Simplex Lattice Designs for Multicomponent Systems

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Abstract
A new method for designing experiments with mixtures has been devised by Scheffe. The fractions of components making up any mixture must add to unity, and hence factor space may be represented by a regular simplex. Points of composition in this simplex are explored in accordance with a lattice arrangement, and responses are represented by simplified general polynomials. These polynomials have been extended to include the quartic. A numerical example shows how the method has been applied to estimation of octane numbers for a ternary gasoline system. Using the method makes possible estimates of the properties of an entire system from a limited number of observations. The method should prove useful for any multicomponent system where intensive properties are to be related to composition and where the behavior of the properties is not so erratic as to preclude satisfactory approximation by low order polynomials.

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