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...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。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.展开更多
文摘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。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.
