Experiments with mixtures: Designs, models, and the analysis of mixture data

Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data

Volumn , Issue , 2011, Pages 1-219

  Cornell, John A ^a  

^a UNIVERSITY OF FLORIDA   (United States)

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EID: 85103070262     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781118204221     Document Type: Chapter

References (290)

1. Agreda, C. L. and V. H. Agreda (1989). Designing mixture experiments. CHEMTECH, Vol. 19, pp. 573-575.
2. Aitchison, J. (1982). The statistical analysis of compositional data (with discussion). Journal of the Royal Statistical Society, B, Vol. 44, pp. 139-147.
3. Aitchison, J. (1985). A general class of distributions on the simplex. Journal of the Royal Statistical Society, B, Vol. 47, pp. 136-146.
4. Aitchison, J. (1986). The Statistical Analysis of Compositional Data. Chapman and Hall, London.
5. Aitchison, J. and J. Bacon-Shone (1984). Log contrast models for experiments with mixtures. Biometrika, Vol. 71, pp. 323-330.
6. Aitkin, M. A. (1974). Simultaneous inference and the choice of variable subsets in multiple regression. Technometrics, Vol. 16, pp. 221-227.
7. Andere-Rendon, J., D. C. Montgomery, and D. A. Rollier (1997). Design of mixture experiments using Bayesian D-optimality. Journal of Quality Technology, Vol. 29, pp. 451-463.
8. Anderson, M. J. and P. J. Whitcomb (1996). Optimization of paint formulations made easy with computer-aided design of experiments for mixtures. Journal of Coatings Technology, Vol. 68, pp. 71-75.
9. Anderson, V. L. and R. A. McLean (1974). Design of Experiments: A Realistic Approach. Marcel Dekker, New York, pp. 335-347.
10. Anik, S. T. and L. Sukumar (1981). Extreme vertices design in formulation development: solubility of butoconazole nitrate in a multicomponent system. Journal of Pharmaceutical Sciences, Vol. 70, pp. 897-900.
11. Atkinson, A. C. and A. N. Donev (1996). Optimum Experimental Designs. Clarendon Press, Oxford.
12. Bayne, C. K. and C. Y. Ma (1987). Optimization of solvent composition for high performance thin-layer chromatography. Journal of Liquid Chromatography, Vol. 10, pp. 3529-3546.
13. Becker, N. G. (1968). Models for the response of a mixture. Journal of the Royal Statistical Society, B, Vol. 30, pp. 349-358.
14. Becker, N. G. (1969). Regression problems when the predictor variables are proportions. Journal of the Royal Statistical Society B, Vol. 31, pp. 107-112.
15. Becker, N. G. (1970). Mixture designs for a model linear in the proportions. Biometrika, Vol. 57, pp. 329-338.
16. Becker, N. G. (1978). Models and designs for experiments with mixtures. Australian Journal of Statistics, Vol. 20, pp. 195-208.
17. Belloto, R. J. Jr., A. M. Dean, M. A. Moustafa, A. M. Molokhia, M. W. Gouda, and T. D. Sokoloski (1985). Statistical techniques applied to solubility predictions and pharmaceutical formulations: an approach to problem solving using mixture response surface methodology. International Journal of Pharmaceutics, Vol. 23, pp. 195-207.
18. Berliner, L. M. (1987). Bayesian control in mixture models. Technometrics, Vol. 29, pp. 455-460.
19. Bohl, A. H. (1988). A formulation tool. CHEMTECH, Vol. 18, pp. 158-163.
20. Bownds, J. M., I. S. Kurotori, and D. R. Cruise (1965). Notes on simplex models in the study of multi-component mixtures, U. S. Naval Ordinance Test Station, NAVWEPS Report 8670, NOTS TP 3719, Copy 197, China Lake, CA, January, pp. 1-40.
21. Box, G. E. P. (1952). Multi-factor designs of first order. Biometrika, Vol. 39, pp. 49-57.
22. Box, G. E. P. (1982). Choice of response surface design and alphabetic optimality. Utilitas Mathematica, Vol. 21B, pp. 11-55.
23. Box, G. E. P. and N. R. Draper (1959). A basis for the selection of a response surface design. Journal of the American Statistical Association, Vol. 54, pp. 622-654.
24. Box, G. E. P. and C. J. Gardiner (1966). Constrained designs - part 1, First order designs. Technical Report No. 89, Department of Statistics, University of Wisconsin, Madison, pp. 1-14.
25. Box, G. E. P. and J. S. Hunter (1957). Multi-factor experimental designs for exploring response surfaces. Annals of Mathematical Statistics, Vol. 28, pp. 195-242.
26. Box, G. E. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building. Wiley, New York.
27. Cain, M. and M. L. R. Price (1986). Optimal mixture choice. Applied Statistics, Vol. 35, pp. 1-17.
28. Chan, L. Y. (1988). Optimal design for a linear log contrast model for experiments with mixtures. Journal of Statistical Planning and Inference, Vol. 20, pp. 105-113.
29. Chan, L. Y. (1992). ©-optimal design for a quadratic log contrast model for experiments with mixtures. Communications in Statistics, Theory and Methods, Vol. 21, pp. 2909-2930.
30. Chan, L. Y. (2000). Optimal designs for experiments with mixtures: a survey. Communications in Statistics, Theory and Methods, Vol. 29, pp. 2281-2312.
31. Chan, L. Y, Y. N. Guan, and C. Q. Zhang (1998). A-optimal designs for an additive quadratic mixture model. Statistica Sinica, Vol. 8, pp. 979-990.
