Developing Blending Models for Gasoline and Other Mixtures

The construction of gasoline blending models is discussed to illustrate some of the practical problems encountered in mixture experimentation. Attention is focused on the use and modification of the simplex and extreme vertices designs in the development of blending models. The XVERT, WYNN, EXCHANGE, CONSIM, and CADEX algorithms are shown to be useful aids in constructing linear and quadratic model designs when the region of feasible blends is restricted by single-component and multiple-component constraints. The evaluation of competing models and the use of the quadratic blending model in conjunction with linear programming calculations are also discussed. The methodology is general and can be used in all types of mixture experiments and product formulation studies, Examples are included to illustrate the use of the design algorithms and models.

[1]  N. N. Chan A-Optimality for Regression Designs. , 1982 .

[2]  John A. Cornell,et al.  Experiments with Mixtures: An Update and Bibliography , 1979 .

[3]  R. Snee Experimental designs for mixture systems with multicomponent constraints , 1979 .

[4]  Ronald D. Snee,et al.  Validation of Regression Models: Methods and Examples , 1977 .

[5]  Ronald D. Snee,et al.  Screening Concepts and Designs for Experiments with Mixtures , 1976 .

[6]  Ronald D. Snee,et al.  Experimental Designs for Quadratic Models in Constrained Mixture Spaces , 1975 .

[7]  R. C. St. John,et al.  D-Optimality for Regression Designs: A Review , 1975 .

[8]  R. Snee,et al.  Extreme Vertices Designs for Linear Mixture Models , 1974 .

[9]  Ronald D. Snee Techniques for the Analysis of Mixture Data , 1973 .

[10]  John A. Cornell,et al.  EXPERIMENTS WITH MIXTURES: A REVIEW , 1973 .

[11]  M. J. Box,et al.  Factorial Designs, the |X′X| Criterion, and Some Related Matters , 1971 .

[12]  R. Snee Design and Analysis of Mixture Experiments , 1971 .

[13]  O. Dykstra The Augmentation of Experimental Data to Maximize [X′X] , 1971 .

[14]  H. Wynn The Sequential Generation of $D$-Optimum Experimental Designs , 1970 .

[15]  J. W. Gorman Fitting Equations to Mixture Data with Restraints on Compositions , 1970 .

[16]  John A. Cornell,et al.  The Mixture Problem for Categorized Components , 1970 .

[17]  A. E. Hoerl,et al.  Ridge Regression: Applications to Nonorthogonal Problems , 1970 .

[18]  L. A. Stone,et al.  Computer Aided Design of Experiments , 1969 .

[19]  N. G. Becker Models for the Response of a Mixture , 1968 .

[20]  CONSTRAINED DESIGNS. PART I. FIRST ORDER DESIGNS. , 1966 .

[21]  Virgil L. Anderson,et al.  Extreme Vertices Design of Mixture Experiments , 1966 .

[22]  J. W. Gorman Discussion of "Extreme Vertices Design of Mixture Experiments" by R. A. McLean , 1966 .

[23]  H. Scheffé The Simplex‐Centroid Design for Experiments with Mixtures , 1963 .

[24]  John W. Gorman,et al.  Simplex Lattice Designs for Multicomponent Systems , 1962 .

[25]  H. Scheffé Reply to Mr Quenouille's Comments About My Paper on Mixtures , 1961 .

[26]  M. H. Quenouille Experiments with Mixtures , 1959 .

[27]  H. Scheffé Experiments with Mixtures , 1958 .

[28]  J. S. Hunter,et al.  Multi-Factor Experimental Designs for Exploring Response Surfaces , 1957 .

[29]  J. S. Hunter,et al.  MULTIFACTOR EXPERIMENTAL DESIGN FOR EXPLORING THE RESPONSE SURFACES , 1957 .

[30]  R. J. Hader,et al.  Effect of Raw‐Material Ratios on Absorption of Whiteware Compositions , 1956 .

[31]  G. Elfving Optimum Allocation in Linear Regression Theory , 1952 .