Constructing Optimal Factorial Designs for Multiple Groups of Factors: Theory, Methods and Applications

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Fractional factorial designs (FFDs) are among the most popularly usedexperimental plans in practice. Most existing theory and methods forFFDs assume that the factors involved in an experiment are symmetrical.In many applications, however, this assumption does not hold, becauseexperiments can involve multiple groups (or types) of factors (MGFs).Different types of factors have different implications for design andanalysis, therefore they need to be treated differently. Three typicalexamples are Taguchi's robust parameter design experiments, Addelman'scompromise plans and experiments with both qualitative and quantitativefactors. This project is intended to develop general theory and methodsfor constructing optimal designs with MFGs. Based on the preliminaryresults on robust parameter design, various trade-off strategies willbe generalized to designs with MFGs and their theoretical propertieswill be studied and characterized. Due to the presenceof different types of factors, the aliasing properties of these designsare much complicated. The investigator will study the letter patternsand the coset patterns so as to propose proper criteria for theconstruction of optimal designs. The structure function approach developedby the investigator earlier will be further extended and used in thisresearch. The theory and methods for constructing nonregular FFDs withMGFs will also be investigated and developed. Based on the theory andmethods developed in this project, optimal designs with economical runsize will be constructed and tabulated for experimenters in practice.Statistical design and analysis of experiments are widely used inscientific investigation and industrial research and development. Thestudy of experimental design is aimed at constructing optimal experimentalplans that allow experimenters to collect data and discover knowledge inan economical and efficient way. This project is motivated by theapplication of experimental design methodology for quality improvementin manufacturing industry, especially the robust parameter designtechnology. An experiment in robust parameter design usually involvesmultiple groups (or types) of factors, which have different implicationsin design and analysis. Most existing design theory andmethods assume the symmetry between factors, thus are not directlyapplicable for robust parameter design. In general, experiments caninclude multiple groups of factors (MGFs), which should be treateddifferently in order to generate optimal experimental plans. In thisproject, the investigator intends to develop general theory and methodsfor constructing optimal factorial designs for experiments with MGFs.The project consists of three major components. The first component isto investigate the combinatorial and aliasing properties of fractionalfactorial designs with MGFs; the second component is to propose variousoptimality criteria for the construction of optimal designs with MGFs;the third component is to theoretically characterize the optimal designsand tabulate them for experimenters in practice. The project will advancethe theory and methodology of experimental design as well as enhanceefficient data collection and knowledge discovery in scientificinvestigation, quality improvement and other applications.