32. Chan, L. Y, J. H. Meng, Y. C. Jiang, and Y. N. Guan (1998). D-optimal axial designs for quadratic and cubic additive mixture models. Australian and New Zealand Journal of Statistics, Vol. 40, pp. 359-371.
33. Chan, L. Y. and M. K. Sandhu (1999). Optimal orthogonal block designs for a quadratic mixture model for three components. Journal of Applied Statistics, Vol. 26, pp. 19-34.
34. Charnet, R. and R. J. Beaver (1988). Design and analysis of paired comparison experiments involving mixtures. Journal of Statistical Planning and Inference, Vol. 20, pp. 91-103.
35. Chen, J. J., L.-A. Li, and C. D. Jackson (1996). Analysis of quantal response data from mixture experiments. Environmetrics, Vol. 7, pp. 503-512.
36. Chick, L. A. and G. F. Piepel (1984). Statistically designed optimization of a glass composition. Journal of the American Ceramic Society, Vol. 67, pp. 763-768.
37. Chick, L. A., G. F. Piepel, W. J. Gray, G. B. Mellinger, and B. O. Barnes (1980). Statistically designed study of a nuclear waste glass system. Scientific Basis for Nuclear Waste Management, Vol. 2, edited by D. J. M. Northrup, Jr. Plenum Press, New York, pp. 175-181.
38. Chick, L. A., G. F. Piepel, and G. B. Mellinger (1981). The effects of composition on properties in an 11-component nuclear waste glass system. PNL-3188, Battelle, Pacific Northwest Laboratories, Richland, WA.
39. Claringbold, P. J. (1955). Use of the simplex design in the study of the joint action of related hormones. Biometrics, Vol. 11, pp. 174-185.
40. Cornell, J. A. (1971). Process variables in the mixture problem for categorized components. Journal of the American Statistical Association, Vol. 66, pp. 42-48.
41. Cornell, J. A. (1973). Experiments with mixtures: a review. Technometrics, Vol. 15, pp. 437-455.
42. Cornell, J. A. (1975). Some comments on designs for Cox’s mixture polynomial. Technometrics, Vol. 17, pp. 25-35.
43. Cornell, J. A. (1977). Weighted versus unweighted estimates using Scheffé‘s mixture model for symmetrical error variances patterns. Technometrics, Vol. 19, pp. 237-247.
44. Cornell, J. A. (1979). Experiments with mixtures: an update and bibliography. Technometrics, Vol. 21, pp. 95-106.
45. Cornell, J. A. (1985). Mixture experiments. In Encyclopedia of Statistical Sciences, Vol. 5, Wiley, New York, pp. 569-579.
46. Cornell, J. A. (1986). A comparison between two ten-point designs for studying three-component mixture systems. Journal of Quality Technology, Vol. 18, pp. 1-15.
47. Cornell, J. A. (1988). Analyzing data from mixture experiments containing process variables: a split-plot approach. Journal of Quality Technology, Vol. 20, pp. 2-23.
48. Cornell, J. A. (1990a). How to Run Mixture Experiments for Product Quality, 2nd ed., Vol. 5, The ASQC Basic References in Quality Control: Statistical Techniques. American Society for Quality Control, Milwaukee, WI, pp. 1-71.
49. Cornell, J. A. (1990b). Embedding mixture experiments inside factorial experiments. Journal of Quality Technology, Vol. 22, pp. 265-276.
50. Cornell, J. A. (1990c). Mixture experiments. In Statistical Design and Analysis of Industrial Experiments, Chapter 7, edited by Subir Ghosh. Marcel Dekker, New York, pp. 175-209.
51. Cornell, J. A. (1991a). Mixture designs for product improvement. Communications in Statistics, Theory and Methods, Vol. 20, pp. 391-416.
52. Cornell, J. A. (1991b). The fitting of Scheffé-type models for estimating solubilities of multisolvent systems. Journal of Biopharmaceutical Statistics, Vol. 1, pp. 303-329.
53. Cornell, J. A. (1993). Saving money with a mixture experiment. ASQC Statistics Division Newsletter, Vol. 14, pp. 11-12.
54. Cornell, J. A. (1995). Fitting models to data from mixture experiments containing other factors. Journal of Quality Technology, Vol. 27, pp. 13-33.
55. Cornell, J. A. (2000). Fitting a slack-variable model to mixture data: some questions raised. Journal of Quality Technology, Vol. 32, pp. 133-147.
56. Cornell, J. A. and I. J. Good (1970). The mixture problem for categorized components. Journal of the American Statistical Association, Vol. 65, pp. 339-355.
57. Cornell, J. A. and L. Ott (1975). The use of gradients to aid in the interpretation of mixture response surfaces. Technometrics, Vol. 17, pp. 409-424.
58. Cornell, J. A. and J. W. Gorman (1978). On the detection of an additive blending component in multicomponent mixtures. Biometrics, Vol. 34, pp. 251-263.
59. Cornell, J. A. and A. I. Khuri (1979). Obtaining constant prediction variance on concentric triangles for ternary mixture systems. Technometrics, Vol. 21, pp. 147-157.
60. Cornell, J. A. and J. C. Deng (1982). Combining process variables and ingredient components in mixing experiments. Journal of Food Science, Vol. 47, pp. 836-843, 848.
61. Cornell, J. A., J. T. Shelton, R. Lynch, and G. F. Piepel (1983). Plotting three-dimensional response surfaces for three-component mixtures or two-factor systems. Bulletin 836, Agricultural Experiment Stations. Institute of Food and Agricultural Sciences, University of Florida, Gainesville, pp. 1-31.
62. Cornell, J. A. and J. W. Gorman (1984). Fractional design plans for process variables in mixture experiments. Journal of Quality Technology, Vol. 16, pp. 20-38.
