Constructing Optimal Factorial Designs for Multiple Groups of Factors: Theory, Methods and Applications

构建多组因子的最佳因子设计：理论、方法和应用

• 批准号: 0405694
• 负责人: Yu Michael Zhu
• 金额: $ 7.7万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405694&HistoricalAwards=false
• 关键词: Constructing; Optimal; Factorial; Designs; Multiple

Fractional factorial designs (FFDs) are among the most popularly usedexperimental plans in practice. Most existing theory and methods forFFDs assume that the factors involved in an experiment are symmetrical.In many applications, however, this assumption does not hold, becauseexperiments can involve multiple groups (or types) of factors (MGFs).Different types of factors have different implications for design andanalysis, therefore they need to be treated differently. Three typicalexamples are Taguchi's robust parameter design experiments, Addelman'scompromise plans and experiments with both qualitative and quantitativefactors. This project is intended to develop general theory and methodsfor constructing optimal designs with MFGs. Based on the preliminaryresults on robust parameter design, various trade-off strategies willbe generalized to designs with MFGs and their theoretical propertieswill be studied and characterized. Due to the presenceof different types of factors, the aliasing properties of these designsare much complicated. The investigator will study the letter patternsand the coset patterns so as to propose proper criteria for theconstruction of optimal designs. The structure function approach developedby the investigator earlier will be further extended and used in thisresearch. The theory and methods for constructing nonregular FFDs withMGFs will also be investigated and developed. Based on the theory andmethods developed in this project, optimal designs with economical runsize will be constructed and tabulated for experimenters in practice.Statistical design and analysis of experiments are widely used inscientific investigation and industrial research and development. Thestudy of experimental design is aimed at constructing optimal experimentalplans that allow experimenters to collect data and discover knowledge inan economical and efficient way. This project is motivated by theapplication of experimental design methodology for quality improvementin manufacturing industry, especially the robust parameter designtechnology. An experiment in robust parameter design usually involvesmultiple groups (or types) of factors, which have different implicationsin design and analysis. Most existing design theory andmethods assume the symmetry between factors, thus are not directlyapplicable for robust parameter design. In general, experiments caninclude multiple groups of factors (MGFs), which should be treateddifferently in order to generate optimal experimental plans. In thisproject, the investigator intends to develop general theory and methodsfor constructing optimal factorial designs for experiments with MGFs.The project consists of three major components. The first component isto investigate the combinatorial and aliasing properties of fractionalfactorial designs with MGFs; the second component is to propose variousoptimality criteria for the construction of optimal designs with MGFs;the third component is to theoretically characterize the optimal designsand tabulate them for experimenters in practice. The project will advancethe theory and methodology of experimental design as well as enhanceefficient data collection and knowledge discovery in scientificinvestigation, quality improvement and other applications.

在实践中，分数阶乘设计（FFD）是最常用的实验性计划之一。大多数现有的理论和方法假设实验中涉及的因素是对称的。但是，在许多应用中，这种假设不存在，因为涉及多种因素（或类型）因素（或类型）（MGFS）。各种因素类型的因素对设计和分析的影响不同，因此需要不同的治疗方式。 三个典型的示例是Taguchi的鲁棒参数设计实验，Addelman的Compromise计划以及具有定性和定量捕获器的实验。该项目旨在开发使用MFGS构建最佳设计的一般理论和方法。基于关于鲁棒参数设计的初步重新考虑，将研究和表征各种具有MFG及其理论属性的设计的权衡策略。由于存在不同类型的因素，因此这些设计的混叠性能非常复杂。研究人员将研究字母模式和固定模式，以提出适当的最佳设计标准。通过研究者将进一步扩展并在本研究中使用结构函数方法。还将研究和开发使用MGF构建非规范FFD的理论和方法。基于该项目中开发的理论和方法，将在实践中为实验者构建具有经济跑步的最佳设计。实验的统计设计和分析是广泛使用的实心研究以及工业研究和开发。实验设计的基础旨在构建最佳实验计划，使实验者能够收集数据并发现知识INAN经济有效的方式。该项目是由针对质量改善制造业的实验设计方法进行的，尤其是强大的参数设计技术学的动机。鲁棒参数设计中的实验通常涉及数量组（或类型）因素，这些因素在设计和分析中具有不同的影响。大多数现有的设计理论和方法都假定因子之间的对称性，因此对于鲁棒参数设计不可直接应用。一般而言，实验可以可以划定多个因素（MGF），应对其进行治疗，以生成最佳的实验计划。在此项目中，研究人员打算开发用于使用MGF实验的最佳阶乘设计的一般理论和方法。该项目由三个主要组成部分组成。首个使用MGF进行分数式设计的组合和混叠性能的组件；第二个组成部分是针对使用MGFS构建最佳设计的各种访问性标准；第三个组成部分是从理论上表征最佳设计，并将其列为实践中的实验者。该项目将进步实验设计的理论和方法，以及在科学研究，质量改进和其他应用中提高效率的数据收集和知识发现。