Construction and Analysis of Nonregular and Supersaturated Designs

非规则和过饱和设计常用于筛选实验，其目标是在大量候选因子中识别少数主导因子。 本建议的目标是构建高效的非规则和过饱和设计，并开发新的方法来分析这些实验的数据。 给出了有限环上线性码构造非正则设计的一般方法。 这些非规则设计在像差、分辨率和投射率方面比文献中现有的设计具有更好的统计特性。 利用编码理论中等重码的概念研究过饱和设计。线性规划技术被用来建立新的上限的列数在一个过饱和设计。 新的算法被开发用于构造有效的非正则和过饱和设计以供实际使用。 本文提出了一种用于筛选非正则和过饱和设计的有效效应的图解法和自动法。 仿真结果表明，该方法与文献中已有的方法相比，具有较好的性能，并且在估计模型大小方面更有效。实验的统计设计和分析已广泛应用于科学和工业研究与开发。 随着科学技术的发展，研究人员越来越有兴趣和能力通过计算机模拟和高性能计算来研究大规模系统。 两个基本问题是如何设计一个有效的实验，以及如何正确地分析实验数据。 本研究的目的是开发新的方法来构建最优设计和分析这样的实验。 新的高效非规则和过饱和设计已经构建，并将在网上提供，以广泛和快速传播。所提出的研究结果可以迅速吸收到研究生课程的实验设计和分析。该建议采用了数学和计算工具的组合，并强调了信息理论和设计理论之间的重要跨学科联系。 该研究将在设计理论和数据分析实践方面带来显著的新进展。

Nonregular and supersaturated designs are commonly used in screening experiments where the goal is to identify a few dominant factors among a large number of candidate factors. The objectives of this proposal are to construct efficient nonregular and supersaturated designs and to develop new methodology for analyzing data from such experiments. A general method is introduced for constructing nonregular designs from linear codes over a finite ring. These nonregular designs have better statistical properties than the existing designs in the literature in terms of aberration, resolution and projectivity. The concept of constant weight codes in coding theory is used for studying supersaturated designs. Linear programming technique is used to establish new upper bounds on the number of columns in a supersaturated design. New algorithms are developed for constructing efficient nonregular and supersaturated designs for practical use. A graphical procedure and an automatic procedure are proposed for screening active effects for nonregular and supersaturated designs. Simulation shows that this method performs well compared to existing methods in the literature and is more efficient at estimating the model size.Statistical design and analysis of experiments have been widely used in scientific and industrial research and development. As science and technology have advanced to a higher level, investigators are becoming more interested in and capable of studying large-scale systems via computer simulations and high-performance computing. Two fundamental questions are how to design an efficient experiment and how to analyze the data properly from the experiment. This proposed research aims at developing novel methods for constructing optimal designs and for analyzing such experiments. New efficient nonregular and supersaturated designs are constructed and will be made available online for broad and quick dissemination. The results of the proposed research can be quickly assimilated into graduate courses on design and analysis of experiments. This proposal employs a combination of mathematical and computational tools and emphasizes an important interdisciplinary connection between information theory and design theory. The proposed research will lead to remarkable new advances in design theory and better practice in data analysis.