63. Cornell, J. A. and R. D. Berger (1987). Factors that influence the value of the coefficient of determination in simple linear and nonlinear regression models. Phytopathology, Vol. 77, pp. 63-70.
64. Cornell, J. A. and S. B. Linda (1991). Models and designs for experiments with mixtures. Part I: Exploring the whole simplex region. Bulletin 879, Agricultural Experiment Station. Institute of Food and Agricultural Sciences, University of Florida, Gainesville, pp. 1-49.
65. Cornell, J. A. and D. C. Montgomery (1996). Interaction models as alternatives to low-order polynomials. Journal of Quality Technology, Vol. 28, pp. 163-176.
66. Cornell, J. A. and J. M. Harrison (1997). Models and Designs for Experiments with Mixtures, Part II: Exploring a subregion of the simplex and the inclusion of other factors in mixture experiments. Bulletin 899, Agricultural Experiment Station. Institute of Food and Agricultural Sciences, University of Florida, Gainesville, pp. 1-78.
67. Cornell, J. A. and P. J. Ramsey (1998). A generalized mixture model for categorized-component problems with an application to a photoresist-coating experiment. Technometrics, Vol. 40, pp. 48-61.
68. Cox, D. R. (1971). A note on polynomial response functions for mixtures. Biometrika, Vol. 58, pp. 155-159.
69. Crosier, R. B. (1984). Mixture experiments: geometry and pseudo-components. Technometrics, Vol. 26, pp. 209-216.
70. Crosier, R. B. (1986). The geometry of constrained mixture experiments. Technometrics, Vol. 28, pp. 95-102.
71. Crosier, R. B. (1991). Symmetry in mixture experiments. Communications in Statistics, Theory and Methods, Vol. 20, pp. 1911-1935.
72. Cruise, D. R. (1966). Plotting the composition of mixtures on simplex coordinates. Journal of Chemical Education, Vol. 43, pp. 30-33.
73. Czitrom, V. (1988). Mixture experiments with process variables: D-optimal orthogonal experimental designs. Communications in Statistics, Theory and Methods, Vol. 17, pp. 105-121.
74. Czitrom, V. (1989). Experimental design for four mixture components with process variables. Communications in Statistics, Theory and Methods, Vol. 18, pp. 4561-4581.
75. Czitrom, V. (1992). Note on a mixture experiment with process variables. Communications in Statistics Part B: Simulation and Computation, Vol. 21, pp. 493-498.
76. Daniel, C. (1963). Discussion on Professor Scheffé‘s paper. Journal of the Royal Statistical Society, B, Vol. 25, pp. 256-257.
77. Daniel, C. and F. S. Wood (1971). Fitting Equations to Data. Computer Analysis of Multifactor Data for Scientists and Engineers. Wiley, New York.
78. Darroch, J. N. and J. Waller (1985). Additivity and interaction in three-component experiments with mixtures. Biometrika, Vol. 72, pp. 153-163.
79. Debets, H. J. G. (1985). Optimization methods for HPLC. Journal of Liquid Chromatography, Vol. 8, pp. 2725-2780.
80. Del Castillo, E. and D. C. Montgomery (1993). A nonlinear programming solution to the dual response problem. Journal of Quality Technology, Vol. 25, pp. 199-204.
81. Derringer, G. C. (1994). A balancing act: optimizing a product’s properties. Quality Progress, Vol. 27, pp. 51-58.
82. Derringer, G. C. and R. Suich (1980). Simultaneous optimization of several response variables. Journal of Quality Technology, Vol. 12, pp. 214-219.
83. Diamond, W. J. (1967). Three dimensional models of extreme vertices designs for four component mixtures. Technometrics, Vol. 9, pp. 472-475.
84. Diamond, W. J. (1981). Practical Experiment Designs for Engineers and Scientists. Lifetime Learning Publications, Belmont, CA, pp. 263-274.
85. Donelson, D. H. and J. T. Wilson (1960). Effect of the relative quantity of flour fractions on cake quality. Cereal Chemistry, Vol. 37, pp. 241-262.
86. Donev, A. N. (1989). Design of experiments with both mixture and qualitative factors. Journal of the Royal Statistical Society, B, Vol. 51, pp. 297-302.
87. Draper, N. R. and W. E. Lawrence (1965a). Mixture designs for three factors.. Journal of the Royal Statistical Society, B, Vol. 27, pp. 450-465.
88. Draper, N. R. and W. E. Lawrence (1965b). Mixture designs for four factors.. Journal of the Royal Statistical Society, B, Vol. 27, pp. 473-478.
89. Draper, N. R. and A. M. Herzberg (1971). On lack of fit. Technometrics, Vol. 13, pp. 231-241.
90. Draper, N. R. and R. C. St. John (1977a). A mixtures model with inverse terms.. Technometrics, Vol. 19, pp. 37-46.
91. Draper, N. R. and R. C. St. John (1977b). Designs in three and four components for mixtures models with inverse terms.. Technometrics, Vol. 19, pp. 117-130.
92. Draper, N. R. and H. Smith (1981). Applied Regression Analysis, 2nd ed., Wiley, New York.
93. Draper, N. R., P. Prescott, S. M. Lewis, A. M. Dean, P. W. M. John, and M. G. Tuck (1993). Mixture designs for four components in orthogonal blocks. Technometrics, Vol. 35, pp. 268-276. Correction in Technometrics, 1994, Vol. 36, pp. 234.
94. Draper, N. R. and F. Pukelsheim (1997). Mixture models based on homogeneous polynomials. Journal of Statistical Planning and Inference, Vol. 71, pp. 303-311.
