范围固定二三混水平扩充设计的均匀性
Uniformity of the Range-Fixed Level-Augmented Designs of Mixed Two and Three Levels
摘要: 扩充设计在生物制药，化学化工等领域运用广泛。Gao在2020年构造了一类范围固定二三混水平扩充设计。本文从设计的均匀性角度出发，研究了范围固定水平扩充设计在可卷型L2-偏差下的均匀型。首先建立水平扩充设计的可卷型L2-偏差与二水平基石设计的相遇数之间的解析联系，并获得其下界。其次基于距离分布和字长型模式分别建立水平扩充设计与基石设计之间的解析联系。最后通过数值例子解释所获得理论结果。
Abstract: Augmented designs are widely applied in biological pharmacy, chemistry and chemical engineering, and so on. Gao constructed a class of range-fixed level-augmented designs in 2020. The article, starting from the perspective of design uniformity, investigates the uniformity of range-fixed level-augmented designs under the condition of wrap L2-discrepancy. Firstly, the analytical connection between the wrap L2-discrepancy of the range-fixed level-augmented designs of mixed two and three levels and the coincidence number of the footstone-designs with two levels is established, and its lower bound is obtained. Secondly, based on distance distribution and wordlength pattern, the analytical connections between the level-augmented designs and the footstone-designs are built respectively. Finally, the obtained theoretical results are explained by some numerical examples.
文章引用：熊烽景, 肖宇佳. 范围固定二三混水平扩充设计的均匀性[J]. 应用数学进展, 2024, 13(11): 4813-4822. https://doi.org/10.12677/aam.2024.1311463

参考文献

[1] Gupta, V.K., Singh, P., Kole, B. and Parsad, R. (2010) Addition of Runs to a Two-Level Supersaturated Design. Journal of Statistical Planning and Inference, 140, 2531-2535. [Google Scholar] [CrossRef] 
[2] Gupta, V.K., Chatterjee, K., Das, A. and Kole, B. (2012) Addition of Runs to an S-Level Supersaturated Design. Journal of Statistical Planning and Inference, 142, 2402-2408. [Google Scholar] [CrossRef] 
[3] Qin, H., Chatterjee, K. and Ghosh, S. (2015) Extended Mixed-Level Supersaturated Designs. Journal of Statistical Planning and Inference, 157, 100-107. [Google Scholar] [CrossRef] 
[4] 郑春玮. 添加新因子情形下超饱和设计的扩充方法[D]: [硕士学位论文]. 天津: 南开大学, 2021.
[5] Qin, H., Gou, T. and Chatterjee, K. (2016) A New Class of Two-Level Optimal Extended Designs. Journal of the Korean Statistical Society, 45, 168-175. [Google Scholar] [CrossRef] 
[6] Gou, T., Qin, H. and Chatterjee, K. (2017) A New Extension Strategy on Three-Level Factorials under Wrap-Around L2-Discrepancy. Communications in Statistics—Theory and Methods, 46, 9063-9074. [Google Scholar] [CrossRef] 
[7] Gou, T., Qin, H. and Chatterjee, K. (2018) Efficient Asymmetrical Extended Designs under Wrap-Around L2-Discrepancy. Journal of Systems Science and Complexity, 31, 1391-1404. [Google Scholar] [CrossRef] 
[8] Yang, F., Zhou, Y. and Zhang, A. (2019) Mixed-Level Column Augmented Uniform Designs. Journal of Complexity, 53, 23-39. [Google Scholar] [CrossRef] 
[9] Liu, J., Ou, Z., Hu, L. and Wang, K. (2018) Lee Discrepancy on Mixed Two-and Three-Level Uniform Augmented Designs. Communications in Statistics—Theory and Methods, 48, 2409-2424. [Google Scholar] [CrossRef] 
[10] 雷轶菊, 欧祖军, 赵国喜. 混水平列扩充设计的混偏差的下界[J]. 数学物理学报, 2021, 41(3): 882-891.
[11] Wang, H., He, D., Tan, N., Wang, W., Wang, J., Dong, H., et al. (2010) Note: An Anvil-Preformed Gasket System to Extend the Pressure Range for Large Volume Cubic Presses. Review of Scientific Instruments, 81, Article ID: 166102. [Google Scholar] [CrossRef] [PubMed]
[12] Dilipkumar, M., Rajasimman, M. and Rajamohan, N. (2011) Application of Statistical Design for the Production of Inulinase by Streptomyces sp. Using Pressmud. Frontiers of Chemical Science and Engineering, 5, 463-470. [Google Scholar] [CrossRef] 
[13] Gao, Y., Yi, S. and Zhou, Y. (2021) Level-Augmented Uniform Designs. Statistical Papers, 63, 441-460. [Google Scholar] [CrossRef] 
[14] Gao, Y., Yi, S. and Zhou, Y. (2022) Maximin l1-Distance Range-Fixed Level-Augmented Designs. Statistics & Probability Letters, 186, Article ID: 109470. [Google Scholar] [CrossRef] 
[15] Chatterjee, K., Li, Z. and Qin, H. (2012) Some New Lower Bounds to Centered and Wrap-Round-Discrepancies. Statistics & Probability Letters, 82, 1367-1373. [Google Scholar] [CrossRef] 

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