A novel method for constructing mixed two- and three-level uniform factorials with large run sizes
The methods of doubling and tripling have been used to construct two-level and three-level symmetrical fractional factorial designs with optimal properties. In this paper, the construction of symmetrical designs is generalized to an asymmetrical case, a novel construction method by amplifying is pre...
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| Veröffentlicht in: | Statistical papers (Berlin, Germany) Germany), 2021-12, Vol.62 (6), p.2907-2921 |
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| container_title | Statistical papers (Berlin, Germany) |
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| creator | Li, Hongyi Huang, Xingyou Xue, Huili Qin, Hong |
| description | The methods of doubling and tripling have been used to construct two-level and three-level symmetrical fractional factorial designs with optimal properties. In this paper, the construction of symmetrical designs is generalized to an asymmetrical case, a novel construction method by amplifying is presented for constructing mixed two- and three-level uniform designs with large run sizes. The analytic relationship between the squared wrap-around
L
2
- discrepancy value of the amplified design constructed by amplifying and the wordlength pattern of the initial design is built. Furthermore, the relationships of uniformity and aberration between the amplified design and the corresponding initial design are respectively considered. These results provide a theoretical basis for constructing mixed two- and three-level uniform designs with large run sizes. Finally, some numerical results are provided to support our theoretical results. |
| doi_str_mv | 10.1007/s00362-020-01219-8 |
| format | Article |
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L
2
- discrepancy value of the amplified design constructed by amplifying and the wordlength pattern of the initial design is built. Furthermore, the relationships of uniformity and aberration between the amplified design and the corresponding initial design are respectively considered. These results provide a theoretical basis for constructing mixed two- and three-level uniform designs with large run sizes. Finally, some numerical results are provided to support our theoretical results.</description><identifier>ISSN: 0932-5026</identifier><identifier>EISSN: 1613-9798</identifier><identifier>DOI: 10.1007/s00362-020-01219-8</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Amplification ; Construction ; Economic Theory/Quantitative Economics/Mathematical Methods ; Economics ; Factorials ; Finance ; Insurance ; Management ; Mathematics ; Mathematics and Statistics ; Operations Research/Decision Theory ; Probability Theory and Stochastic Processes ; Regular Article ; Statistics ; Statistics for Business</subject><ispartof>Statistical papers (Berlin, Germany), 2021-12, Vol.62 (6), p.2907-2921</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c352t-34b7a4ed6ce760c2176873948b9a891ca081014069771c05a50e6c83996aa143</citedby><cites>FETCH-LOGICAL-c352t-34b7a4ed6ce760c2176873948b9a891ca081014069771c05a50e6c83996aa143</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00362-020-01219-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00362-020-01219-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Li, Hongyi</creatorcontrib><creatorcontrib>Huang, Xingyou</creatorcontrib><creatorcontrib>Xue, Huili</creatorcontrib><creatorcontrib>Qin, Hong</creatorcontrib><title>A novel method for constructing mixed two- and three-level uniform factorials with large run sizes</title><title>Statistical papers (Berlin, Germany)</title><addtitle>Stat Papers</addtitle><description>The methods of doubling and tripling have been used to construct two-level and three-level symmetrical fractional factorial designs with optimal properties. In this paper, the construction of symmetrical designs is generalized to an asymmetrical case, a novel construction method by amplifying is presented for constructing mixed two- and three-level uniform designs with large run sizes. The analytic relationship between the squared wrap-around
L
2
- discrepancy value of the amplified design constructed by amplifying and the wordlength pattern of the initial design is built. Furthermore, the relationships of uniformity and aberration between the amplified design and the corresponding initial design are respectively considered. These results provide a theoretical basis for constructing mixed two- and three-level uniform designs with large run sizes. Finally, some numerical results are provided to support our theoretical results.</description><subject>Amplification</subject><subject>Construction</subject><subject>Economic Theory/Quantitative Economics/Mathematical Methods</subject><subject>Economics</subject><subject>Factorials</subject><subject>Finance</subject><subject>Insurance</subject><subject>Management</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operations Research/Decision Theory</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Regular Article</subject><subject>Statistics</subject><subject>Statistics for Business</subject><issn>0932-5026</issn><issn>1613-9798</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp9kE1LAzEQhoMoWKt_wFPAc3SS7ObjWIpfIHjpPaRptt2yTWqSteqvd-sK3mQOMzDPMwMvQtcUbimAvMsAXDACDAhQRjVRJ2hCBeVES61O0QQ0Z6QGJs7RRc5bAKqUgglaznCI777DO182cYWbmLCLIZfUu9KGNd61H36FyyESbMMwbJL3pPNHpQ_tgO9wY12JqbVdxoe2bHBn09rj1Aec2y-fL9FZM-z81W-fosXD_WL-RF5eH5_nsxfieM0K4dVS2sqvhPNSgGNUCiW5rtRSW6Wps6Ao0AqElpI6qG0NXjjFtRbW0opP0c14dp_iW-9zMdvYpzB8NKxWQtRDqYFiI-VSzDn5xuxTu7Pp01AwxyjNGKUZojQ_UZqjxEcpD3BY-_R3-h_rG5I-dis</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Li, Hongyi</creator><creator>Huang, Xingyou</creator><creator>Xue, Huili</creator><creator>Qin, Hong</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8C1</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>FYUFA</scope><scope>F~G</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M2P</scope><scope>M7S</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20211201</creationdate><title>A novel method for constructing mixed two- and three-level uniform factorials with large run sizes</title><author>Li, Hongyi ; 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In this paper, the construction of symmetrical designs is generalized to an asymmetrical case, a novel construction method by amplifying is presented for constructing mixed two- and three-level uniform designs with large run sizes. The analytic relationship between the squared wrap-around
L
2
- discrepancy value of the amplified design constructed by amplifying and the wordlength pattern of the initial design is built. Furthermore, the relationships of uniformity and aberration between the amplified design and the corresponding initial design are respectively considered. These results provide a theoretical basis for constructing mixed two- and three-level uniform designs with large run sizes. Finally, some numerical results are provided to support our theoretical results.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00362-020-01219-8</doi><tpages>15</tpages></addata></record> |
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| source | SpringerLink Journals - AutoHoldings; EBSCOhost Business Source Complete |
| subjects | Amplification Construction Economic Theory/Quantitative Economics/Mathematical Methods Economics Factorials Finance Insurance Management Mathematics Mathematics and Statistics Operations Research/Decision Theory Probability Theory and Stochastic Processes Regular Article Statistics Statistics for Business |
| title | A novel method for constructing mixed two- and three-level uniform factorials with large run sizes |
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