Mixture Experiments

Abstract

Abstract A mixture experiment involves combining two or more components in various proportions or amounts and then measuring one or more responses for the resulting end products. Other factors that affect the response(s), such as process variables and/or the total amount of the mixture, may also be studied in the experiment. A mixture experiment design specifies the combinations of mixture components and other experimental factors (if any) to be studied and the response variable(s) to be measured. Mixture experiment data analyses are then used to achieve the desired goals, which may include (a) understanding the effects of components and other factors on the response(s), (b) identifying components and other factors with significant and nonsignificant effects on the response(s), (c) developing models for predicting the response(s) as functions of the mixture components and any other factors, and (d) developing end products with desired values and uncertainties of the response(s). Given a mixture experiment problem, a practitioner must consider the possible approaches for designing the experiment and analyzing the data, and then select the approach best suited to the problem. Eight possible approaches are (a) component proportions, (b) mathematically independent variables, (c) slack variable, (d) mixture amount, (e) component amounts, (f) mixture‐process variable, (g) mixture of mixtures, and (h) multifactor mixture. The article provides an overview of the mixture experiment designs, models, and data analyses for these approaches.