Studies in Fractional Factorial Design

作者研究了部分析因设计理论中的几个问题。在某些重要情况下，有限射影几何中的一些最新结果为刻画正则分式析因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种综合的理论，以确定和构造在最小像差标准下分辨率为IV的最优正则部分析因设计。结果进一步推广到非规则设计和实验单元被分成更均匀的区块以提高精度的情况。非正则设计的研究为构造强度三正交表提供了新的方法。还研究了多水平设计的隐投影性质。在效应稀疏性的假设下，一个在小因素子集上有良好投影的设计可以在识别出少量的活跃因素后提供有用的信息。实验设计被广泛应用于科学和工业研究。在工业实验中，往往要研究大量的因素，但进行实验的费用很高。在这种情况下，所有可能的组合中只有一小部分可以观察到，如何选择一个好的比例是一个重要的问题。近年来，这种部分析因设计受到了相当大的关注，这主要是因为它们在工业制造中成功地应用于提高质量和生产率的实验。本研究旨在研究如何构建高效的设计，以提取更多的信息。实验者将受益于拥有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。做好工业试验，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.