The University of Southampton
University of Southampton Institutional Repository

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.

PDF
CIS_2012b.pdf - Version of Record
Restricted to Repository staff only
Request a copy

More information

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

Identifiers

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

Catalogue record

Date deposited: 13 Feb 2013 11:12
Last modified: 18 Jul 2017 04:52

Export record

Altmetrics

Contributors

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

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×