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

部分析因设计(FFD)是实践中最常用的实验方案之一。现有的FFD理论和方法大多假定实验所涉及的因素是对称的，但在许多应用中，这一假设并不成立，因为实验可能涉及多组(或多类型)因素(MGFs)。不同类型的因素对设计和分析有不同的含义，因此需要区别对待。三个典型的例子是田口的稳健参数设计实验，Addelman的折衷方案和定性和定量因素的实验。该项目旨在发展利用MFG构造最优设计的一般理论和方法。在稳健参数设计的初步结果的基础上，将各种权衡策略推广到具有MFGS的设计中，并对其理论性质进行研究和刻画。由于存在不同类型的因素，这些设计的混叠特性非常复杂。研究人员将研究字母模式和陪集模式，以便为最优设计的构造提出适当的准则。前人提出的结构函数方法将在本研究中进一步推广和使用。还将研究和发展用MGFs构造非规则FFD的理论和方法。根据本课题所提出的理论和方法，设计出具有经济运行规模的优化设计，并在实践中为实验人员编制表格。实验的统计设计和分析在科学研究和工业研发中得到了广泛的应用。实验设计的研究目的是构建最优的实验方案，使实验者能够以经济有效的方式收集数据和发现知识。本项目是基于制造业质量改进的实验设计方法学的应用，特别是稳健参数设计技术的应用。稳健参数设计试验通常涉及多组(或多类)因素，这些因素在设计和分析中具有不同的含义。现有的设计理论和方法大多假定因素之间的对称性，因此不能直接适用于稳健的参数设计。一般来说，实验可以包括多组因素(MGFs)，这些因素应该被区别对待，以便产生最佳的实验计划。在这个项目中，研究人员打算发展一般的理论和方法来构建用于MGFs试验的最佳析因设计。该项目由三个主要部分组成。第一个组成部分是研究含有MGFs的分式析因设计的组合和混叠性质；第二个组成部分是为构造含有MGFs的最优设计提出各种最优性准则；第三个组成部分是从理论上表征最优设计，并将它们列成表格，以供实践中的实验者使用。该项目将推进实验设计的理论和方法，并在科学调查、质量改进和其他应用中提高数据收集和知识发现的效率。

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.