Fractional Factorial Designs: Minimum Aberration and Related Topics

最小像差是选择分数因子设计的公认标准。本研究研究了几种不同设置下最小像差标准的变体，包括将实验单元分组到更均匀的块中以提高精度的块设计，以及在每个块中保持某些因素不变的分块设计。当一些因素需要比其他因素更大的实验单位时，或者当某些因素的影响不是主要兴趣，但它们被包括在实验中以研究它们与其他因素的相互作用时，就会出现分裂图。后者在质量改进的鲁棒参数设计中有着重要的应用。这些设置有自己的特殊功能，需要不同的最优性标准。现有的工作没有解决分裂图结构中存在两种不同错误的问题。本研究的最终目标是获得各种设置下最优设计结构的一般结果，并开发有用的算法来构建可以包含用户提供的先验知识和需求的设计。对于前者，首席研究员使用来自编码理论和有限射影几何的工具。最后，在新引入的广义最小像差准则下，研究了非规则设计，包括过饱和设计。实验设计广泛应用于各种科学和工业研究。在工业实验中，通常需要研究大量的因素，但实验的成本很高。在这种情况下，所谓的分数阶乘设计特别有用，其中只观察到所有可能组合的一小部分。近年来，因子设计受到了相当大的关注，主要是由于将其成功地应用于提高工业制造质量和生产率的实验中。本研究旨在研究有效设计的构建，以提取更多的信息，特别是当需要消除系统变异源（如实验材料的异质性或日常环境变化）以提高精度时。

Cheng, Ching-ShuiDMS-0071438AbstractMinimum aberration has been a well accepted criterion for choosing good fractional factorial designs. This research studies variants of the minimum aberration criterion in several different settings including block designs in which the experimental units are grouped into more homogeneous blocks to improve the precision, and split-plot designs in which some factors are held constant within each block. Split plots arise when some factors require larger experimental units than others, or when the effects of certain factors are not of major interest, but they are included in the experiment to study their interactions with other factors. The latter has a very important application to robust parameter designs in quality improvement. These settings have their own special features that call for different optimality criteria. Existing work did not address the issue that there are two different errors in split-plot structures. The ultimate goal of this research is to obtain general results on the structures of optimal designs in various settings, and to develop useful algorithms for constructing designs which can incorporate user-supplied prior knowledge and requirements. For the former, the Principal Investigator uses tools from coding theory and finite projective geometry. Finally, nonregular designs, including supersaturated designs, are studied under a newly introduced criterion of generalized minimum aberration.Experimental design is used extensively in a wide range of scientific and industrial investigations. In industrial experiments, often a large number of factors have to be studied, but the experiments are expensive to conduct. In this case, the so called fractional factorial designs, in which only a small fraction of all the possible combinations are observed, are particularly useful. In recent years, factorial designs have received considerable attention, mainly due to the success in applying them to conduct experiments for improving quality and productivity in industrial manufacturing. This research is to study the construction of efficient designs to extract more information, especially when systematic sources of variation (such as heterogeneity of experimental material or day-to-day environmental variations) need to be eliminated to improve the precision.