Improved Split-Plot and Multistratum Designs

Many industrial experiments involve some factors whose levels are harder to set than others. The best way to deal with these is to plan the experiment carefully as a split-plot, or more generally a multi-stratum, design. Several different approaches for constructing splitplot type response surface designs have been proposed in the literature since 2001, which has allowed experimenters to make better use of their resources by using more efficient designs than the classical balanced ones. One of these approaches, the stratum-by-stratum strategy, has been shown to produce designs that are less efficient than locally D-optimal designs. An improved stratum-by-stratum algorithm is given, which, though more computationally intensive than the old one, makes better use of the advantages of this approach, i.e. it can be used for any structure and does not depend on prior estimates of the variance components. This is shown to be almost as good as the locally optimal designs in terms of their own criteria and more robust across a range of criteria. Supplementary material is available online.