Cluster Analysis as an Experimental Design Generator, With Application to Gasoline Blend ing Experiments

Abstract

This article concerns the selection of experimental design points from existing series of candidates when the design variables are too interrelated to be manipulated independently. Designs with an even spread of points are shown to estimate the parameters of an assumed linear or polynomial model reasonably efficiently while providing good tests of lack of fit. Furthestneighbor cluster analysis can be used to select the points of such a design under either the Euclidean or the Mahalanobis measure of distance. The technique is used to select the base fuels in actual series of experiments to measure the effect of blending a particular alcohol into gasolines. A new blending model parameterization is proposed, which relates the blending octane number of this alcohol to both its concentration and to the properties of the base fuel. An analagous generalized least squares model is discussed, which gives a simple expression for the expected mean squares in different error strata.

KEY WORDS:

• Furthest-neighbor method
• Computer-aided design
• Mahalanobis distance
• Mixture experiments
• Generalized least squares
• Error structure