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Staggered-level designs for response surface modeling

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  • ARNOUTS, Heidi
  • GOOS, Peter

Abstract

In industrial experiments, there are often restrictions in randomization caused by equipment and resource constraints, as well as budget and time restrictions. Next to the split-plot and the split-split-plot design, the staggered-level design is an interesting design option for experiments involving two hard-to-change factors. The staggered-level design allows both hard-to-change factors to be reset at different points in time, resulting in a typical staggering pattern of factor level resettings. It has been shown that, for two-level designs, this staggering pattern leads to statistical benefits in comparison to the split-plot and the split-split-plot design. In this paper, we investigate whether the benefits of the staggered-level design carry over to situations where the objective is to optimize a response, and where a second-order response surface model is in place. To this end, we study several examples of D-and I-optimal staggered-level response surface designs.

Suggested Citation

  • ARNOUTS, Heidi & GOOS, Peter, 2013. "Staggered-level designs for response surface modeling," Working Papers 2013027, University of Antwerp, Faculty of Applied Economics.
  • Handle: RePEc:ant:wpaper:2013027
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    File URL: https://repository.uantwerpen.be/docman/irua/67f839/1781b5f7.pdf
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    References listed on IDEAS

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    1. MACHARIA, Harrison & GOOS, Peter, 2010. "D-optimal and D-efficient equivalent-estimation second-order split-plot designs," Working Papers 2010011, University of Antwerp, Faculty of Applied 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. Bradley Jones & Peter Goos, 2009. "D-optimal design of split-split-plot experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 67-82.
    4. ARNOUTS, Heidi & GOOS, Peter, 2008. "Staggered designs for experiments with more than one hard-to-change factor," Working Papers 2008018, University of Antwerp, Faculty of Applied Economics.
    5. JONES, Bradley & GOOS, Peter, 2012. "I-optimal versus D-optimal split-plot response surface designs," Working Papers 2012002, University of Antwerp, Faculty of Applied Economics.
    6. 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.
    7. 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.
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    More about this item

    Keywords

    D- and I-optimality criterion; Cost; Response surface model; Split-plot design; Split-split-plot design; Staggered-level design;

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