Order-of-addition mixture experiments

Abstract

In a mixture experiment, m components are mixed to produce a response. The total amount of the mixture is a constant. Existing literature on mixture designs ignores the order of addition of the mixture components. This paper considers the Order-of-Addition (OofA) mixture experiment, where the response depends on both the mixture proportions of components and their order of addition. Empirical study demonstrates that if mixture-order interactions exist, then the optimal mixture proportions identified by traditional models may be misleading. Full Mixture OofA designs are created which ensure orthogonality between mixture model terms and addition order effects. These designs allow for the estimation of (1) typical mixture model parameters and (2) order-of-addition effects. Moreover, models which include both main effects and key mixture-order interactions are introduced.