Proposal #DMS-9704548 Studies in Efficient Design of Experiments Ching-Shui Cheng University of California ABSTRACT This research involves several problems in experimental design. Optimal blocking of fractional factorial designs is studied. Blocking is an effective method for improving the efficiency of an experiment by grouping the experimental units into more homogeneous blocks. How to choose a fractional factorial design and a blocking scheme simultaneously in an optimal way is of interest to both theoreticians and practitioners. A new criterion for choosing good blocking schemes by examining the alias patterns of the interactions is formulated. Methods of constructing optimal and efficient designs under this criterion are investigated. Some unsolved problems in the unblocked case are also studied. Another area of research is the projection properties of orthogonal arrays. In factor screening, often only a few factors among a large pool of potential factors are active. Under such assumption of effect sparsity, it is important to consider projections onto small subsets of factors. An extensive study of the projection properties of orthogonal arrays is carried out. Connections with search designs are also explored. In addition to factorial designs, optimal and efficient regression designs under random block-effects models are studied by adopting the approach of approximate theory. 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 Japanese success in applying them to improve quality and productivity in industrial manufa cturing. One objective of 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. Since often only a few of the many potential factors are actually important, this research also looks into the properties of some commonly used designs when only a small number of factors are active. Another research involves a problem arising from a recent optometry experiment, which also has industrial applications.