95. Draper, N. R. and F. Pukelsheim (1999). Kiefer ordering of simplex designs for first- and second-degree mixture models. Journal of Statistical Planning and Inference, Vol. 79, pp. 325-348.
96. Drew, B. A. (1967). Experiments with mixtures. The Minnesota Chemist, Vol. 19, pp. 4-9.
97. Duineveld, C. A. A., A. K. Smilde, and D. A. Doornbos (1993). Comparison of experimental designs combining process and mixture variables. Parts I and II. Design construction and theoretical evaluation. Chemometrics and Intelligent Laboratory Systems, Vol. 19, pp. 295-308.
98. Farrand, E. A. (1969). Starch damage and alpha-amylase as bases for mathematical models relating to flour-water absorption. Cereal Chemistry, Vol. 46, 103-116.
99. Galil, Z. and J. Kiefer (1977a). Comparison of Box-Draper and D-optimum designs for experiments with mixtures.. Technometrics, Vol. 19, pp. 441-444.
100. Galil, Z. and J. Kiefer (1977b). Comparison of simplex designs for quadratic mixture models.. Technometrics, Vol. 19, pp. 445-453.
101. Glajch, J. L., J. J. Kirkland, K. M. Squire, and J. M. Minor (1980). Optimization of solvent strength and selectivity for reversed-phase liquid chromatography using an interactive mixture-design statistical technique. Journal of Chromatography, Vol. 199, pp. 57-79.
102. Glajch, J. L., J. J. Kirkland, and L. R. Snyder (1982). Practical optimization of solvent selectivity in liquid-solid chromatography using a mixture-design statistical technique. Journal of Chromatography, Vol. 238, pp. 269-280.
103. Goel, B. S. (1980a). Systematic designs for experiments with mixtures.. Biometrical Journal, Vol. 22, pp. 345-350.
104. Goel, B. S. (1980b). Designs for restricted exploration in mixture experiments.. Biometrical Journal, Vol. 22, pp. 351-358.
105. Goel, B. S. and A. K. Nigam (1979). Sequential exploration in mixture experiments. Biometrical Journal, Vol. 21, pp. 277-285.
106. Gorman, J. W. (1966). Discussion of extreme vertices designs of mixture experiments by R. A. McLean and V. L. Anderson. Technometrics, Vol. 8, pp. 455-456.
107. Gorman, J. W. (1970). Fitting equations to mixture data with restraints on compositions. Journal of Quality Technology, Vol. 2, pp. 186-194.
108. Gorman, J. W. and J. E. Hinman (1962). Simplex-lattice designs for multicomponent systems. Technometrics, Vol. 4, pp. 463-487.
109. Gorman, J. W. and J. A. Cornell (1982). A note on model reduction for experiments with both mixture components and process variables. Technometrics, Vol. 24, pp. 243-247.
110. Gorman, J. W. and J. A. Cornell (1985). A note on fitting equations to freezing point data exhibiting eutectics for binary and ternary mixture systems. Technometrics, Vol. 27, pp. 229-239.
111. Graybill, F. A. (1961). An Introduction to Linear Statistical Models. McGraw-Hill, New York.
112. Green, J. R. (1971). Testing departure from a regression, without using replication. Technometrics, Vol. 13, pp. 609-615.
113. Hackler, W. C, W. W. Kriegel, and R. J. Hader (1956). Effect of raw-material ratios on absorption of whiteware compositions. Journal of the American Ceramic Society, Vol. 39, pp. 20-25.
114. Hahn, G. J., W. Q. Meeker, and P. I. Feder (1976). The evaluation and comparison of experimental designs for fitting regression relationships. Journal of Quality Technology, Vol. 8, pp. 140-157.
115. Hare, L. B. (1974). Mixture designs applied to food formulation. Food Technology, Vol. 28, pp. 50-62.
116. Hare, L. B. (1979). Designs for mixture experiments involving process variables. Technometrics, Vol. 21, pp. 159-173.
117. Hare, L. B. (1985). Graphical display of the results of mixture experiments. In Experiments in Industry: Design, Analysis, and Interpretation of Results, edited by R. D. Snee, L. B. Hare, and R. Trout, sponsored by ASQC Chemical and Process Industries Division, ASQC, pp. 99-109.
118. Hare, L. B. and P. L. Brown (1977). Plotting response surface contours for three-component mixtures. Journal of Quality Technology, Vol. 9, 193-197.
119. Harris, I. A. and P. J. Bray (1984). B-nuclear magnetic resonance studies of borate glasses containing tellurium dioxide. Physics and Chemistry of Glasses, Vol. 25, pp. 44-51.
120. Heinsman, J. A. and D. C. Montgomery (1995). Optimization of a household product formulation using a mixture experiment. Quality Engineering, Vol. 7, pp. 583-599.
121. Henika, R. G. and M. R. Henselman (1969). Stable brew concentrate for whey cysteine batch breadmaking and methods. Cereal Science Today, Vol. 14, pp. 248-253.
122. Hester, K. K. and J. R. Lofstrom (1981). Application of simplex lattice design experimentation to coatings research. Journal of Coatings Technology, Vol. 53, pp. 33-40.
123. Hewlett, P. S. and R. L. Plackett (1961). Models for quantal responses to mixtures of two drugs. Quantitative Methods in Pharmacology, North-Holland, Amsterdam, pp. 328-336.
124. Hilgers, R. D. and P. Bauer (1995). Optimal designs for mixture amount experiments. Journal of Statistical Planning and Inference, Vol. 48, pp. 241-246.
125. Hoerl, R. W. (1987). The application of ridge techniques to mixture data: ridge analysis. Technometrics, Vol. 29, pp. 161-172.
