Fractional Factorial Designs: Minimum Aberration and Related Topics

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Cheng, Ching-ShuiDMS-0071438AbstractMinimum aberration has been a well accepted criterion for choosing good fractional factorial designs. This research studies variants of the minimum aberration criterion in several different settings including block designs in which the experimental units are grouped into more homogeneous blocks to improve the precision, and split-plot designs in which some factors are held constant within each block. Split plots arise when some factors require larger experimental units than others, or when the effects of certain factors are not of major interest, but they are included in the experiment to study their interactions with other factors. The latter has a very important application to robust parameter designs in quality improvement. These settings have their own special features that call for different optimality criteria. Existing work did not address the issue that there are two different errors in split-plot structures. The ultimate goal of this research is to obtain general results on the structures of optimal designs in various settings, and to develop useful algorithms for constructing designs which can incorporate user-supplied prior knowledge and requirements. For the former, the Principal Investigator uses tools from coding theory and finite projective geometry. Finally, nonregular designs, including supersaturated designs, are studied under a newly introduced criterion of generalized minimum aberration.Experimental design is used extensively in a wide range of scientific and industrial investigations. In industrial experiments, often a large number of factors have to be studied, but the experiments are expensive to conduct. In this case, the so called fractional factorial designs, in which only a small fraction of all the possible combinations are observed, are particularly useful. In recent years, factorial designs have received considerable attention, mainly due to the success in applying them to conduct experiments for improving quality and productivity in industrial manufacturing. This research is to study the construction of efficient designs to extract more information, especially when systematic sources of variation (such as heterogeneity of experimental material or day-to-day environmental variations) need to be eliminated to improve the precision.