Designing Fractional Factorial Split-Plot Experiments Using Integer Programming; Doctoral thesis

摘要

Split-plot designs are commonly used in industrial experiments when there are hard-to-change and easy-to-change factors. Due to the number of factors and resource limitations, it is more practical to run a fractional factorial split-plot (FFSP) design. These designs are variations of the fractional factorial (FF) design, with the restricted randomization structure to account for the whole plots and subplots. We begin by discussing the formulation of FFSP designs using integer programming (IP) to achieve various design criteria. We specifically look at the maximum number of clear two-factor interactions and variations on this criterion. By making restrictions on some of the general linear constraints, we are able to customize the alias structure of these FFSP designs. Additional constraints allow for the generation of blocked FFSP designs that are shown to meet performance standards shown in today's literature. By generalizing the model formulation, we show how designs for numerous stages can be generated. In addition, we explore using a genetic algorithm heuristic to search for split-plot designs from a candidate matrix of factor effects generated using the Kronecker product.