General Theory of Minimum Aberration and its Applications

最小像差一般理论及其应用

• 批准号: 0204594
• 负责人: Boxin Tang
• 金额: $ 11.18万
• 依托单位: University of Memphis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0204594&HistoricalAwards=false
• 关键词: General; Theory; Minimum; Aberration; its

Proposal ID: DMS-0204594PI: Boxin TangTitle: General theory of minimum aberration and its applicationsAbstractThe investigator and his colleagues consider the problem of design selection for fractional factorials. In situations where there is little or no knowledge about effects that are potentially important, it is appropriate to select designs using the minimum aberration criterion. Very often, the experimenter may have reasons to believe that certain two-factor interactions are important. Appropriate designs under such circumstances are those allowing joint estimation of all main effects and these potentially important interactions.If the effects not in the postulated model, which consists of the main effects and potentially important interactions, cannot be completely ignored, they bias the estimates of the effects in the model. In the proposed research, this problem of design selection is solved by developing a general theory of minimum aberration. The general criterion of aberration to be introduced generalizes the usual criterion of minimum aberration, and it has the robust property that the best designs given by this criterion sequentially minimize the contamination of nonnegligible effects on the estimation of the effects in the postulated model. Developing a general theory of minimum aberration is also motivated by the desire of unifying various versions of minimum aberration in the literature. Is it possible to derive these versions of minimum aberration from a general theory that is based on a sound statistical principle? The general theory of aberration provides a positive answer to this question. What is more important is that such a general theory enables researchers to derive other versions of minimum aberration that may be more appropriate for given design situations. In the proposal, many research problems are discussed and in some cases, solutions are outlined. Design of experiments is an area of study in statistics that concerns efficient data collection for industrial experiments and many other areas of scientific investigation. Fractional factorial designs are a class of experimental plans and their importance, both theoretical and practical, cannot be overstated. As exploratory designs, they are directly useful in identifying important factors at the early stage of an investigation. They also form a basis on which other more sophisticated designs can be built. In the proposed research, the investigator and his colleagues study the problem of selecting the best fractional factorial designs when certain prior knowledge regarding the effects of factors is available. The problem is solved by developing a general theory of design selection criteria. In addition to solving the above practical problem, the general theory unifies various existing design selection criteria, and allows researchers to derive other criteria that are more appropriate for their situations. Involving students in research activities is an important aspect of the proposed research. The proposed research sheds new light on the study of fractional factorial designs, leads to new economical designs for the experiments in the physical, chemical, and engineering sciences, and most importantly, promotes the application of factorial designs in the areas such as biotechnology and medical research that have huge potential to benefit further from the design methodology.

提案ID：最小像差的一般理论及其应用摘要研究者和他的同事考虑了分数因子的设计选择问题。 在对潜在重要效应知之甚少或一无所知的情况下，使用最小像差准则选择设计是适当的。很多时候，实验者可能有理由相信某些双因素相互作用是重要的。在这种情况下，适当的设计是允许联合估计所有主效应和这些潜在重要的交互作用的设计。如果假设模型（由主效应和潜在重要的交互作用组成）中未包含的效应不能完全忽略，则它们会使模型中效应的估计值产生偏倚。在建议的研究中，这个问题的设计选择解决了发展的一般理论的最小像差。引入的一般像差准则推广了通常的最小像差准则，它具有稳健性，即由该准则给出的最佳设计依次最小化不可忽略的效应对假设模型中效应估计的污染。发展最小像差的一般理论也是出于统一文献中各种最小像差理论的愿望。有没有可能从基于可靠统计原理的一般理论中推导出这些最小像差的版本？光行差的一般理论为这个问题提供了一个肯定的答案。 更重要的是，这样一个一般的理论，使研究人员能够得到其他版本的最小像差，可能更适合于给定的设计情况。在建议中，许多研究问题进行了讨论，并在某些情况下，解决方案概述。实验设计是统计学的一个研究领域，涉及工业实验和许多其他科学调查领域的有效数据收集。部分因子设计是一类实验方案，其重要性，无论是理论还是实践，都不能被夸大。作为探索性设计，它们直接有助于在调查的早期阶段确定重要因素。它们还构成了构建其他更复杂设计的基础。在拟议的研究中，研究者和他的同事研究了当某些关于因素影响的先验知识可用时选择最佳部分析因设计的问题。这个问题是解决发展的一般理论的设计选择标准。除了解决上述实际问题外，一般理论还统一了各种现有的设计选择标准，并允许研究人员推导出更适合他们情况的其他标准。 让学生参与研究活动是拟议研究的一个重要方面。该研究为部分析因设计的研究提供了新的思路，为物理、化学和工程科学的实验提供了新的经济设计，最重要的是，促进了析因设计在生物技术和医学研究等领域的应用，这些领域有巨大的潜力进一步受益于设计方法。