Mathematical Sciences: Design of Experiments: Improving Practicability of Some Useful Concepts

提案：DMS 9504882 PI: John Stufken Institution: Iowa State University题目：实验设计：提高一些有用概念的实用性摘要：本研究的重点是开发工具，以获得各种设置的有效设计。它涉及到算法的发展，必要时还包括理论支持。解决的问题包括混合实验中的阻塞，在析因实验中避免不受欢迎的水平组合，以及将给定的块设计转换为该设计的无趋势或几乎无趋势的版本。一个关键的概念是对块设计中权衡思想的概括。在大多数工业实验和许多科学研究领域中，设计好的实验是必不可少的。有效地利用有限的可用资源，并确保收集到的数据能够可靠地回答感兴趣的问题，这几乎总是至关重要的。应用领域包括工业生产过程中产品质量评估和改进的实验，以及农业科学、社会科学和工程学科中定量研究的实验。许多关于实验设计的研究都集中在确定针对特定问题的有效设计上，这些设计通常不够广泛，不足以适用于多个应用领域。以前的工作的有用性有时受到用于推导结果的主要数学工具对结果的限制。其中一些方法的应用也受到用户要求的数学复杂性的影响。研究者开发新的方法和算法，为各种具体问题找到有效的设计。这些算法可以很容易地用现有的计算机软件实现，促进了新方法的使用，并且不需要用户有任何复杂的数学知识。

Proposal: DMS 9504882 PI: John Stufken Institution: Iowa State University Title: Design of Experiments: Improving Practicability of some Useful Concepts Abstract: This research focuses on developing tools to obtain efficient designs for various settings. It involves the development of algorithms and, where needed, supporting theory. Issues that are addressed include blocking in mixture experiments, avoiding undesirable level combinations in factorial experiments, and converting a given block design to a trend-free or nearly trend-free version of that design. A critical concept is a generalization of the idea of trade-off in block designs. Designed experiments are essential in most industrial experiments and in many areas of scientific research. It is almost always crucial to use limited available resources efficiently, and to assure that the collected data can be used to answer questions of interest reliably. Areas of application include experiments for product quality assessment and improvement in industrial production processes, and experiments for quantitative research in, for example, agricultural sciences, social sciences, and engineering disciplines. Much of the research in design of experiments concentrates on identifying efficient designs for a specific problem, often not broad enough to be relevant for more than one area of application. The usefulness of previous work has at times been limited by restrictions on the results induced by the mostly mathematical tools used to derive the results. Application of some of these methods has also suffered from the mathematical sophistication that is required from a user. The investigator develops new methods and algorithms to find efficient designs for various specific problems. These algorithms, which can be implemented easily with existing computer software, facilitate use of the new methods, and do not require any mathematical sophistication of a user.