Topics on Design of Experiments and Computer Experiments

实验设计是科学、工程和工业等许多领域中应用的一种有效和常用的研究技术。所处理的数据结构的类型与应用一样多种多样。本研究的目的是发展新的设计理论和方法，并提供有效的设计，以供实际使用的物理实验和计算机实验。该提案将解决与定性和定量因素的物理和计算机实验的设计和分析的关键问题。预计所提出的研究将导致新的进展，在设计理论和更好的实践中的实验。 在进行计算机实验时，选择尽可能均匀地覆盖设计区域的设计点已成为惯例。当关于哪种模型合适的先验信息或背景知识很少时，就会使用这些所谓的空间填充设计，并且输入可以设置为相应范围内的任何值。然而，先验信息或背景知识可能会建议响应面的一些特征，因此某些模型更合适。将引入顺序设计方法来生成包含这些信息或知识的设计。在许多应用中，因素本质上是定性的。如何设计和分析计算机实验，既要考虑定性因素，又要考虑定量因素，这是一个尚未完全解决的问题。该建议旨在为此类计算机实验开发新的设计方法。 部分因子设计是物理实验中应用最广泛的实验方案之一。该研究将为定性和定量输入因子的实验以及基于模型的设计构建有效的部分因子设计。介绍了因子筛选和响应面探索的新设计类别。提出了评估此类设计的标准。研究了新设计的统计性质和最优性。当某些双因子交互作用可忽略时，可变分辨率设计提供了一类很好的设计。本提案从各个方面系统地研究了此类设计。

Experimental design is an effective and commonly used technique in investigations for applications in many areas of science, engineering and industry. The types of data structures dealt with are as varied as the applications. The objectives of the proposed research are to develop new design theories and methodology with certain data structures and provide efficient designs for practical use in both physical experiments and computer experiments. The proposal will address the critical issues on the design and analysis of physical and computer experiments with both qualitative and quantitative factors. It is expected that the proposed research will lead to new advances in design theory and better practice in experimentation. In conducting computer experiments, it has become common practice to select the design points that cover a design region as uniformly as possible. These so-called space-filling designs are used when little a priori information or background knowledge is available about which model would be appropriate, and inputs can be set to any value in the respective ranges. However, prior information or background knowledge might suggest some features of the response surfaces and thus certain models are more appropriate. Sequential design approaches will be introduced to generate designs that incorporate such information or knowledge. In many applications, factors are qualitative by nature. The problem of how to design and analyze computer experiment with both qualitative and quantitative factors are not yet completely solved. This proposal aims to develop new design methodology for such computer experiments. Fractional factorial designs are among the most widely used experimental plans in physical experiments. The proposed research will construct efficient fractional factorial designs for experiments with both qualitative and quantitative input factors and model-based designs. New classes of designs for factor screening and response surface exploration are introduced. Criteria for assessing such designs are proposed. The statistical properties and optimality of new designs are studied. Designs of variable resolution provide a good class of designs when certain two-factor interactions are negligible. This proposal systematically studies such designs from various aspects.