Design and Analysis of Experiments for Screening, Optimization and Robustness

摘要：本方案的目标是研究实验的三个重要方面：筛选、优化和稳健性。第一节提出了一种新的方法，通过使用单一的设计和实验来实现这两个目标的因素筛选和响应面探索。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，包括两阶段分析和投影效率准则。将研究四个问题：(I)规则设计中合格投影的理论，(Ii)最优非规则设计的组合和算法构造，(Iii)与最大估计能力准则的联系，(Iv)响应面探索对因素筛选中的错误的敏感性，以及两阶段分析的贝叶斯替代方案。第二节讨论了一个基本的和实际重要的问题，即对设计矩阵的各列进行因素的最佳分配。已有的工作只能应用于具有两水平因子的正则部分析因设计和非正则设计。通过定义B污染准则和使用Kronecker演算，我们提出了一种可以处理非常一般的设计的方法。将研究三个问题：(I)寻找污染项的表达式，(Ii)关于互补设计的表征，(Iii)对分块设计的扩展。第三节讨论稳健参数设计的试验方案的最佳选择问题。当实验成本与总游程大小成正比时，交叉阵列格式可能相当昂贵，而单一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最佳地选择单个阵列，并根据什么标准？通过使用效果排序原则，我们建议定义新的准则，并使用它们来选择最优的单阵。试验统计设计与分析是科学与工程研究中一种有效而常用的工具。它在制造、电子、材料、农业和能源等多个研发领域产生了重大影响。它将通过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，继续作出重要贡献。使用拟议的新方法的潜在收益包括节省实验运行、实验时间，以及发现新的/更好的工程设计和产品。关于因素分配的结果将为分配因素提供明确的指导方针，并大大改善目前进行任意分配和往往是次优分配的做法。参数设计已成为减少偏差、改进产品和工艺的主要工具。这项拟议的工作将开发进行此类实验的新的、更经济和高效的技术。

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.