A Case Study Involving Mixture-Process Variable Experiments within a Split-Plot Structure

When an experiment involves both mixture and process variables, the size of the experiment can increase dramatically and the assumption of complete randomization may be violated due to the cost or time to change some factor levels. In this situation, restrictions on the randomization of experimental runs are necessary, resulting in a split-plot structure. Furthermore, when some process variables are noise variables, it is important to consider the noise variables at the design stage of the process to find the robust parameter setting that makes the response "robust'' to the variability transmitted from the noise factors. However, many mixture-process experiments are analyzed without considering this randomization issue. We provide a real example of a mixture-process experiment with noise variables within a split-plot structure. Our example demonstrates show to minimize the prediction error with noise variables in a situation where the standard analysis results in poor estimation for the prediction due to the restricted randomization. Without a proper analysis, the experiment leads to the wrong model and results in poor prediction. When the noise variables are ignored in the experiments, the model provides large random errors due to the effect of noise variables. We show that dual optimization using a mean model and a variance model can find the robust settings for the noise variables.