Models for Mixture Experiments When the Response Depends on the Total Amount

The usual definition of a mixture experiment requires that the response depend only on the proportions of the mixture components and not on the total amount of the mixture. We consider mixture experiments in which the response also depends on the total amount, and we develop mixture-amount models appropriate for such situations. Models in the component amounts are also considered and are shown to be reduced forms of the mixture-amount models. Examples are used to illustrate the development, interpretation, and comparison of the models.