126. Huor, S. S., E. M. Ahmed, P. V. Rao, and J. A. Cornell (1980). Formulation and sensory evaluation of a fruit punch containing watermelon juice. Journal of Food Science, Vol. 45, pp. 809-813.
127. Jang, D. H. and G. J. Na (1996). A graphical method for evaluating mixture designs with respect to the slope. Communications in Statistics, Theory and Methods, Vol. 25, pp. 1043-1058.
128. John, P. W. M. (1984). Experiments with mixtures involving process variables. Technical Report #8, Center for Statistical Sciences, University of Texas, Austin, pp. 1-17.
129. Kenworthy, O. O. (1963). Factorial experiments with mixtures using ratios. Industrial Quality Control, Vol. 19, pp. 24-26.
130. Kettaneh-Wold, N. (1992). Analysis of mixture data with partial least squares. Chemometrics and Intelligent Laboratory Systems, Vol. 14, pp. 57-69.
131. Keviczky, L. (1970). The analysis of first and second order simplex designs. Periodica Polytechnia, Vol. 14, pp. 231-241.
132. Khuri, A. I. and J. A. Cornell (1996). Response Surfaces: Designs and Analyses, 2nd ed, Marcel Dekker, New York.
133. Khuri, A. I., J. M. Harrison, and J. A. Cornell (1999). Using quantile plots of the prediction variance for comparing designs for a constrained mixture region: an application involving a fertilizer experiment. Applied Statistics, C, Vol. 49, pp. 521-532.
134. Kissell, L. T. (1959). A lean-formula cake method for varietal evaluation and research. Cereal Chemistry, Vol. 36, pp. 168-175.
135. Kissell, L. T. (1967). Optimization of white layer cake formulations by a multiple-factor experimental design. Cereal Chemistry, Vol. 44, pp. 253-268.
136. Kissell, L. T. and B. D. Marshall (1962). Multi-factor responses of cake quality to basic ingredient ratios. Cereal Chemistry, Vol. 39, pp. 16-30.
137. Kojouharoff, V. and H. Ionchev (1986). Experimental-statistical method for investigation of multicomponent yttrium garnet systems. Journal of American Ceramic Society, Vol. 69, pp. 767-769.
138. Koons, G. F. (1989). Effect of sinter composition on emissions: a multi-component, highly constrained mixture experiment. Journal of Quality Technology, Vol. 21, pp. 261-267.
139. Koons, G. F. and R. H. Heasley (1981). Response surface contour plots for mixture problems. Journal of Quality Technology, Vol. 13, pp. 207-212.
140. Koons, G. F. and M. H. Wilt (1985). Design and analysis of an ABS pipe compound experiment. In Experiments in Industry: Design, Analysis, and Interpretation of Results, edited by R. D. Snee, L. B. Hare, and R. Trout, sponsored by ASQC Chemical and Process Industries Division, ASQC, pp. 111-117.
141. Korn, E. L. and P. Lin (1983). Interactive effects of mixtures of stimuli in life table analysis. Biometrika, Vol. 70, pp. 103-110.
142. Kowalski, S., J. A. Cornell, and G. G. Vining (2000). A new model and class of designs for mixture experiments with process variables. Communications in Statistics, Theory and Methods, Vol. 29, pp. 312-341.
143. Krol, L. H. (1966). Butadiene and isoprene rubber in giant tire treads. Rubber Chemistry and Technology, Vol. 39, pp. 452-459.
144. Kurotori, I. S. (1966). Experiments with mixtures of components having lower bounds. Industrial Quality Control, Vol. 22, pp. 592-596.
145. Laake, P. (1975). On the optimal allocation of observations in experiments with mixtures. Scandinavian Journal of Statistics, Vol. 2, pp. 153-157.
146. Lambrakis, D. P. (1968a). Estimated regression function of the {q, m} simplex-lattice design.. Bulletin of Hellenic Mathematical Society, Vol. 9, pp. 13-19.
147. Lambrakis, D. P. (1968b). Experiments with mixtures: a generalization of the simplex-lattice design.. Journal of the Royal Statistical Society, B, Vol. 30, pp. 123-136.
148. Lambrakis, D. P. (1969a). Experiments with p-component mixtures.. Journal of the Royal Statistical Society, B, Vol. 30, pp. 137-144.
149. Lambrakis, D. P. (1969b). Experiments with mixtures: an alternative to the simplex-lattice design.. Journal of the Royal Statistical Society, B, Vol. 31, pp. 234-245.
150. Lambrakis, D. P. (1969c). Experiments with mixtures: estimated regression function of the multiple-lattice design.. Journal of the Royal Statistical Society, B, Vol. 31, pp. 276-284.
151. Lee, H. H. and J. C. Warner (1935). The system biphenly-bibenzyl-naphthalene: nearly ideal binary and ternary systems. Journal of the American Chemical Society, Vol. 37, pp. 318-321.
152. Leonpacker, R. M. (1978). The Ethyl Technique of Octane Prediction. Ethyl Corporation Petroleum Chemicals Division Report No. RTM-400, Ethyl Corporation, Baton Rouge, La.
153. Lewis, S. M., A. M. Dean, N. R. Draper, and P. Prescott (1994). Mixture designs for q components in orthogonal blocks. Journal of the Royal Statistical Society, B, Vol. 56, pp. 457-467.
154. Li, J. C. (1971). Design of experiments with mixtures and independent variable factors. Unpublished Ph.D. dissertation. Department of Statistics, Rutgers University, New Brunswick, NJ.
155. Lim, Y. B. (1987). Symmetric £>-optimal designs for log contrast models with mixtures. Journal of Korean Statistical Society, Vol. 16, pp. 71-79.
