Balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs
Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial propert...
Ausführliche Beschreibung
Autor*in: |
Yamamoto, Sumiyasu [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
1975 |
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Schlagwörter: |
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Anmerkung: |
© The Institute of Statistical Mathematics 1975 |
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Übergeordnetes Werk: |
Enthalten in: Annals of the Institute of Statistical Mathematics - Kluwer Academic Publishers, 1949, 27(1975), 1 vom: Dez., Seite 143-157 |
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Übergeordnetes Werk: |
volume:27 ; year:1975 ; number:1 ; month:12 ; pages:143-157 |
Links: |
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DOI / URN: |
10.1007/BF02504632 |
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Katalog-ID: |
OLC2071674278 |
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10.1007/BF02504632 doi (DE-627)OLC2071674278 (DE-He213)BF02504632-p DE-627 ger DE-627 rakwb eng 510 VZ Yamamoto, Sumiyasu verfasserin aut Balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs 1975 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics 1975 Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional $ 2^{m} $ factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular. Factorial Design Orthogonal Array Information Matrix Fractional Factorial Design Association Scheme Shirakura, Teruhiro aut Kuwada, Masahide aut Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers, 1949 27(1975), 1 vom: Dez., Seite 143-157 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:27 year:1975 number:1 month:12 pages:143-157 https://doi.org/10.1007/BF02504632 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 27 1975 1 12 143-157 |
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10.1007/BF02504632 doi (DE-627)OLC2071674278 (DE-He213)BF02504632-p DE-627 ger DE-627 rakwb eng 510 VZ Yamamoto, Sumiyasu verfasserin aut Balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs 1975 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics 1975 Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional $ 2^{m} $ factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular. Factorial Design Orthogonal Array Information Matrix Fractional Factorial Design Association Scheme Shirakura, Teruhiro aut Kuwada, Masahide aut Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers, 1949 27(1975), 1 vom: Dez., Seite 143-157 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:27 year:1975 number:1 month:12 pages:143-157 https://doi.org/10.1007/BF02504632 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 27 1975 1 12 143-157 |
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10.1007/BF02504632 doi (DE-627)OLC2071674278 (DE-He213)BF02504632-p DE-627 ger DE-627 rakwb eng 510 VZ Yamamoto, Sumiyasu verfasserin aut Balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs 1975 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics 1975 Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional $ 2^{m} $ factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular. Factorial Design Orthogonal Array Information Matrix Fractional Factorial Design Association Scheme Shirakura, Teruhiro aut Kuwada, Masahide aut Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers, 1949 27(1975), 1 vom: Dez., Seite 143-157 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:27 year:1975 number:1 month:12 pages:143-157 https://doi.org/10.1007/BF02504632 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 27 1975 1 12 143-157 |
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10.1007/BF02504632 doi (DE-627)OLC2071674278 (DE-He213)BF02504632-p DE-627 ger DE-627 rakwb eng 510 VZ Yamamoto, Sumiyasu verfasserin aut Balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs 1975 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics 1975 Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional $ 2^{m} $ factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular. Factorial Design Orthogonal Array Information Matrix Fractional Factorial Design Association Scheme Shirakura, Teruhiro aut Kuwada, Masahide aut Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers, 1949 27(1975), 1 vom: Dez., Seite 143-157 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:27 year:1975 number:1 month:12 pages:143-157 https://doi.org/10.1007/BF02504632 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 27 1975 1 12 143-157 |
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10.1007/BF02504632 doi (DE-627)OLC2071674278 (DE-He213)BF02504632-p DE-627 ger DE-627 rakwb eng 510 VZ Yamamoto, Sumiyasu verfasserin aut Balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs 1975 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics 1975 Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional $ 2^{m} $ factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular. Factorial Design Orthogonal Array Information Matrix Fractional Factorial Design Association Scheme Shirakura, Teruhiro aut Kuwada, Masahide aut Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers, 1949 27(1975), 1 vom: Dez., Seite 143-157 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:27 year:1975 number:1 month:12 pages:143-157 https://doi.org/10.1007/BF02504632 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 27 1975 1 12 143-157 |
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Yamamoto, Sumiyasu Shirakura, Teruhiro Kuwada, Masahide |
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balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs |
title_auth |
Balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs |
abstract |
Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional $ 2^{m} $ factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular. © The Institute of Statistical Mathematics 1975 |
abstractGer |
Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional $ 2^{m} $ factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular. © The Institute of Statistical Mathematics 1975 |
abstract_unstemmed |
Summary A connection between a balanced fractional $ 2^{m} $ factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional $ 2^{m} $ factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular. © The Institute of Statistical Mathematics 1975 |
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Balanced arrays of strength 2l and balanced fractional $ 2^{m} $ factorial designs |
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