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New foundations for designing U-optimal follow-up experiments with flexible levels

Author

Listed:
  • A. M. Elsawah

    (Zagazig University
    BNU-HKBU United International College)

  • Kai-Tai Fang

    (BNU-HKBU United International College
    The Chinese Academy of Sciences)

Abstract

Follow-up experiments are used extensively to provide precious information about the relationships between inputs and outputs to gain a better understanding of a process or system under study. This article gives a new look at designing optimal follow-up experiments that involve any number of factors with any number of different levels in light of the uniformity behaviour of the corresponding two stage sequential experiments, which are composed of initial experiments and follow-up experiments. Novel analytical expressions and lower bounds of the wrap-around $$L_2$$L2-discrepancy, as a uniformity measure, for sequential experimental designs are proposed for evaluating the optimality of the follow-up experimental designs. Finding equivalent follow-up experimental designs is investigated, which can be used to reduce the computational complexity. Our results show that two stage sequential experimental designs give greater precision than single stage experimental designs with the same size.

Suggested Citation

  • A. M. Elsawah & Kai-Tai Fang, 2020. "New foundations for designing U-optimal follow-up experiments with flexible levels," Statistical Papers, Springer, vol. 61(2), pages 823-849, April.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0963-z
    DOI: 10.1007/s00362-017-0963-z
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    References listed on IDEAS

    as
    1. Elsawah, A.M. & Qin, Hong, 2015. "A new strategy for optimal foldover two-level designs," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 116-126.
    2. Elsawah, A.M., 2016. "Constructing optimal asymmetric combined designs via Lee discrepancy," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 24-31.
    3. Tong, Charles, 2006. "Refinement strategies for stratified sampling methods," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1257-1265.
    4. 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.
    5. Durrieu, Gilles & Briollais, Laurent, 2009. "Sequential Design for Microarray Experiments," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 650-660.
    6. A. M. Elsawah & Hong Qin, 2017. "A new look on optimal foldover plans in terms of uniformity criteria," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1621-1635, February.
    7. Ai, Mingyao & Hickernell, Fred J. & Lin, Dennis K.J., 2008. "Optimal foldover plans for regular s-level fractional factorial designs," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 896-903, May.
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