Studies in Efficient Design of Experiments

摘要本研究涉及实验设计中的几个问题。研究了分数因子设计的最优阻塞。分块是一种有效的方法，通过将实验单元分组成更均匀的块来提高实验效率。如何以最优的方式同时选择分数因子设计和阻塞方案是理论界和实践界都感兴趣的问题。提出了一种通过检测相互作用的混叠模式来选择良好阻塞方案的新准则。研究了在此准则下构建最优、高效设计的方法。并对未结案案件中尚未解决的问题进行了研究。另一个研究领域是正交阵列的投影特性。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。在这种效应稀疏性的假设下，重要的是考虑在小的因子子集上的投影。本文对正交阵列的投影特性进行了广泛的研究。还探讨了与搜索设计的联系。除因子设计外，采用近似理论的方法研究了随机块效应模型下的最优有效回归设计。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，主要是由于日本成功地将其应用于提高工业制造的质量和生产率。本研究的一个目标是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性的变化来源（如实验材料的异质性或日常环境变化）以提高精度时。由于通常只有少数潜在因素是真正重要的，本研究还研究了当只有少数因素是活跃的时候，一些常用设计的特性。另一项研究涉及最近的验光实验中出现的问题，该实验也具有工业应用价值。

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.