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Split-plot experiments with factor-dependent whole-plot sizes

Author

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  • SCHOEN, Eric D.
  • JONES, Bradley
  • GOOS, Peter

Abstract

In industrial split-plot experiments, the number of runs within each whole plot is usually determined independently from the factor settings. As a matter of fact, it is often equal to the number of runs that can be done within a given period of time or to the number of samples that can be processed in one oven run or with one batch. In such cases, the size of every whole plot in the experiment is fixed no matter what factor levels are actually used in the experiment. In this article, we discuss the design of a real-life experiment on the production of coffee cream where the number of runs within a whole plot is not fixed, but depends on the level of one of the whole-plot factors. We provide a detailed discussion of various ways to set up the experiment and discuss how existing algorithms to construct optimal split-plot designs can be modified for that purpose. We conclude the paper with a few general recommendations.

Suggested Citation

  • SCHOEN, Eric D. & JONES, Bradley & GOOS, Peter, 2010. "Split-plot experiments with factor-dependent whole-plot sizes," Working Papers 2010001, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2010001
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    File URL: https://repository.uantwerpen.be/docman/irua/0ede3c/ecb19a19.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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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    Cited by:

    1. Sambo, Francesco & Borrotti, Matteo & Mylona, Kalliopi, 2014. "A coordinate-exchange two-phase local search algorithm for the D- and I-optimal designs of split-plot experiments," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1193-1207.
    2. JONES, Bradley & GOOS, Peter, 2012. "I-optimal versus D-optimal split-plot response surface designs," Working Papers 2012002, University of Antwerp, Faculty of Business and Economics.

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    More about this item

    Keywords

    Coordinate-exchange algorithm; D-optimum designs; Point-exchange algorithm; Restricted randomization;
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