Fitting Equations to Mixture Data with Restraints on Compositions

Fitting polynomials to mixture data by linear least squares often leads to inaccurate computer solutions when there are restraints on composition. When the restricted region in composition contains enough properly distributed points, accuracy can be achieved by suitable transformations which improve conditioning of the normal equations. Two transformations are discussed which use the Scheffé polynomial forms for mixtures and are easy to apply to data from undesigned experiments. An application of both transformations to data from an extreme vertices design illustrates the improvement in conditioning.