Studies in Fractional Factorial Design

这个项目是关于如何选择好的分数因子设计。最小像差是选择所谓的规则分数因子设计的公认的最优准则。利用有限射影几何和编码理论的结果，研究者继续他对最小像差设计的确定，特别是分辨率IV的设计。分辨率IV设计具有良好的结构和良好的统计特性，但在过去没有得到很好的研究，部分原因是缺乏良好的结构理论。最近有限射影几何的一些结果为理解分辨率IV设计的结构和帮助解决构建最优和有效设计的问题提供了强大的工具。研究者还研究了强度3的新正交阵列的构建，这是分辨率IV的规则设计的非规则对应物。最后，研究者解决了涉及多个处理阶段的设计实验的几个问题，从最优性标准的制定到良好设计的理论和算法构建。实验的统计设计广泛应用于科学和工业调查中。实验需要合理设计，以较低的成本提取有效的信息。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的因素组合中的一小部分，如何选择一个好的部分是一个重要的问题。这种设计的研究受到了相当大的关注，主要是因为在提高工业制造质量和生产率的实验中取得了成功。本研究旨在研究有效设计的构建，以提取更多的信息。更好的工业实验可以提高产品质量，降低生产成本。实验者将受益于拥有更多可供他们使用的新的和好的设计，并且能够更有效地进行他们的实验。例如，提议的活动之一是涉及在集成电路制造等工业应用中经常出现的多个处理阶段的实验。

This project is concerned with how to choose good fractional factorial designs. Minimum aberration is a well accepted optimality criterion for selecting the so called regular fractional factorial designs. Using results from finite projective geometry and coding theory, the investigator continues his work on the determination of minimum aberration designs, in particular, those of resolution IV. Resolution IV designs have nice structures and good statistical properties, but have not been well studied in the past, partly due to the lack of a good structural theory. Some recent results in finite projective geometry provide powerful tools for understanding the structures of resolution IV designs and for helping solve the problem of constructing optimal and efficient designs. The investigator also studies the construction of new orthogonal arrays of strength three, the nonregular counterpart of regular designs of resolution IV. Finally, the investigator addresses several issues of designing experiments that involve multiple processing stages, ranging from formulation of optimality criteria to theoretical and algorithmic construction of good designs.Statistical design of experiments is used in a wide range of scientific and industrial investigations. Experiments need to be properly designed so that valid information can be extracted at a lower cost. 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 of the factors can be observed, and how to choose a good fraction is an important issue. The study of such designs has received considerable attention, mainly due to the success in applications to experiments for improving quality and productivity in industrial manufacturing. This research is to study the construction of efficient designs to extract more information. Better industrial experiments can improve the quality of products and reduce production cost. Experimenters will be benefited by having a greater repertoire of new and good designs at their disposal, and will be able to run their experiments more efficiently. For example, one of the proposed activities is concerned with experiments with multiple processing stages which often arise in industrial applications such as the fabrication of integrated circuits.