156. Lim, Y. B. (1990). D-optimal design for cubic polynomial regression on the q-simplex. Journal of Statistical Planning and Inference, Vol. 25, pp. 141-152.
157. Liu, S. and H. Neudecker (1995). A V-optimal design for Scheffé‘s polynomial model. Statistics & Probability Letters, Vol. 23, pp. 253-258.
158. Liu, S. and H. Neudecker (1997). Experiments with mixtures: optimal allocations for Becker’s models. Metrika, Vol. 45, pp. 53-66.
159. MacDonald, I. A. and D. A. Bly (1966). Determination of optimal levels of several emulsifiers in cake mix shortenings. Cereal Chemistry, Vol. 43, pp. 571-584.
160. p. Technometrics, Vol. 15, pp. 661-675.
161. Marquardt, D. W. (1970). Generalized inverses, ridge regression, biased linear estimation and nonlinear estimation. Technometrics, Vol. 12, pp. 591-612.
162. Marquardt, D. W. and R. D. Snee (1974). Test statistics for mixture models. Technometrics, Vol. 16, pp. 533-537.
163. McLean, R. A. and V. L. Anderson (1966). Extreme vertices design of mixture experiments. Technometrics, Vol. 8, pp. 447-454.
164. Mikaeili, F. (1988). Allocation of measurements in experiments with mixtures. Keio Science and Technology Reports, Vol. 41, pp. 25-37.
165. Mikaeili, F. (1989). D-optimum design for cubic without 3-way effect on the simplex. Journal of Statistical Planning and Inference, Vol. 21, pp. 107-115.
166. Mikaeili, F. (1993). D-optimum design for full cubic on q-simplex. Journal of Statistical Planning and Inference, Vol. 35, pp. 121-130.
167. Minitab (1999). User’s Guide 2: Data Analysis and Quality Tools, Release 13. Minitab Inc., State College, PA.
168. Mitchell, T. J. (1974). An algorithm for construction of “D-optimal” experimental designs. Technometrics, Vol. 16, pp. 203-210.
169. Mendieta, E. J., H. N. Linssen, and R. Doornbos (1975). Optimal designs for linear mixture models. Statistical Neerlandica, Vol. 29, pp. 145-150.
170. Montgomery, D. C. and S. M. Voth (1994). Multicollinearity and leverage in mixture experiments. Journal of Quality Technology, Vol. 26, pp. 96-108.
171. Montgomery, D. C, E. A. Peck, and G. G. Vining (2001). Introduction to Linear Regression Analysis. 3rd ed., Wiley, New York.
172. Morgan, S. L. and C. H. Jacques (1978). Response surface evaluation and optimization in gas chromatography. Journal of Chromatographic Science, Vol. 16, pp. 500-505.
173. Morris, W. E. (1975). The Interaction Approach to Gasoline Blending, Petroleum Chemicals Division Report AM-75-30. E. I. DuPont de Nemours and Co., Inc., Newark, DE.
174. Morris, W. E. and R. D. Snee (1979). Blending relationships among gasoline component mixtures. Automotive Technologist, Vol. 3, pp. 56-61.
175. Moustafa, M. A., A. M. Molokhia, and M. W. Gouda (1981). Phenobarbital solubility in propylene glycol-glycerol-water systems. Journal of Pharmaceutical Sciences, Vol. 70, pp. 1172-1174.
176. Murty, J. S. and M. N. Das (1968). Design and analysis of experiments with mixtures. Annals of Mathematical Statistics, Vol. 39, pp. 1517-1539.
177. Murthy, M. S. R. and J. S. Murty (1982). A note on mixture designs derived from factorials. Journal of the Indian Society of Agricultural Statistics, Vol. 34, pp. 87-93.
178. Murthy, M. S. R. and J. S. Murty (1983). Restricted region simplex design for mixture experiments. Communications in Statistics, Theory and Methods, Vol. A12, pp. 2605-2615.
179. Murthy, M. S. R. and J. S. Murty (1989). Restricted region designs for multifactor mixture experiments. Communications in Statistics, Theory and Methods, Vol. 18, pp. 1279-1295.
180. Murthy, M. S. R. and J. S. Murty (1993). Block designs for mixture experiments. Journal of the Indian Society of Agricultural Statistics, Vol. 44, pp. 55-71.
181. Murthy, M. S. R. and P. L. Manga (1996). Restricted region simplex designs for mixture experiments in the presence of process variables. Sankhyā, Vol. 58, pp. 231-239.
182. Myers, R. H. (1964). Methods for estimating the composition of a three component liquid mixture. Technometrics, Vol. 6, pp. 343-356.
183. Myers, R. H. (1986). Classical and Modem Regression with Applications. Duxbury Press, Boston, MA.
184. Naes, T., E. M. Faergestad, and J. A. Cornell (1998). A comparison of methods for analyzing data from a three-component mixture experiment in the presence of variation created by two process variables. Chemometrics & Intelligent Laboratory Systems, Vol. 41, pp. 221-235.
185. Narcy, J. P. and J. Renaud (1972). Use of simplex experimental design in detergent formulation. Journal of the American Oil Chemists Society, Vol. 49, pp. 598-608.
186. Nelson, C, E. V. Thomas, and P. R. Wengert (1986). Compositional quality control study of CON-2 glass. SAND-0430, Sandia National Laboratories, Albuquerque, NM.
187. Nigam, A. K. (1970). Block designs for mixture experiments. Annals of Mathematical Statistics, Vol. 41, pp. 1861-1869.
188. Nigam, A. K. (1973). Multifactor mixture experiments. Journal of the Royal Statistical Society, B, Vol. 35, pp. 51-66.
