU) two-stage experimental designs (TSED) that involve a mixture of $$\omega _1\ge 1$$ ω 1 ≥ 1 factors with $$\mu _1\ge 2$$ μ 1 ≥ 2 levels and $$\omega _2\ge 1$$ ω 2 ≥ 1 factors with $$\mu _2\ge 2$$ μ 2 ≥ 2 levels whether regular or nonregular. Through theoretical justification, this paper proves that the SSED is uniform (GATU) if and only if the FSED is uniform (GATU), the TSED is uniform (GATU) if and only if its corresponding complementary TSED is uniform (GATU), and the TSED is uniform or at least GATU if and only if the FSED is uniform.

Suggested Citation

  • A. M. Elsawah, 2018. "Choice of optimal second stage designs in two-stage experiments," Computational Statistics, Springer, vol. 33(2), pages 933-965, June.
  • Handle: RePEc:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0778-3
    DOI: 10.1007/s00180-017-0778-3
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    References listed on IDEAS

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    1. Fang, Kai-Tai & Lin, Dennis K. J. & Qin, Hong, 2003. "A note on optimal foldover design," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 245-250, April.
    2. 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.
    3. Zhou, Yong-Dao & Ning, Jian-Hui & Song, Xie-Bing, 2008. "Lee discrepancy and its applications in experimental designs," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1933-1942, September.
    4. Elsawah, A.M., 2016. "Constructing optimal asymmetric combined designs via Lee discrepancy," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 24-31.
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    Cited by:

    1. A. M. Elsawah, 2021. "Multiple doubling: a simple effective construction technique for optimal two-level experimental designs," Statistical Papers, Springer, vol. 62(6), pages 2923-2967, December.
    2. A. M. Elsawah & Kai-Tai Fang & Xiao Ke, 2021. "New recommended designs for screening either qualitative or quantitative factors," Statistical Papers, Springer, vol. 62(1), pages 267-307, February.

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