Most of existing augmented designs are to add some runs in the follow-up stages. While in many cases, the level of factors should be augmented and these augmented designs are called level-augmented designs. According to whether the experimental domain is extended or not, they can be divided into range-extended and range-fixed level-augmented designs. For different types of initial designs, the symmetrical and asymmetrical level-augmented designs are discussed, respectively. Based on the property of robustness, a uniformity criterion is a suitable choice to obtain an optimal level-augmented design when the model is unknown. In this paper, the wrap-around \(L_2\)-discrepancy (WD) is chosen as the uniformity measure. We give the expressions and the tight lower bounds of WD of level-augmented designs under some special parameters. A method to construct a special case of symmetrical level-augmented designs is given. Some examples and level-augmented uniform designs are also provided.

大多数现有的增强设计都是在后续阶段添加一些运行。而在很多情况下，因子的水平应该被增强，这些增强的设计被称为水平增强设计。根据实验域是否扩展，可分为范围扩展设计和范围固定水平增强设计。对于不同类型的初始设计，分别讨论了对称和非对称水平增强设计。基于稳健性的特性，当模型未知时，均匀性准则是获得最优水平增强设计的合适选择。在本文中，环绕\(L_2\)-discrepancy (WD) 被选为均匀性度量。我们给出了在一些特殊参数下水平增强设计的表达式和 WD 的紧下界。给出了一种构造对称水平增强设计特例的方法。还提供了一些示例和级别增强的统一设计。