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Designing fractional two-level experiments with nested error structures

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  • Eric Schoen

Abstract

A common feature of experiments with a random blocking factor and splitplot experiments is their nested error structure. This paper proposes a general strategy to handle fractional two-level experiments with such error structures. The strategy aims to create error strata with sufficient numbers of contrasts to separate active effects from inactive effects. The strategy also details the construction of treatment generators, given the constraints of a predetermined error structure. The key elements of the strategy are illustrated with a chemical experiment that has 16 factors and 32 runs blocked according to working days, and a cheese-making experiment that has 11 factors and 128 runs, divided over milk supplies as whole plots, curds productions as subplots and sets of identically treated cheeses as sub-subplots.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:4:p:495-508
    DOI: 10.1080/02664769922377
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    Cited by:

    1. Bradley Jones & Peter Goos, 2009. "D-optimal design of split-split-plot experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 67-82.
    2. ARNOUTS, Heidi & GOOS, Peter, 2013. "Staggered-level designs for response surface modeling," Working Papers 2013027, University of Antwerp, Faculty of Business and Economics.
    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. 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.
    5. Xiaoxue Han & Jianbin Chen & Min-Qian Liu & Shengli Zhao, 2020. "Asymmetrical split-plot designs with clear effects," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 779-798, October.
    6. M. Arvidsson & P. Kammerlind & A. Hynen & B. Bergman, 2001. "Identification of factors influencing dispersion in split-plot experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(3-4), pages 269-283.

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