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

Purdue University, West Lafayette IN

Investigators

Abstract

Fractional factorial designs (FFDs) are among the most popularly used experimental plans in practice. Most existing theory and methods for FFDs assume that the factors involved in an experiment are symmetrical. In many applications, however, this assumption does not hold, because experiments can involve multiple groups (or types) of factors (MGFs). Different types of factors have different implications for design and analysis, therefore they need to be treated differently. Three typical examples are Taguchi's robust parameter design experiments, Addelman's compromise plans and experiments with both qualitative and quantitative factors. This project is intended to develop general theory and methods for constructing optimal designs with MFGs. Based on the preliminary results on robust parameter design, various trade-off strategies will be generalized to designs with MFGs and their theoretical properties will be studied and characterized. Due to the presence of different types of factors, the aliasing properties of these designs are much complicated. The investigator will study the letter patterns and the coset patterns so as to propose proper criteria for the construction of optimal designs. The structure function approach developed by the investigator earlier will be further extended and used in this research. The theory and methods for constructing nonregular FFDs with MGFs will also be investigated and developed. Based on the theory and methods developed in this project, optimal designs with economical run size will be constructed and tabulated for experimenters in practice. Statistical design and analysis of experiments are widely used in scientific investigation and industrial research and development. The study of experimental design is aimed at constructing optimal experimental plans that allow experimenters to collect data and discover knowledge in an economical and efficient way. This project is motivated by the application of experimental design methodology for quality improvement in manufacturing industry, especially the robust parameter design technology. An experiment in robust parameter design usually involves multiple groups (or types) of factors, which have different implications in design and analysis. Most existing design theory and methods assume the symmetry between factors, thus are not directly applicable for robust parameter design. In general, experiments can include multiple groups of factors (MGFs), which should be treated differently in order to generate optimal experimental plans. In this project, the investigator intends to develop general theory and methods for constructing optimal factorial designs for experiments with MGFs. The project consists of three major components. The first component is to investigate the combinatorial and aliasing properties of fractional factorial designs with MGFs; the second component is to propose various optimality criteria for the construction of optimal designs with MGFs; the third component is to theoretically characterize the optimal designs and tabulate them for experimenters in practice. The project will advance the theory and methodology of experimental design as well as enhance efficient data collection and knowledge discovery in scientific investigation, quality improvement and other applications.