Mixture experiments with mixing errors

In mixture experiments the properties of mixtures are usually studied by mixing the amounts of the mixture components that are required to obtain the necessary proportions. This paper considers the impact of inaccuracies in discharging the required amounts of the mixture components on the statistical analysis of the data. It shows how the regression calibration approach can be used to minimize the resulting bias in the model and in the estimates of the model parameters, as well as to find correct estimates of the corresponding variances. Its application is made difficult by the complex structure of these errors. We also show how knowledge of the form of the model bias allows for choosing a manufacturing setting for a mixture product that is not biased and has smaller signal to noise ratio.