Orthogonally blocked mixture experiments in ellipsoidal restricted regions
Orthogonally blocked mixture experiments in ellipsoidal restricted regions
In practical situations involving mixtures formed from several ingredients, interest is sometimes centered on the response in an ellipsoidal neighborhood around a standard formulation. We show that standard, orthogonally blocked, response surface designs, defined on a q-1 dimensional unit sphere, may be transformed into similarly orthogonally blocked q-ingredient mixture designs defined within an ellipsoid centered at the standard formulation. The method is illustrated using several examples of mixture experiments with three, four, and five ingredients, arranged in two, three or four orthogonal blocks, obtained by projecting standard central composite designs and Box-Behnken designs into the ellipsoidal mixture region. Rotations of the resulting designs within the ellipsoidal regions are also considered
bounded mixture regions, box-behnken designs, central composite designs, ellipsoidal regions, orthogonal transformations, spherical designs, unit spheres
763-784
Prescott, Philip
cf0adfdd-989b-4f15-9e60-ef85eed817b2
2011
Prescott, Philip
cf0adfdd-989b-4f15-9e60-ef85eed817b2
Prescott, Philip
(2011)
Orthogonally blocked mixture experiments in ellipsoidal restricted regions.
Communications in Statistics: Theory and Methods, 40 (5), .
Abstract
In practical situations involving mixtures formed from several ingredients, interest is sometimes centered on the response in an ellipsoidal neighborhood around a standard formulation. We show that standard, orthogonally blocked, response surface designs, defined on a q-1 dimensional unit sphere, may be transformed into similarly orthogonally blocked q-ingredient mixture designs defined within an ellipsoid centered at the standard formulation. The method is illustrated using several examples of mixture experiments with three, four, and five ingredients, arranged in two, three or four orthogonal blocks, obtained by projecting standard central composite designs and Box-Behnken designs into the ellipsoidal mixture region. Rotations of the resulting designs within the ellipsoidal regions are also considered
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Submitted date: June 2009
Accepted/In Press date: June 2009
Published date: 2011
Keywords:
bounded mixture regions, box-behnken designs, central composite designs, ellipsoidal regions, orthogonal transformations, spherical designs, unit spheres
Organisations:
Statistics
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Local EPrints ID: 69640
URI: http://eprints.soton.ac.uk/id/eprint/69640
ISSN: 0361-0926
PURE UUID: fe1fcd5b-668c-4541-8e98-1094f6b335cb
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Date deposited: 25 Nov 2009
Last modified: 08 Jan 2022 14:25
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