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

分数因子设计（FFDs）是实践中最常用的实验方案之一。大多数现有的ffd理论和方法都假设实验中涉及的因素是对称的。然而，在许多应用中，这一假设并不成立，因为实验可能涉及多组（或类型）因素（mgf）。不同类型的因素对设计和分析有不同的影响，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的折衷计划和定性和定量因素的实验。本课题的目的是发展用mfg进行优化设计的一般理论和方法。基于鲁棒参数设计的初步结果，将各种权衡策略推广到mfg设计中，并对其理论性质进行研究和表征。由于不同类型因素的存在，这些设计的混叠特性非常复杂。研究者将研究字母模式和辅助模式，以便为构建最佳设计提出适当的标准。本研究将进一步扩展和使用研究者先前开发的结构函数方法。本文还将研究和发展用mgfs构造不规则ffd的理论和方法。基于本课题所开发的理论和方法，将构建具有经济运行规模的最优设计，并将其制成表格供实践中的实验人员使用。实验的统计设计和分析被广泛应用于科学调查和工业研究与开发。实验设计研究的目的是建立最优的实验方案，使实验人员能够以经济有效的方式收集数据和发现知识。本课题的研究灵感来自于实验设计方法在制造业质量改进中的应用，尤其是鲁棒参数设计技术。稳健参数设计中的实验通常涉及多组（或类型）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是对称的，因此不能直接适用于鲁棒参数设计。一般来说，实验可以包括多组因素（mgf），为了产生最佳的实验计划，应该对这些因素进行不同的处理。在这个项目中，研究者打算发展一般理论和方法来构建最优因子设计的实验用mgf。该项目由三个主要部分组成。第一部分是研究分数因子设计的组合和混叠特性；第二部分是提出各种最优性准则，用于构建mgf优化设计；第三部分是从理论上描述最佳设计，并将其制成表格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加强有效的数据收集和知识发现。

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.