Design and Analysis of Experiments for Screening, Optimization and Robustness

翻译后摘要：本建议的目标是研究实验的三个重要方面：筛选，优化和鲁棒性。第一节提出了一种新的方法，因子筛选和响应面探索使用一个单一的设计和实验，以实现这两个目标。这不同于标准的响应面方法，该方法采用单独的设计进行因子筛选和响应面探索。 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。 四个问题进行了研究：（一）合格的预测在定期设计的理论，（二）组合和算法建设的最佳非定期设计，（三）连接的最大估计能力标准，（四）灵敏度的响应面探索错误的因素筛选和贝叶斯替代的两阶段分析。第二节解决了一个基本的和实际上重要的问题，最佳分配的因素列的设计矩阵。现有的工作仅适用于正则部分因子设计和两水平因子的非正则设计。通过定义一个B-污染标准和采用克罗内克演算，我们提出了一种方法，可以处理非常一般的设计。 有三个问题要研究：（i）找到污染项的表达式，（ii）在互补设计方面的表征，（iii）扩展到阻塞设计。第三节讨论了稳健参数设计实验计划的最佳选择问题。 当实验成本与总运行大小成比例时，交叉阵列格式可能相当昂贵，并且单一阵列格式成为有吸引力的选择。 一个重要的问题是如何选择最佳的单阵列，根据什么标准？通过使用效果排序原则，我们建议定义新的标准，并使用它们来选择最佳的单个阵列。 试验统计设计与分析是科学和工程调查中常用的有效工具。它在许多研究和开发领域产生了重大影响，如制造业，电子，材料，农业和能源。它将继续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作出重要贡献。使用所提出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。系数分配的结果将为系数分配提供明确的指导，并大大改善目前任意分配和往往不理想的做法。 参数化设计已成为减少偏差、改进产品和过程的主要工具。拟议的工作将开发新的和更经济和有效的技术进行这种实验。

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.