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Designing fractional factorial split‐plot experiments with few whole‐plot factors

Author

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  • D. R. Bingham
  • E. D. Schoen
  • R. R. Sitter

Abstract

Summary. When it is impractical to perform the experimental runs of a fractional factorial design in a completely random order, restrictions on the randomization can be imposed. The resulting design is said to have a split‐plot, or nested, error structure. Similarly to fractional factorials, fractional factorial split‐plot designs can be ranked by using the aberration criterion. Techniques that generate the required designs systematically presuppose unreplicated settings of the whole‐plot factors. We use a cheese‐making experiment to demonstrate the practical relevance of designs with replicated settings of these factors. We create such designs by splitting the whole plots according to one or more subplot effects. We develop a systematic method to generate the required designs and we use the method to create a table of designs that is likely to be useful in practice.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:53:y:2004:i:2:p:325-339
    DOI: 10.1046/j.1467-9876.2003.05029.x
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    Cited by:

    1. K. Chatterjee & C. Koukouvinos, 2021. "Construction of mixed-level supersaturated split-plot designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 949-967, October.
    2. K. Chatterjee & C. Koukouvinos & K. Mylona, 2020. "Construction of supersaturated split-plot designs," Statistical Papers, Springer, vol. 61(5), pages 2203-2219, October.
    3. 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.
    4. Minyang Hu & Shengli Zhao, 2022. "Minimum Aberration Split-Plot Designs Focusing on the Whole Plot Factors," Mathematics, MDPI, vol. 10(5), pages 1-12, February.
    5. Bradley Jones & Peter Goos, 2009. "D-optimal design of split-split-plot experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 67-82.
    6. Smucker, Byran J. & Castillo, Enrique del & Rosenberger, James L., 2012. "Model-robust designs for split-plot experiments," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4111-4121.
    7. ARNOUTS, Heidi & GOOS, Peter, 2013. "Staggered-level designs for response surface modeling," Working Papers 2013027, University of Antwerp, Faculty of Business and Economics.
    8. 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 Business and Economics.
    9. Steven G. Gilmour & Peter Goos, 2009. "Analysis of data from non‐orthogonal multistratum designs in industrial experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 467-484, September.
    10. 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.
    11. 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.
    12. Yang, Jianfeng & Zhang, Runchu & Liu, Minqian, 2007. "Construction of fractional factorial split-plot designs with weak minimum aberration," Statistics & Probability Letters, Elsevier, vol. 77(15), pages 1567-1573, September.

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