Generating blocked fractional factorial split-plot designs using integer programming

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 randomisation structure to account for the whole plots and subplots. When all the experimental runs cannot be performed under the same conditions, the designs are split into blocks. We discuss the formulation of blocked fractional factorial split-plot (BFFSP) designs using integer programming (IP) to achieve various design criteria.