两水平U-型设计的扩大设计在投影加权对称偏差下的均匀性

Uniformity of Combined Two-level U-type Designs Under Projection Weighted Symmetric L2-discrepancy

均匀设计以其稳健和使用方便、灵活的特性而广受欢迎.为获得实验目标区域内散布均匀的设计点集,不同的均匀度量标准相继被提出.目前被广泛应用的有中心化L_(2)-偏差、可卷型L_(2)-偏差、混合偏差等.对称化L_(2)-偏差具有更好的几何性质,但受限于投影均匀性差的缺陷,使用范围十分有限.为了改进对称化L_(2)-偏差的低维投影均匀性,基于指数加权方式的投影加权对称化L_(2)-偏差的概念被提出,加权后的对称化L_(2)-偏差既能保留原偏差的各种优良性质,同时有效克服原来的缺陷并有更优异的表现.折叠翻转是构造因子设计时非常有用的技巧.本文利用投影加权对称偏差来作为评价折叠翻转方案的最优性准则,得到了两水平U-型设计在一般折叠翻转方案下扩大设计的投影加权对称偏差的下界,该下界可以作为寻找最优折叠翻转方案的基准.

The uniform designs are accepted widely because of its robust and easy to use,fexible characteristics.In order to distribute the points evenly in the experimental domain,many criteria(L_(2)-discrepancy)have been forwarded to measure the uniformity of the design array.At present,centered L_(2)-discrepancy,wrap-around L_(2)-discrepancy,mixed discrepancy and so on are widely used.Symmetric L_(2)-discrepancy has better geometric sense,but the poor performance at projection uniformity limits the use of SD.To refine the projection properties of SD,a projection weighted SD is proposed.The SD was exponentially weighted.The projection weighted SD can retain the excellent properties of the original discrepancy,and overcome the original defects effectively,and has better performance.The foldover is a useful technique in construction of factorial designs.In this paper,the projection weighted symmetric L_(2)-discrepancy is used as the optimality criterion to evaluate the quality of the foldover scheme.Lower bounds for projection weighted symmetric L2-discrepancy on combined two-level U-type designs under a general foldover plan are obtained,which can be used as a benchmark for searching optimal foldover plans.