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D-optimal design of split-split-plot experiments

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  • BRADLEY, Jones
  • GOOS, Peter

Abstract

In industrial experimentation there is growing interest in studies that span more than one processing step. Convenience often dictates restrictions in randomization in passing from one processing step to another. When the study encompasses three processing steps, this leads to split-split-plot designs. We provide an algorithm for computing D-optimal split-split-plot designs and provide many illustrative examples. We then apply our methods to construct D-optimal alternatives to a previously run split-split-plot design for cheese production.

Suggested Citation

  • BRADLEY, Jones & GOOS, Peter, 2007. "D-optimal design of split-split-plot experiments," Working Papers 2007017, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2007017
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    File URL: https://repository.uantwerpen.be/docman/irua/734733/ae72117e.pdf
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    References listed on IDEAS

    as
    1. GOOS, Peter, "undated". "The usefulness of optimal design for generating blocked and split-plot response surface experiments," Working Papers 2005033, University of Antwerp, Faculty of Business and Economics.
    2. Eric Schoen, 1999. "Designing fractional two-level experiments with nested error structures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 495-508.
    3. C. J. Brien & R. A. Bailey, 2006. "Multiple randomizations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 571-609, September.
    4. Bradley Jones & Peter Goos, 2007. "A candidate‐set‐free algorithm for generating D‐optimal split‐plot designs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(3), pages 347-364, May.
    5. D. R. Bingham & E. D. Schoen & R. R. Sitter, 2004. "Designing fractional factorial split‐plot experiments with few whole‐plot factors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(2), pages 325-339, April.
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    Citations

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    Cited by:

    1. Loeza-Serrano, S. & Donev, A.N., 2014. "Construction of experimental designs for estimating variance components," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1168-1177.
    2. Murat Kulahci & John Tyssedal, 2017. "Split-plot designs for multistage experimentation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(3), pages 493-510, February.
    3. ARNOUTS, Heidi & GOOS, Peter, 2009. "Design and analysis of industrial strip-plot experiments," Working Papers 2009007, University of Antwerp, Faculty of Business and Economics.
    4. Xiaodong Li & Xu He & Yuanzhen He & Hui Zhang & Zhong Zhang & Dennis K. J. Lin, 2017. "The Design and Analysis for the Icing Wind Tunnel Experiment of a New Deicing Coating," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1417-1429, October.
    5. ARNOUTS, Heidi & GOOS, Peter, 2013. "Staggered-level designs for response surface modeling," Working Papers 2013027, University of Antwerp, Faculty of Business and Economics.
    6. Ke Sun & Linglong Kong & Hongtu Zhu & Chengchun Shi, 2024. "Optimal Treatment Allocation Strategies for A/B Testing in Partially Observable Time Series Experiments," Papers 2408.05342, arXiv.org, revised Oct 2024.
    7. Lin, Chang-Yun & Yang, Po, 2019. "Data-driven multistratum designs with the generalized Bayesian D-D criterion for highly uncertain models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 222-238.
    8. Palhazi Cuervo, Daniel & Goos, Peter & Sörensen, Kenneth, 2017. "An algorithmic framework for generating optimal two-stratum experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 224-249.
    9. Borrotti, Matteo & Sambo, Francesco & Mylona, Kalliopi, 2023. "Multi-objective optimisation of split-plot designs," Econometrics and Statistics, Elsevier, vol. 28(C), pages 163-172.

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    More about this item

    Keywords

    D-optimality; Exchange algorithm; Hard-to-change factors; Multi-stratum design; Split-plot design; Tailor-made design;
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