Tailor-Made Split-Plot Designs for Mixture and Process Variables

The design of efficient small experiments involving mixture variables and process variables is a difficult problem. An additional complication is that such experiments are often conducted using split-plot designs and therefore lead to correlated observations. The present article demonstrates how algorithmic search can be used for constructing efficient tailor-made split-plot mixture-process variable designs, when there may be constraints on the mixture components. The D-optimality criterion is used as the main design criterion. The article also shows how to construct efficient split-plot mixture-process variable designs when replication is required for independently estimating the variance components in the split-plot model. It is argued that it is better to spread the replications over different points of the design than to concentrate them in the center.