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Perspective Chapter: Cyclic Generation of Box-Behnken Designs and New Second-Order Designs

In: Response Surface Methodology - Research Advances and Applications

Author

Listed:
  • Nam-Ky Nguyen
  • Mai Phuong Vuong
  • John J. Borkowski

Abstract

Box-Behnken designs (BBDs) are three-level second-order spherical designs with all points lying on a sphere, introduced by Box and Behnken, for fitting the second-order response surface models. They are available for 3-12 and 16 factors. Together with the central composite designs for the second-order model, BBDs are very popular response surface designs, especially for 3-7 factors. This chapter introduces an algorithm to produce cyclic generators for BBDs and similar designs, which we call cyclic BBDs (CBBDs). The new CBBDs offer more flexibility in choosing the designs for a specified number of factors. Comparisons between some BBDs and the new CBBDs indicate the superiority of the new CBBDs with respect to multiple design quality measures and graphical tools assessing prediction variance properties. A catalog of 24 new CBBDs, which includes orthogonally blocked CBBDs for 11, 13, and 14 factors, will be given.

Suggested Citation

  • Nam-Ky Nguyen & Mai Phuong Vuong & John J. Borkowski, 2023. "Perspective Chapter: Cyclic Generation of Box-Behnken Designs and New Second-Order Designs," Chapters, in: Palanikumar Kayaroganam (ed.), Response Surface Methodology - Research Advances and Applications, IntechOpen.
    • Handle: RePEc:ito:pchaps:277170
    DOI: 10.5772/intechopen.107178
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    Keywords

    circulant matrices; foldover designs; interchange algorithm; response surface designs; spherical designs;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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