Nonregular and supersaturated designs are commonly used in screening experiments where the goal is to identify a few dominant factors among a large number of candidate factors. The objectives of this proposal are to construct efficient nonregular and supersaturated designs and to develop new methodology for analyzing data from such experiments. A general method is introduced for constructing nonregular designs from linear codes over a finite ring. These nonregular designs have better statistical properties than the existing designs in the literature in terms of aberration, resolution and projectivity. The concept of constant weight codes in coding theory is used for studying supersaturated designs. Linear programming technique is used to establish new upper bounds on the number of columns in a supersaturated design. New algorithms are developed for constructing efficient nonregular and supersaturated designs for practical use. A graphical procedure and an automatic procedure are proposed for screening active effects for nonregular and supersaturated designs. Simulation shows that this method performs well compared to existing methods in the literature and is more efficient at estimating the model size.
Statistical design and analysis of experiments have been widely used in scientific and industrial research and development. As science and technology have advanced to a higher level, investigators are becoming more interested in and capable of studying large-scale systems via computer simulations and high-performance computing. Two fundamental questions are how to design an efficient experiment and how to analyze the data properly from the experiment. This proposed research aims at developing novel methods for constructing optimal designs and for analyzing such experiments. New efficient nonregular and supersaturated designs are constructed and will be made available online for broad and quick dissemination. The results of the proposed research can be quickly assimilated into graduate courses on design and analysis of experiments. This proposal employs a combination of mathematical and computational tools and emphasizes an important interdisciplinary connection between information theory and design theory. The proposed research will lead to remarkable new advances in design theory and better practice in data analysis.
