Topics on Design of Experiments and Computer Experiments

在许多科学、工程和工业领域的应用研究中，实验设计是一种有效和常用的技术。所处理的数据结构类型与应用程序一样多种多样。这项研究的目的是开发具有一定数据结构的新的设计理论和方法，并为物理实验和计算机实验的实际使用提供有效的设计。该提案将涉及设计和分析具有定性和定量因素的物理和计算机实验的关键问题。预计拟议的研究将导致设计理论的新进步和更好的实验实践。 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一种常见的做法。这些所谓的空间填充设计是在关于哪种模型合适的先验信息或背景知识很少的情况下使用的，并且输入可以设置为各自范围内的任何值。然而，先验信息或背景知识可能会暗示响应面的某些特征，因此某些模型更合适。将采用顺序设计方法来生成包含此类信息或知识的设计。在许多应用中，因素本质上是定性的。如何设计和分析既有定性因素又有定量因素的计算机实验，这一问题尚未完全解决。这项建议旨在为此类计算机实验开发新的设计方法。 部分析因设计是物理实验中应用最广泛的实验方案之一。这项研究将为具有定性和定量输入因素的实验和基于模型的设计构建有效的部分析因设计。介绍了用于因子筛选和响应面探索的新设计类。提出了评价此类设计的标准。研究了新设计的统计性质和最优性。当某些双因素相互作用可以忽略时，可变分辨率的设计提供了一类很好的设计。本方案从多个方面对此类设计进行了系统研究。

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.