| Minimum secondary aberration fractional factorial split-plot designs in terms of consulting designs |
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| 引用本文： | AI Mingyao & ZHANG Runchu Key Laboratory of Pure and Applied Mathematics,School of Mathematical Sciences,Peking University,Beijing 100871,China Key Laboratory of Pure Mathematics and Combinatorics and School of Mathematical Sciences,Nankai University,Tianjin 300071,China. Minimum secondary aberration fractional factorial split-plot designs in terms of consulting designs[J]. 中国科学A辑(英文版), 2006, 49(4): 494-512. DOI: 10.1007/s11425-006-0494-x |
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| 作者姓名： | AI Mingyao & ZHANG Runchu Key Laboratory of Pure and Applied Mathematics School of Mathematical Sciences Peking University Beijing 100871 China Key Laboratory of Pure Mathematics and Combinatorics and School of Mathematical Sciences Nankai University Tianjin 300071 China |
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| 作者单位： | AI Mingyao & ZHANG Runchu Key Laboratory of Pure and Applied Mathematics，School of Mathematical Sciences，Peking University，Beijing 100871，China Key Laboratory of Pure Mathematics and Combinatorics and School of Mathematical Sciences，Nankai University，Tianjin 300071，China |
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| 摘 要： | It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.
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| 收稿时间： | 2004-11-30 |
| 修稿时间： | 2005-10-19 |
Minimum secondary aberration fractional factorial split-plot designs in terms of consulting designs |
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| Al Mingyao,ZHANG Runchu. Minimum secondary aberration fractional factorial split-plot designs in terms of consulting designs[J]. Science in China(Mathematics), 2006, 49(4): 494-512. DOI: 10.1007/s11425-006-0494-x |
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| Authors: | Al Mingyao ZHANG Runchu |
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| Affiliation: | 1. Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
2. Key Laboratory of Pure Mathematics and Combinatorics and School of Mathematical Sciences, Nankai University, Tianjin 300071, China |
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| Abstract: | It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs. |
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| Keywords: | coding theory consulting design minimum secondary aberration fractional factorial split-plot design projective geometry wordlength pattern |
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