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Augmented box-behnken designs for fitting third-order response surfaces

Augmented box-behnken designs for fitting third-order response surfaces
Augmented box-behnken designs for fitting third-order response surfaces
Box-Behnken designs are popular with experimenters who wish to estimate a second-order model, due to their having three levels, their simplicity and their high efficiency for the second-order model. However, there are situations in which the model is inadequate due to lack of fit caused by higher-order terms. These designs have little ability to estimate third-order terms. Using combinations of factorial points, axial points, and complementary design points, we augment these designs and develop catalogues of third-order designs for 3–12 factors. These augmented designs can be used to estimate the parameters of a third-order response surface model. Since the aim is to make the most of a situation in which the experiment was designed for an inadequate model, the designs are clearly suboptimal and not rotatable for the third-order model, but can still provide useful information.
0361-0926
4225-4239
Arshad, Hafiz Muhammad
07b53fb0-4e1b-4a9c-b233-a505e57522ec
Akhtar, Munir
fa0d18ff-37f1-4327-8439-5681b9d3e9ac
Gilmour, Steven G.
984dbefa-893b-444d-9aa2-5953cd1c8b03
Arshad, Hafiz Muhammad
07b53fb0-4e1b-4a9c-b233-a505e57522ec
Akhtar, Munir
fa0d18ff-37f1-4327-8439-5681b9d3e9ac
Gilmour, Steven G.
984dbefa-893b-444d-9aa2-5953cd1c8b03

Arshad, Hafiz Muhammad, Akhtar, Munir and Gilmour, Steven G. (2012) Augmented box-behnken designs for fitting third-order response surfaces. Communications in Statistics: Theory and Methods, 41 (23), 4225-4239. (doi:10.1080/03610926.2011.568154).

Record type: Article

Abstract

Box-Behnken designs are popular with experimenters who wish to estimate a second-order model, due to their having three levels, their simplicity and their high efficiency for the second-order model. However, there are situations in which the model is inadequate due to lack of fit caused by higher-order terms. These designs have little ability to estimate third-order terms. Using combinations of factorial points, axial points, and complementary design points, we augment these designs and develop catalogues of third-order designs for 3–12 factors. These augmented designs can be used to estimate the parameters of a third-order response surface model. Since the aim is to make the most of a situation in which the experiment was designed for an inadequate model, the designs are clearly suboptimal and not rotatable for the third-order model, but can still provide useful information.

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e-pub ahead of print date: 10 October 2012
Organisations: Statistics

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Local EPrints ID: 348386
URI: http://eprints.soton.ac.uk/id/eprint/348386
ISSN: 0361-0926
PURE UUID: 3c905dbf-59e9-4b09-b283-7da2e5612307

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Date deposited: 13 Feb 2013 11:12
Last modified: 14 Mar 2024 12:58

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Contributors

Author: Hafiz Muhammad Arshad
Author: Munir Akhtar
Author: Steven G. Gilmour

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