Split-plot design for mixture experiments with process variables: A comparison of design strategies

In many industrial processes with mixtures, the end-product quality depends both on the proportions of the mixture components and on the levels of the process variables. The experimental region is often just a sub-region of the entire mixture simplex, and standard mixture designs are usually not applicable. In addition, large-scale experiments are often not run in random order due to practical and economical considerations. This leads to a split-plot structure of the data, and affects both the experimental design and the statistical modelling. D-optimal designs are widely used for these kinds of restricted mixture–process experiments. We have compared the performance of D-optimal designs to a less known design strategy; projection designs. Projection designs are generated from standard orthogonal designs, e.g. fractional factorials, and the mixture variables are projected onto the subspace defined by the mixture restrictions. Main focus of the comparisons is precision of coefficient estimates and predictive ability of the fitted models. It was found that the different designs have different properties when it comes to precision of coefficient estimates. While D-optimal designs produce overall good precision for all coefficients, projection designs have the possibility to prioritise between coefficients, i.e. assure that some coefficients are more precisely estimated than others. The predictive abilities of the fitted models were quite similar for all the designs.