DETECTION OF AN ADDITIVE BLENDING COMPONENT IN MULTICOMPONENT MIXTURES

Properties such as the fluffiness of cake, the combustion rate of rocket fuel or the toxicity of agricultural pesticides are realized as outcomes (responses) of mixture experiments. In mixture experiments, the response depends only on the proportions of the components (constituents) present in the mixtures and not on the total amount of the mixtures. Polynomial forms introduced by Scheffe (1958) are frequently used to express the response as a function of composition. However, when one of the components blends linearly (its effect on the response is strictly additive) with all the other components as well as with their mixtures and the remaining components blend non-linearly, the polynomial form may fail. What is required to model the additive effect is a non-polynomial model which is homogeneous of degree one. The additivity of a component goes undetected when fitting standard polynomial forms and in this paper we show how to determine when the simpler non-polynomial form is a more realistic model. The methodology is illustrated using data from a greenhouse experiment.