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Partially orthogonal blocked three-level response surface designs

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  • Großmann, Heiko
  • Gilmour, Steven G.

Abstract

When fitting second-order response surface models in a hypercuboidal region of experimentation, the variance matrices of D-optimal continuous designs have a particularly attractive structure, as do many regular unblocked exact designs. Methods for constructing blocked exact designs which preserve this structure and are orthogonal, or nearly orthogonal, are developed. Partially orthogonal designs are built using a small irregular fraction of a two- or three-level design and a regular fractional factorial design as building blocks. Results are derived which relate the properties of the blocked design to these components. Moreover, it is shown how the designs can be augmented to ensure that the model can be fitted and a method for constructing designs with small blocks is presented. Examples illustrate that partially orthogonal designs can compete with more traditional designs in terms of both efficiency and overall size of the experiment.

Suggested Citation

  • Großmann, Heiko & Gilmour, Steven G., 2023. "Partially orthogonal blocked three-level response surface designs," Econometrics and Statistics, Elsevier, vol. 28(C), pages 138-154.
    • Handle: RePEc:eee:ecosta:v:28:y:2023:i:c:p:138-154
    DOI: 10.1016/j.ecosta.2021.08.007
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    References listed on IDEAS

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    1. Yong-Dao Zhou & Hongquan Xu, 2017. "Composite Designs Based on Orthogonal Arrays and Definitive Screening Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1675-1683, October.
    2. Neil A. Butler, 2003. "Some theory for constructing minimum aberration fractional factorial designs," Biometrika, Biometrika Trust, vol. 90(1), pages 233-238, March.
    3. Steven G. Gilmour, 2006. "Response Surface Designs for Experiments in Bioprocessing," Biometrics, The International Biometric Society, vol. 62(2), pages 323-331, June.
    4. Trinca, Luzia A. & Gilmour, Steven G., 2000. "An algorithm for arranging response surface designs in small blocks," Computational Statistics & Data Analysis, Elsevier, vol. 33(1), pages 25-43, March.
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