New families of QB-optimal saturated two-level main effects screening designs
New families of QB-optimal saturated two-level main effects screening designs
In this paper, we study saturated two-level main effects designs which are commonly used for screening experiments. The QB criterion, which incorporates experimenters' prior beliefs about the probability of factors being active is used to compare designs. We show that under priors with more weight on models of small size, p-efficient designs should be recommended; when models with more parameters are of interest, A-optimal designs would be better. We identify new classes of saturated main effects designs between these two designs under different priors. The way in which the choice of designs depends on experimenters' prior beliefs will be demonstrated for the cases when the number of runs N = 2 mod 4. A novel method of construction of QB-optimal designs using conference matrices is introduced. Complete families of optimal designs are given for N = 6; 10; 14; 18; 26; 30.
605-617
Tsai, Pi-Wen
752a8e50-aabf-4f40-bb8a-1313d2c60edf
Gilmour, Steven G.
984dbefa-893b-444d-9aa2-5953cd1c8b03
April 2016
Tsai, Pi-Wen
752a8e50-aabf-4f40-bb8a-1313d2c60edf
Gilmour, Steven G.
984dbefa-893b-444d-9aa2-5953cd1c8b03
Tsai, Pi-Wen and Gilmour, Steven G.
(2016)
New families of QB-optimal saturated two-level main effects screening designs.
Statistica Sinica, 26, .
(doi:10.5705/ss.202015.0084).
Abstract
In this paper, we study saturated two-level main effects designs which are commonly used for screening experiments. The QB criterion, which incorporates experimenters' prior beliefs about the probability of factors being active is used to compare designs. We show that under priors with more weight on models of small size, p-efficient designs should be recommended; when models with more parameters are of interest, A-optimal designs would be better. We identify new classes of saturated main effects designs between these two designs under different priors. The way in which the choice of designs depends on experimenters' prior beliefs will be demonstrated for the cases when the number of runs N = 2 mod 4. A novel method of construction of QB-optimal designs using conference matrices is introduced. Complete families of optimal designs are given for N = 6; 10; 14; 18; 26; 30.
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screenQB_ss_revised_submitted.pdf
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screeQB_ss_2015_supp.pdf
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Accepted/In Press date: May 2015
e-pub ahead of print date: April 2016
Published date: April 2016
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Local EPrints ID: 377523
URI: http://eprints.soton.ac.uk/id/eprint/377523
ISSN: 1017-0405
PURE UUID: 4214a58c-8d2b-42f1-bf38-2533a393bc67
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Date deposited: 12 Jun 2015 07:43
Last modified: 14 Mar 2024 20:05
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Author:
Pi-Wen Tsai
Author:
Steven G. Gilmour
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