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A candidate‐set‐free algorithm for generating D‐optimal split‐plot designs

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  • Bradley Jones
  • Peter Goos

Abstract

Summary. We introduce a new method for generating optimal split‐plot designs. These designs are optimal in the sense that they are efficient for estimating the fixed effects of the statistical model that is appropriate given the split‐plot design structure. One advantage of the method is that it does not require the prior specification of a candidate set. This makes the production of split‐plot designs computationally feasible in situations where the candidate set is too large to be tractable. The method allows for flexible choice of the sample size and supports inclusion of both continuous and categorical factors. The model can be any linear regression model and may include arbitrary polynomial terms in the continuous factors and interaction terms of any order. We demonstrate the usefulness of this flexibility with a 100‐run polypropylene experiment involving 11 factors where we found a design that is substantially more efficient than designs that are produced by using other approaches.

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  • 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.
    • Handle: RePEc:bla:jorssc:v:56:y:2007:i:3:p:347-364
    DOI: 10.1111/j.1467-9876.2007.00581.x
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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. 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.
    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, 2010. "Update formulas for split-plot and block designs," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3381-3391, December.
    5. 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.
    6. Kalliopi Mylona & Harrison Macharia & Peter Goos, 2013. "Three-level equivalent-estimation split-plot designs based on subset and supplementary difference set designs," IISE Transactions, Taylor & Francis Journals, vol. 45(11), pages 1153-1165.
    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. 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. Moein Saleh & Ming-Hung Kao & Rong Pan, 2017. "Design D-optimal event-related functional magnetic resonance imaging experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 73-91, January.
    10. ARNOUTS, Heidi & GOOS, Peter, 2009. "Design and analysis of industrial strip-plot experiments," Working Papers 2009007, University of Antwerp, Faculty of Business and Economics.
    11. 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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