Constructing response surface designs with orthogonal quadratic effects using cyclic generators

Pham, Tung-Dinh; Nguyen, Nam-Ky; Tran, Cuong-Manh; Vuong, Mai Phuong

doi:10.1016/j.chemolab.2019.103918

Cited by 4 publications

(1 citation statement)

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“…Our CBBD algorithm is the generalization of the algorithm in Nguyen et al [7] and Pham et al [8]. Using the results in Section 2, we present the steps of the algorithm for generating a CBBD for m factors in n ¼ 2rm þ n c runs (where n c is the number of center points) with points on a sphere of radius ρ, and 1 3 m ≤ ρ 2 < m ÀÁ .…”

Section: The Cbbd Algorithmmentioning

confidence: 99%

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

Nguyen¹,

Borkowski²,

Vuong³

2023

Response Surface Methodology - Research Advances and Applications

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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.

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Section: The Cbbd Algorithmmentioning

confidence: 99%