Design and Analysis of Experiments for Screening, Optimization and Robustness

摘要：本课题旨在研究实验的三个重要方面：筛选、优化和鲁棒性。第一部分提出了一种利用单一设计和实验来实现因子筛选和响应面探索的新方法。这与标准响应面方法不同，标准响应面方法采用单独的设计进行因素筛选和响应面探索。提出了新的概念、理论和分析方法，包括两阶段分析和投影效率准则。将研究四个问题：(i)规则设计中合格预测的理论，（ii）最优非规则设计的组合和算法构建，（iii）与最大估计能力准则的联系，（iv）响应面探索对因素筛选错误的敏感性和贝叶斯替代两阶段分析。第二节解决了一个基本的和实际重要的问题，优化分配的因素，列的设计矩阵。现有的工作只能应用于规则的分数因子设计和非规则的双水平因子设计。通过定义b污染标准并采用克罗内克演算，我们提出了一种可以处理非常一般设计的方法。要研究三个问题：(i)寻找污染项的表达式，（ii）根据互补设计进行表征，（iii）对阻塞设计的扩展。第三节讨论了稳健参数设计实验方案的最佳选择问题。当实验成本与总运行大小成正比时，交叉阵列格式可能相当昂贵，而单阵列格式成为一个有吸引力的选择。一个重要的问题是如何选择最优的单个数组，并根据什么标准？利用效应排序原理，我们提出了新的标准，并使用它们来选择最优的单阵列。实验的统计设计和分析是科学和工程调查中常用的有效工具。它在制造业、电子、材料、农业和能源等许多研究和开发领域产生了重大影响。它将继续在方法和理论发展方面的创新以及在生物技术、药物发现和信息技术等新领域的应用方面作出重要贡献。使用拟议的新方法的潜在收益包括节省实验运行时间，发现新的/更好的工程设计和产品。因子分配的结果将为因子分配提供明确的指导方针，并大大改进目前武断且往往不理想的分配做法。参数设计已成为减少变异、改进产品和工艺的主要工具。拟议的工作将为进行这类实验开发新的、更经济和更有效的技术。

Abstract:The goal of this proposal is to study three important aspects of experimentation: screening, optimization and robustness. Section I proposes a novel approach to factor screening and response surface exploration by using a single design and experiment to achieve both objectives. This differs from the standard response surface methodology, which employs separate designs for factor screening and for response surface exploration. New concepts, theory and analysis are proposed, which include a two-stage analysis and a projection-efficiency criterion. Four problems are to be studied: (i) a theory for eligible projections in regular designs, (ii) combinatorial and algorithmic construction of optimal nonregular designs, (iii) connection with the maximum estimation capacity criterion, (iv) sensitivity of response surface exploration to errors in factor screening and a Bayesian alternative to the two-stage analysis. Section II addresses a fundamental and practically important issue of optimal assignment of factors to columns of a design matrix. Existing work can only be applied to regular fractional factorial designs and nonregular designs with two-level factors. By defining a B-contamination criterion and employing the Kronecker calculus, we propose an approach that can handle very general designs. Three problems are to be studied: (i) Finding expressions for the contamination terms, (ii) characterization in terms of complementary designs, (iii) extensions to blocked designs. Section III addresses the issue of optimal selection of experimental plans for robust parameter design. When the experimental cost is proportional to the total run size, the cross array format can be quite costly and the single array format becomes an attractive option. An important question is how to select single arrays optimally and according to what criteria? By using an effect ordering principle, we propose to define new criteria and use them to select optimal single arrays. Statistical design and analysis of experiments is an effective and commonly used tool in scientific and engineering investigation. It has made significant impact in many areas of research and development such as manufacturing, electronics, materials, agriculture and energy. It will continue to make important contributions by innovation in methodological and theoretical development and applications in new areas such as biotechnology, drug discovery, and information technology. Potential gains from using the proposed new methods include savings in experimental runs, experimentation time, and discovery of new/better engineering designs and products. The results on factor assignment will provide clear guidelines on the assignment of factors and a substantial improvement over the prevailing practice of making arbitrary and often suboptimal assignment. Parameter design has become a major tool for variation reduction and product and process improvement. The proposed work will develop new and more economical and efficient techniques for conducting such experiments.