Studies in Factorial and Response Surface Designs

这项建议的目标是发展新的设计理论和方法，用于因素筛选和响应面探索，并为实际使用构建有效的析因设计和复合设计。该方案的第一部分研究通过四进制码构造的部分析因设计。这些设计往往具有复杂的混叠结构，并引入了一种新的方法来寻找因素之间的定义关系。发展了获得诸如分辨率和字长图案等重要设计特性的一般理论。提出了构造最优设计的新方法和新算法。这些设计在像差、分辨率和投影性方面比文献中现有的设计具有更好的统计特性。第二部分研究了由两水平析因设计和三水平正交表组成的基于正交表的组合设计。这些组合设计具有许多理想的特征，对于因素筛选和响应面建模是有效的。它们可以在单个实验中使用，也可以在连续实验中使用。有效的组合设计是为实际使用而构造的，它们被证明比中心组合设计和其他现有的设计更好。该方案综合运用了数学、编码理论和计算工具来解决各种重要问题，如设计特性和施工方法。实验设计和分析是科学研究和工业应用中的一种有效和常用的工具。析因设计是具有成本效益的实验计划，用于从变量池中确定重要因素；响应面设计对于理解过程或系统和建立经验模型至关重要。这种设计已经成功地应用于工业制造中，以提高质量和生产率。最近的新应用包括在加州大学洛杉矶分校进行的生物医学实验，以寻找有效的抗病毒药物组合或药物鸡尾酒来治疗单纯疱疹病毒和水泡性口炎病毒。这项建议旨在开发新的方法来构造新的有效的析因设计和响应面设计。建议的研究结果可以很快被吸收到本科生和研究生的课程中，以设计和分析实验来丰富课程。建议的方法和设计可应用于广泛的应用领域，包括工程、物理和化学科学、医学和生命科学。所提出的研究可以更好地指导实验实践，有助于缩短研究时间，大大降低实验成本。

The objectives of this proposal are to develop new design theories and methodology for factor screening and response surface exploration and to construct efficient factorial and composite designs for practical use. The first part of this proposal studies fractional factorial designs constructed via quaternary codes. These designs often have a complex aliasing structure and a novel approach is introduced for finding defining relations among factors. A general theory is developed for obtaining important design properties such as resolution and wordlength pattern. Novel methods and algorithms are proposed for constructing optimal designs. These designs are shown to have better statistical properties than existing ones in the literature in terms of aberration, resolution and projectivity. The second part studies orthogonal array-based composite designs that consist of a two-level factorial design and a three-level orthogonal array. These composite designs have many desirable features and are effective for factor screening and response surface modeling. They can be used in a single experiment or in a sequential experiment. Efficient composite designs are constructed for practical use and they are shown to be better than central composite designs and other existing designs. This proposal employs a combination of mathematical, coding-theoretical and computational tools to tackle various important issues such as design properties and construction methods. Experimental design and analysis is an effective and commonly used tool in scientific investigations and industrial applications. Factorial designs are cost-efficient experimental plans for identifying important factors from a pool of variables; response surface designs are crucial for understanding a process or system and building empirical models. Such designs have been successfully used in industrial manufacturing for improving quality and productivity. Recent novel applications include biomedical experiments conducted at UCLA in order to find effective antiviral drug combinations or drug cocktails for treating herpes simplex virus and vesicular stomatitis virus. This proposal aims at developing novel methodology for constructing new efficient factorial and response surface designs. The results of the proposed research can be quickly assimilated into undergraduate and graduate courses on design and analysis of experiments for course enrichment. The proposed methods and designs can be applied in a wide variety of fields of application, including engineering, physical and chemical sciences, medicine and life sciences. The proposed research can lead to better practice in experimentation and help shorten investigation time and reduce experimental cost tremendously.