Studies in Fractional Factorial Design

研究者研究了分数因子设计理论中的几个问题。有限射影几何中最近的一些结果为在某些重要情况下描述分辨率IV的正则分数阶乘设计的结构提供了有力的工具。一个主要的研究活动是扩展这些工具并应用它们来发展一个综合理论，以确定和构建最小像差准则下分辨率IV的最佳规则分数因子设计。结果进一步推广到不规则设计和将实验单元划分为更均匀的块以提高精度的情况。不规则设计的研究为构造正交三强度阵列提供了新的方法。研究了多层次设计的隐投影特性。在效应稀疏性假设下，在识别出少量的有效因子后，一个在小因子子集上有良好投影的设计可以提供有用的信息。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，只能观察到所有可能组合中的一小部分，如何选择一个好的部分是一个重要的问题。近年来，这种分数因子设计受到了相当大的关注，主要是因为将其成功地应用于工业制造中提高质量和生产率的实验。本研究旨在研究有效设计的构建，以提取更多的信息。实验者将受益于丰富的新的和好的设计来源，并将能够更有效地运行他们的实验。更好的工业实验可以提高产品质量，降低生产成本。

The investigator studies several problems in the theory of fractional factorial design. Some recent results in finite projective geometry provide powerful tools for characterizing the structures of regular fractional factorial designs of resolution IV in certain important cases. One major research activity is to expand these tools and apply them to develop a comprehensive theory for the determination and construction of optimal regular fractional factorial designs of resolution IV under the criterion of minimum aberration. The results are further extended to nonregular designs and the situation where the experimental units are divided into more homogeneous blocks to improve precision. The research on nonregular designs provides new methods for constructing orthogonal arrays of strength three. Hidden projection properties of multi-level designs are also investigated. Under the assumption of effect sparsity, a design with good projections onto small subsets of factors can provide useful information after the small number of active factors have been identified.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, only a small fraction of all the possible combinations can be observed, and how to choose a good fraction is an important issue. In recent years, such fractional 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. Experimenters will be benefited by having a rich source of new and good designs, and will be able to run their experiments more efficiently. Better industrial experiments can improve the quality of products and reduce production cost.