Measuring Component Effects in Constrained Mixture Experiments

In a mixture experiment, the response to a mixture of q components is a function of the proportions x 1, x 2, …, x q of components in the mixture. The proporitons satisfy the constraint Σx i = 1, and the nature of a particular situation may impose other restrictions. The problem considered is the measurement of the effect each component has on the response. A new mixture component effect measure is presented and compared to previously suggested measures. This new measure incorporates more information concerning the size, shape, and location of the constraint region than do the previous suggestions. A distinction between partial and total effects is made, and the uses of these effects in modifying and interpreting mixture response prediction equations are considered. The methods of the article are illustrated in an example from a glass development study in a waste vitrification program.