Mixture-process variable experiments including control and noise variables within a split-plot structure

In mixture-process variables experiments, it is common that the experimental runs are larger than the mixture only design or basic experimental design to estimate the increased coefficient parameters due to the mixture components, process variable, and interaction between mixture and process variables, some of which are hard to change or cannot be controlled under normal operating condition. These situations often prohibit a complete randomisation for the experimental runs due to the time or financial reason. These types of experiments can be analysed in a model for the mean response and a model for the slope of the response within a split-plot structure. When considering the experimental designs, low prediction variances for the mean and slope model are desirable. We demonstrate the methods for the mixture-process variable designs with noise variables considering a restricted randomisation and evaluate some mixture-process variable designs that are robust to the coefficients of interaction with noise variables using fraction of design space plots with the respect to the prediction variance properties. Finally, we create the G-optimal design that minimises the maximum prediction variance over the entire design region using a genetic algorithm.