Topics on Design of Experiments and Computer Experiments

实验设计在科学、工程和工业的许多领域都是一种有效和常用的研究技术。所处理的数据结构类型与应用程序一样多种多样。提出的研究目标是发展具有特定数据结构的新设计理论和方法，并为物理实验和计算机实验的实际应用提供有效的设计。该提案将涉及物理和计算机实验的设计和分析的关键问题，包括定性和定量因素。期望所提出的研究能够在设计理论和实验实践方面取得新的进展。**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。这些所谓的空间填充设计是在几乎没有先验信息或背景知识可用的情况下使用的，并且可以将输入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提示响应面的某些特征，因此某些模型更合适。序贯设计方法将被引入以产生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。如何从定性和定量两个方面设计和分析计算机实验的问题还没有完全解决。本提案旨在为此类计算机实验开发新的设计方法。**分数因子设计是物理实验中应用最广泛的实验方案之一。本研究将建构有效的分数因子实验设计，包括定性和定量输入因子及基于模型的设计。介绍了因子筛选和响应面探测的新型设计。提出了评估这类设计的标准。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不计时，可变分辨率的设计提供了一类很好的设计。本文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.