Connections between uniformity and aberration in general multi-level factorials

Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indi...
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Gespeichert in:

Autor*in:	Sun, Fasheng [verfasserIn] Chen, Jie Liu, Min-Qian

Format:	Artikel
Sprache:	Englisch

Erschienen:	2009

Schlagwörter:	Discrepancy Generalized minimum aberration Generalized wordlength pattern Indicator function Uniformity

Anmerkung:	© Springer-Verlag 2009

Übergeordnetes Werk:	Enthalten in: Metrika - Springer-Verlag, 1958, 73(2009), 3 vom: 11. Aug., Seite 305-315
Übergeordnetes Werk:	volume:73 ; year:2009 ; number:3 ; day:11 ; month:08 ; pages:305-315

Links:	Volltext

DOI / URN:	10.1007/s00184-009-0279-7

Katalog-ID:	OLC206139650X

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allfields	10.1007/s00184-009-0279-7 doi (DE-627)OLC206139650X (DE-He213)s00184-009-0279-7-p DE-627 ger DE-627 rakwb eng 510 VZ Sun, Fasheng verfasserin aut Connections between uniformity and aberration in general multi-level factorials 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. Discrepancy Generalized minimum aberration Generalized wordlength pattern Indicator function Uniformity Chen, Jie aut Liu, Min-Qian aut Enthalten in Metrika Springer-Verlag, 1958 73(2009), 3 vom: 11. Aug., Seite 305-315 (DE-627)12908171X (DE-600)3502-6 (DE-576)014414619 0026-1335 nnns volume:73 year:2009 number:3 day:11 month:08 pages:305-315 https://doi.org/10.1007/s00184-009-0279-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_100 GBV_ILN_193 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4324 GBV_ILN_4326 AR 73 2009 3 11 08 305-315
spelling	10.1007/s00184-009-0279-7 doi (DE-627)OLC206139650X (DE-He213)s00184-009-0279-7-p DE-627 ger DE-627 rakwb eng 510 VZ Sun, Fasheng verfasserin aut Connections between uniformity and aberration in general multi-level factorials 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. Discrepancy Generalized minimum aberration Generalized wordlength pattern Indicator function Uniformity Chen, Jie aut Liu, Min-Qian aut Enthalten in Metrika Springer-Verlag, 1958 73(2009), 3 vom: 11. Aug., Seite 305-315 (DE-627)12908171X (DE-600)3502-6 (DE-576)014414619 0026-1335 nnns volume:73 year:2009 number:3 day:11 month:08 pages:305-315 https://doi.org/10.1007/s00184-009-0279-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_100 GBV_ILN_193 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4324 GBV_ILN_4326 AR 73 2009 3 11 08 305-315
allfields_unstemmed	10.1007/s00184-009-0279-7 doi (DE-627)OLC206139650X (DE-He213)s00184-009-0279-7-p DE-627 ger DE-627 rakwb eng 510 VZ Sun, Fasheng verfasserin aut Connections between uniformity and aberration in general multi-level factorials 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. Discrepancy Generalized minimum aberration Generalized wordlength pattern Indicator function Uniformity Chen, Jie aut Liu, Min-Qian aut Enthalten in Metrika Springer-Verlag, 1958 73(2009), 3 vom: 11. Aug., Seite 305-315 (DE-627)12908171X (DE-600)3502-6 (DE-576)014414619 0026-1335 nnns volume:73 year:2009 number:3 day:11 month:08 pages:305-315 https://doi.org/10.1007/s00184-009-0279-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_100 GBV_ILN_193 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4324 GBV_ILN_4326 AR 73 2009 3 11 08 305-315
allfieldsGer	10.1007/s00184-009-0279-7 doi (DE-627)OLC206139650X (DE-He213)s00184-009-0279-7-p DE-627 ger DE-627 rakwb eng 510 VZ Sun, Fasheng verfasserin aut Connections between uniformity and aberration in general multi-level factorials 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. Discrepancy Generalized minimum aberration Generalized wordlength pattern Indicator function Uniformity Chen, Jie aut Liu, Min-Qian aut Enthalten in Metrika Springer-Verlag, 1958 73(2009), 3 vom: 11. Aug., Seite 305-315 (DE-627)12908171X (DE-600)3502-6 (DE-576)014414619 0026-1335 nnns volume:73 year:2009 number:3 day:11 month:08 pages:305-315 https://doi.org/10.1007/s00184-009-0279-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_100 GBV_ILN_193 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4324 GBV_ILN_4326 AR 73 2009 3 11 08 305-315
allfieldsSound	10.1007/s00184-009-0279-7 doi (DE-627)OLC206139650X (DE-He213)s00184-009-0279-7-p DE-627 ger DE-627 rakwb eng 510 VZ Sun, Fasheng verfasserin aut Connections between uniformity and aberration in general multi-level factorials 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. Discrepancy Generalized minimum aberration Generalized wordlength pattern Indicator function Uniformity Chen, Jie aut Liu, Min-Qian aut Enthalten in Metrika Springer-Verlag, 1958 73(2009), 3 vom: 11. Aug., Seite 305-315 (DE-627)12908171X (DE-600)3502-6 (DE-576)014414619 0026-1335 nnns volume:73 year:2009 number:3 day:11 month:08 pages:305-315 https://doi.org/10.1007/s00184-009-0279-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_26 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_100 GBV_ILN_193 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4324 GBV_ILN_4326 AR 73 2009 3 11 08 305-315
language	English
source	Enthalten in Metrika 73(2009), 3 vom: 11. Aug., Seite 305-315 volume:73 year:2009 number:3 day:11 month:08 pages:305-315
sourceStr	Enthalten in Metrika 73(2009), 3 vom: 11. Aug., Seite 305-315 volume:73 year:2009 number:3 day:11 month:08 pages:305-315
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Discrepancy Generalized minimum aberration Generalized wordlength pattern Indicator function Uniformity
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container_title	Metrika
authorswithroles_txt_mv	Sun, Fasheng @@aut@@ Chen, Jie @@aut@@ Liu, Min-Qian @@aut@@
publishDateDaySort_date	2009-08-11T00:00:00Z
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author	Sun, Fasheng
spellingShingle	Sun, Fasheng ddc 510 misc Discrepancy misc Generalized minimum aberration misc Generalized wordlength pattern misc Indicator function misc Uniformity Connections between uniformity and aberration in general multi-level factorials
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topic_title	510 VZ Connections between uniformity and aberration in general multi-level factorials Discrepancy Generalized minimum aberration Generalized wordlength pattern Indicator function Uniformity
topic	ddc 510 misc Discrepancy misc Generalized minimum aberration misc Generalized wordlength pattern misc Indicator function misc Uniformity
topic_unstemmed	ddc 510 misc Discrepancy misc Generalized minimum aberration misc Generalized wordlength pattern misc Indicator function misc Uniformity
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title	Connections between uniformity and aberration in general multi-level factorials
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title_full	Connections between uniformity and aberration in general multi-level factorials
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title_sort	connections between uniformity and aberration in general multi-level factorials
title_auth	Connections between uniformity and aberration in general multi-level factorials
abstract	Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. © Springer-Verlag 2009
abstractGer	Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. © Springer-Verlag 2009
abstract_unstemmed	Abstract Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L2-(CD2) and wrap-around L2-discrepancy (WD2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them. © Springer-Verlag 2009
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title_short	Connections between uniformity and aberration in general multi-level factorials
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