189. Nigam, A. K. (1974). Some designs and models for mixture experiments for the sequential exploration of response surfaces. Journal of the Indian Society of Agricultural Statistics, Vol. 26, pp. 120-124.
190. Nigam, A. K., S. C. Gupta, and S. Gupta (1983). A new algorithm for extreme vertices designs for linear mixture models. Technometrics, Vol. 25, pp. 367-371.
191. Ochsner, A. B., R. J. Belloto, and T. D. Sokoloski (1985). Prediction of xanthine solubilities using statistical techniques. Journal of Pharmaceutical Sciences, Vol. 74, pp. 132-135.
192. Oscik-Mendyk, B. and J. K. Rozylo (1987). Analysis of chromatographic parameters in the systems with ternary mobile phases. Journal of Liquid Chromatography, Vol. 10, 1399-1415.
193. Paku, G. A., A. R. Manson, and L. A. Nelson (1971). Minimum bias estimation in the mixture problem. North Carolina State University Institute of Statistics Mimeo. Series No. 757, Raleigh, NC.
194. Park, S. H. (1978). Selecting contrasts among parameters in Scheffé‘s mixture models: screening components and model reduction. Technometrics, Vol. 20, pp. 273-279.
195. Park, S. H. and J. H. Kim (1982). Axis-slope-rotatable designs for experiments with mixtures. Journal of Korean Statistical Society, Vol. 11, pp. 36-44.
196. Park, S. H. and J. I. Kim (1988). Slope-rotatable designs for estimating the slope of response surfaces in experiments with mixtures. Journal of the Korean Statistical Society, Vol. 17, pp. 121-133.
197. Pearson, E. S. and H. O. Hartley (1972). Biometrika Tables for Statisticians, Vol. 2. Cambridge University Press, Cambridge.
198. Piepel, G. F. (1982). Measuring component effects in constrained mixture experiments. Technometrics, Vol. 24, pp. 29-39.
199. Piepel, G. F. (1983a). Defining consistent constraint regions in mixture experiments.. Technometrics, Vol. 25, pp. 97-101.
200. Piepel, G. F. (1983b). Calculating centroids in constrained mixture experiments.. Technometrics, Vol. 25, pp. 279-283.
201. Piepel, G. F. (1988a). Programs for generating extreme vertices and centroids of linearly constrained experimental regions.. Journal of Quality Technology, Vol. 20, pp. 125-139.
202. Piepel, G. F. (1988b). A note on models for mixture-amount experiments when the total amount takes a zero value.. Technometrics, Vol. 30, pp. 49-50.
203. Piepel, G. F. (1990). Screening designs for constrained mixture experiments derived from classical screening designs. Journal of Quality Technology, Vol. 22, pp. 23-33.
204. ™ Software for the Design and Analysis of Mixture Experiments, User’s Guide, Version 2.0. MIXSOFT - Mixture Experiment Software, Richland, WA.
205. Piepel, G. F. (1991). Screening designs for constrained mixture experiments derived from classical screening designs - an addendum. Journal of Quality Technology, Vol. 23, pp. 96-101.
206. Piepel, G. F. (1997). Survey of software with mixture experiment capabilities. Journal of Quality Technology, Vol. 29, pp. 76-85.
207. Piepel, G. F. (1999). Modeling methods for mixture-of-mixtures experiments applied to a table formulation problem. Pharmaceutical Development and Technology, Vol. 4, pp. 593-606.
208. Piepel, G. F. and J. A. Cornell (1985). Models for mixture experiments when the response depends on the total amount. Technometrics, Vol. 27, pp. 219-227.
209. Piepel, G. F. and J. A. Cornell (1987). Designs for mixture-amount experiments. Journal of Quality Technology, Vol. 19, pp. 11-28.
210. Piepel, G. F., G. B. Mellinger, and M. A. H. Reimus (1989). A statistical approach for characterizing chemical durability within a waste glass compositional region. Nuclear and Chemical Waste Management, Vol. 9, pp. 3-11.
211. Piepel, G. F. and J. A. Cornell (1994). Mixture experiment approaches: examples, discussion, and recommendations. Journal of Quality Technology, Vol. 26, pp. 177-196.
212. Piepel, G. F. and T. Redgate (1996). Mixture experiment techniques for reducing the number of components applied to modeling waste glass sodium release. Journal of the American Ceramic Society, Vol. 80, pp. 3038-3044.
213. Piepel, G. F. and T. Redgate (1998). A mixture experiment analysis of the Hald cement data. The American Statistician, Vol. 52, pp. 23-30.
214. Piepel, G. F. and J. W. Shade (1992). In-situ vitrification and the effects of soil additives - a mixture experiment case study. Journal of the American Ceramic Society, Vol. 75, pp. 112-116.
215. Piepel, M. G. and G. F. Piepel (2000). How soil composition affects density and water capacity - a science fair project using mixture experiment methods. STATS, No. 28, pp. 14-20.
216. Prescott, P. (2000). Projection designs for mixture experiments in orthogonal blocks. Communications in Statistics, Theory and Methods, Vol. 29, pp. 2229-2253.
217. Prescott, P., N. R. Draper, A. M. Dean, and S. M. Lewis (1993). Mixture designs for five components in orthogonal blocks. Journal of Applied Statistics, Vol. 20, pp. 105-117.
218. Prescott, P., N. R. Draper, S. M. Lewis, and A. M. Dean (1997). Further properties of mixture designs for five components in orthogonal blocks. Journal of Applied Statistics, Vol. 24, pp. 147-156.
