Fraction of Design Space Plots for Split-plot Designs

摘要

In industrial experiments, restrictions on the execution of the experimental runs or the existence of one or more hard-to-change factors often leads to split-plot experiments, where there are two types of experimental units and two independent randomizations. The resulting compound symmetric error structure, as well as the settings of whole-plot and subplot factors, play important roles in the performance of split-plot experiments. When the practitioner is interested in predicting the response, a response surface design for a second-order model such as a central composite design (CCD) is often used. The prediction variance of second-order designs under a split-plot error structure is often of interest. In this paper, fraction of design space (FDS) plots are adapted to split-plot designs. In addition to the global curve exploring the entire design space, sliced curves at various whole-plot levels are presented to study prediction performance for subregions in the design space. The different sizes of the constrained subregions are accounted for by the proportional size of the sliced curves. The construction and use of the FDS plots are demonstrated through two examples of the restricted CCD in split-plot schemes. We also consider the impact of the variance ratio on design performance.