Mixture Experiment Alternatives to the Slack Variable Approach

A mixture experiment involves mixing components in various proportions and measuring one or more response variables on each mixture. This article presents mixture experiment approaches for designing experiments and/or modeling the resulting data in situations where the slack variable (SV) approach has been used. The SV approach designates one mixture component as the SV and then designs and analyzes the experiment in terms of the remaining components. In an SV design, the proportion of the SV is obtained by subtracting from one the sum of the proportions of the remaining components (thus "taking up the slack''). The mixture experiment approach designs and analyzes the experiment using all of the mixture components. The article considers four situations in which the SV approach is used and explains for each situation that it is generally preferable to use an appropriate mixture experiment approach. For each situation, the recommended mixture experiment approach is discussed and compared to the SV approach using an example.