Results for Two-Level Designs with General Minimum Lower-Order Confounding
The general minimum lower-order confounding (GMC) criterion for two-level design not only reveals the confounding information of factor effects but also provides a good way to select the optimal design, which was proposed by Zhang et al. (2008). The criterion is based on the aliased effect-number pa...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/163234 |
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| _version_ | 1849472867341697024 |
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| author | Zhi Ming Li Run Chu Zhang |
| author_facet | Zhi Ming Li Run Chu Zhang |
| author_sort | Zhi Ming Li |
| collection | DOAJ |
| description | The general minimum lower-order confounding (GMC) criterion for two-level design not only reveals the confounding information of factor effects but also provides a good way to select the optimal design, which was proposed by Zhang et al. (2008). The criterion is based on the aliased effect-number pattern (AENP). Therefore, it is very important to study properties of AENP for two-level GMC design. According to the ordering of elements in the AENP, the confounding information between lower-order factor effects is more important than that of higher-order effects. For two-level GMC design, this paper mainly shows the interior principles to calculate the leading elements C1#2 and C2#2 in the AENP. Further, their mathematical formulations are obtained for every GMC 2n-m design with N=2n-m according to two cases: (i) 5N/16+1≤n<N/2 and (ii) N/2≤n≤N-1. |
| format | Article |
| id | doaj-art-d9af5e84f0f54d73bb49a9db8643f791 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-d9af5e84f0f54d73bb49a9db8643f7912025-08-20T03:24:22ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/163234163234Results for Two-Level Designs with General Minimum Lower-Order ConfoundingZhi Ming Li0Run Chu Zhang1School of Mathematical Sciences, Xinjiang University, Urumqi 830046, ChinaKLAS and School of Mathematics, Northeast Normal University, Changchun 130024, ChinaThe general minimum lower-order confounding (GMC) criterion for two-level design not only reveals the confounding information of factor effects but also provides a good way to select the optimal design, which was proposed by Zhang et al. (2008). The criterion is based on the aliased effect-number pattern (AENP). Therefore, it is very important to study properties of AENP for two-level GMC design. According to the ordering of elements in the AENP, the confounding information between lower-order factor effects is more important than that of higher-order effects. For two-level GMC design, this paper mainly shows the interior principles to calculate the leading elements C1#2 and C2#2 in the AENP. Further, their mathematical formulations are obtained for every GMC 2n-m design with N=2n-m according to two cases: (i) 5N/16+1≤n<N/2 and (ii) N/2≤n≤N-1.http://dx.doi.org/10.1155/2015/163234 |
| spellingShingle | Zhi Ming Li Run Chu Zhang Results for Two-Level Designs with General Minimum Lower-Order Confounding The Scientific World Journal |
| title | Results for Two-Level Designs with General Minimum Lower-Order Confounding |
| title_full | Results for Two-Level Designs with General Minimum Lower-Order Confounding |
| title_fullStr | Results for Two-Level Designs with General Minimum Lower-Order Confounding |
| title_full_unstemmed | Results for Two-Level Designs with General Minimum Lower-Order Confounding |
| title_short | Results for Two-Level Designs with General Minimum Lower-Order Confounding |
| title_sort | results for two level designs with general minimum lower order confounding |
| url | http://dx.doi.org/10.1155/2015/163234 |
| work_keys_str_mv | AT zhimingli resultsfortwoleveldesignswithgeneralminimumlowerorderconfounding AT runchuzhang resultsfortwoleveldesignswithgeneralminimumlowerorderconfounding |