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

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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.