Studies in Efficient Design of Experiments

提案编号DMS-9704548 有效实验设计的研究 美国加州大学 摘要 本研究涉及实验设计中的几个问题。 研究了部分因子设计的最优区组。 分块是一种有效的方法，通过将实验单元分组为更均匀的块来提高实验效率。 如何同时最优地选择部分析因设计和区组方案是理论工作者和实践工作者都感兴趣的问题。 一个新的标准，选择良好的阻塞计划，通过检查的别名模式的相互作用制定。 在此准则下，构造最优和有效设计的方法进行了研究。 对非阻塞情形下的一些未解决的问题进行了研究。 另一个研究领域是正交表的投影性质。 在因子筛选中，通常在大量潜在因子中只有少数因子是活跃的。 在这种效应稀疏的假设下，考虑到因子的小子集上的投影是很重要的。 对正交表的投影性质进行了广泛的研究。 与搜索设计的连接也进行了探讨。 除析因设计外，本文还用近似理论的方法研究了随机区组效应模型下的最优和有效回归设计。 实验设计被广泛用于各种 科学和工业调查。 在工业实验中，通常需要研究大量的因素，但实验费用昂贵。 在这种情况下，所谓的部分析因设计，其中只有一小部分的所有可能的组合是特别有用的。 近年来，析因设计受到了相当大的关注，这主要是由于日本成功地应用析因设计来提高工业制造业的质量和生产率。 本研究的一个目的是研究有效设计的构建，以提取更多的信息，特别是当系统的变异来源（如实验材料的异质性或日常环境变化）需要消除，以提高精度。 由于经常 在众多的潜在因素中，只有少数因素是真正重要的，本研究还探讨了一些常用设计在只有少数因素起作用时的性质。 另一项研究涉及一个问题， 验光实验，这也有工业应用。

Proposal #DMS-9704548 Studies in Efficient Design of Experiments Ching-Shui Cheng University of California ABSTRACT This research involves several problems in experimental design. Optimal blocking of fractional factorial designs is studied. Blocking is an effective method for improving the efficiency of an experiment by grouping the experimental units into more homogeneous blocks. How to choose a fractional factorial design and a blocking scheme simultaneously in an optimal way is of interest to both theoreticians and practitioners. A new criterion for choosing good blocking schemes by examining the alias patterns of the interactions is formulated. Methods of constructing optimal and efficient designs under this criterion are investigated. Some unsolved problems in the unblocked case are also studied. Another area of research is the projection properties of orthogonal arrays. In factor screening, often only a few factors among a large pool of potential factors are active. Under such assumption of effect sparsity, it is important to consider projections onto small subsets of factors. An extensive study of the projection properties of orthogonal arrays is carried out. Connections with search designs are also explored. In addition to factorial designs, optimal and efficient regression designs under random block-effects models are studied by adopting the approach of approximate theory. 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 Japanese success in applying them to improve quality and productivity in industrial manufa cturing. One objective of 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. Since often only a few of the many potential factors are actually important, this research also looks into the properties of some commonly used designs when only a small number of factors are active. Another research involves a problem arising from a recent optometry experiment, which also has industrial applications.