Nonregular Designs: Classification, Optimality and Construction

提案ID：论文题目：非正则设计：分类、最优性和构造非正则设计，如Plackett-Burman设计和许多其他正交表，由于其运行规模经济和灵活性，在实践中得到广泛应用。 然而，许多常用的非规则设计不是最优的。与近年来研究得比较深入的正则设计不同，非正则设计的理论和构造还很原始，也很迫切。本研究的目标是分类和构造最优非正则设计。在分类部分，提出了一般框架和新的方法来研究以下重要问题：估计能力，设计效率，投影特性，和混叠结构。在构造部分，提出了新的方法和算法，用于构造各种情况下的最优非正则设计，包括过饱和设计和区组设计。 编码理论将被用来建立多水平和混合水平非正则设计的一般结果。实验设计是科学研究中一种有效和常用的工具。在上个世纪，它在许多研究领域，包括农业、生物学、制造业和高科技产业，产生了巨大的影响，并将在可预见的未来继续发挥作用。现有的研究大多集中于规则设计的研究，而本文的研究重点是非规则设计的研究。非规则设计由于其运行规模经济性和灵活性而在实践中得到广泛应用，例如用于过程改进和质量控制的田口设计。 然而，重要的是要注意，许多常用的非规则设计不是最优的。与近年来研究得比较深入的正则设计不同，非正则设计的理论和构造还很原始，也很迫切。本研究的目标是分类和构造最优非正则设计。 这个建议强调了一个重要的跨学科之间的联系纠错码和阶乘设计。所提出的工作将发展的基本结果为非正规设计，并将导致显着的新进展，设计理论和更好的实践中的实验。

Proposal ID: DMS-0204009PI: Hongquan XuTitle: Nonregular designs: Classification, optimality and constructionNonregular designs, such as Plackett-Burman designs and many other orthogonal arrays, are widely used in practice due to their run size economy and flexibility. However, many commonly used nonregular designs are not optimal. Unlike regular designs, which have been studied thoroughly in recent years, theory and construction of nonregular designs are still very primitive and urgently needed. The objectives of this proposed research are to classify and construct optimal nonregular designs. In the classification part, general frameworks and novel approaches are proposed for investigating the following important issues: estimation capacity, design efficiency, projection properties, and aliasing structure. In the construction part, novel methods and algorithms are proposed for constructing optimal nonregular designs for a wide variety of situations, including supersaturated designs and block designs. Coding theory will be employed to develop general results for multi-level and mixed-level nonregular designs.Experimental design is an effective and commonly used tool in scientific investigation. Over the last century, it has made tremendous impact in many areas of research, including agriculture, biology, manufacturing and high-tech industries, and will continue to do so for the foreseeable future. While most of the existing research has concentrated on the study of regular designs, this proposed research focuses on the study of nonregular designs. Nonregular designs are widely used in practice due to their run size economy and flexibility, for example, Taguchi designs for process improvement and quality control. However, it is important to note that many commonly used nonregular designs are not optimal. Unlike regular designs, which have been studied thoroughly in recent years, theory and construction of nonregular designs are still very primitive and urgently needed. The objectives of this proposed research are to classify and construct optimal nonregular designs. This proposal emphasizes an important interdisciplinary connection between error-correcting codes and factorial designs. The proposed work will develop fundamental results for nonregular designs, and will lead to remarkable new advances in design theory and better practice in experimentation.