219. Prescott, P. and N. R. Draper (1998). Mixture designs for constrained components in orthogonal blocks. Journal of Applied Statistics, Vol. 25, pp. 613-638.
220. Price, W. L. (1977). A controlled random search procedure for global optimization. Computer Journal, Vol. 20, pp. 367-370.
221. Quenouille, M. H. (1953). The Design and Analysis of Experiments. Charles Griffin and Company, London, England.
222. Quenouille, M. H. (1959). Experiments with mixtures. Journal of the Royal Statistical Society, B, Vol. 21, pp. 201-202.
223. Rao, P. (1971). Some notes on misspecification in regression. Am. Stat., Vol. 25, pp. 37-39.
224. Reis, C, J. C. de Andrade, R. E. Bruns, and R. C. C. P. Moran (1998). Application of the split-plot experimental design for the optimization of a catalytic procedure for the determination of Cr(VI). Analytica Chimica Acta, Vol. 369, pp. 269-279.
225. Rusin, M. (1975). The structure of nonlinear blending models. Chemical Engineering Science, Vol. 30, pp. 937-944.
226. Rusin, M. H., H. S. Chung, and J. F. Marshall (1981). A “transformation” method for calculating the research and motor octane numbers of gasoline blends. I&EC Fundamentals, Vol. 20, pp. 195-204.
227. Sahrmann, H. F., G. F. Piepel, and J. A. Cornell (1987). In search of the optimum Harvey Wallbanger recipe via mixture experiment techniques. The American Statistician, Vol. 41, pp. 190-194.
228. SAS Institute (1982). SASIGRAPH User’s Guide. SAS Institute, Inc., Cary, NC.
229. SAS Institute (1982). SAS User’s Guide: Statistics, SAS Institute, Inc., Cary, NC.
230. Saxena, S. K. and A. K. Nigam (1973). Symmetric-simplex block designs for mixtures. Journal of the Royal Statistical Society, B, Vol. 35, pp. 466-472.
231. Saxena, S. K. and A. K. Nigam (1977). Restricted exploration of mixtures by symmetric-simplex designs. Technometrics, Vol. 19, pp. 47-52.
232. Scheffé, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, B, Vol. 20, pp. 344-360.
233. Scheffé, H. (1959). Reply to Mr. Quenouille’s comments about my paper on mixtures. Journal of the Royal Statistical Society, B, Vol. 23, pp. 171-172.
234. Scheffé, H. (1963). The simplex-centroid design for experiments with mixtures. Journal of the Royal Statistical Society, B, Vol. 25, pp. 235-263.
235. Shelton, J. T., A. I. Khuri, and J. A. Cornell (1983). Selecting check points for testing lack of fit in response surface models. Technometrics, Vol. 25, pp. 357-365.
236. Shillington, E. R. (1979). Testing lack of fit in regression without replication. Canadian Journal of Statistics, Vol. 7, pp. 137-146.
237. Singh, S. P. and M. Pratap (1985). Analysis of symmetric-simplex designs in mixture experiments. Calcutta Statistical Association Bulletin, Vol. 34, pp. 65-73.
238. Singh, S. P., M. Pratap, and M. N. Das (1982). Analysis of mixture experiments in presence of block effects. Sankhyā B, Vol. 44, pp. 270-277.
239. Smith, W. F. and T. A. Beverly (1997). Generating linear and quadratic Cox mixture models. Journal of Quality Technology, Vol. 29, pp. 211-224.
240. Smith, W. F. and J. A. Cornell (1993). Biplot displays for looking at multiple response data in mixture experiments. Technometrics, Vol. 35, pp. 337-350.
241. Stat-Ease (1998). DESIGN-EXPERT Software for Response Surface Methodology and Mixture Experiments. Version 5.0. (1999) Version 6.0. Stat-Ease, Inc., Minneapolis, MN.
242. Snee, R. D. (1971). Design and analysis of mixture experiments. Journal of Quality Technology, Vol. 3, pp. 159-169.
243. Snee, R. D. (1973). Techniques for the analysis of mixture data. Technometrics, Vol. 15, pp. 517-528.
244. Snee, R. D. (1975a). Experimental designs for quadratic models in constrained mixture spaces.. Technometrics, Vol. 17, pp. 149-159.
245. Snee, R. D. (1975b). Discussion of the use of gradients to aid in the interpretation of mixture response surfaces.. Technometrics, Vol. 17, pp. 425-430.
246. Snee, R. D. (1979a). Experimental designs for mixture systems with multicomponent constraints.. Communications in Statistics, Theory and Methods, Vol. A8, pp. 303-326.
247. Snee, R. D. (1979b). Experimenting with mixtures.. CHEMTECH, Vol. 9, pp. 702-710.
248. Snee, R. D. (1981). Developing blending models for gasoline and other mixtures. Technometrics, Vol. 23, pp. 119-130.
249. Snee, R. D. (1985). Computer-aided design of experiments: some practical experiences. Journal of Quality Technology, Vol. 17, pp. 222-236.
250. Snee, R. D. and D. W. Marquardt (1974). Extreme vertices designs for linear mixture models. Technometrics, Vol. 16, pp. 399-408.
251. Snee, R. D. and D. W. Marquardt (1976). Screening concepts and designs for experiments with mixtures. Technometrics, Vol. 18, pp. 19-29.
252. Snee, R. D. and A. A. Rayner (1982). Assessing the accuracy of mixture model regression calculations. Journal of Quality Technology, Vol. 14, pp. 67-79.
253. Sommerville, D. M. Y. (1958). An Introduction to the Geometry of N Dimensions. ethuen, London, England, 1929; Dover, New York, 1958.
254. Soo, H. M., E. H. Sander, and D. W. Kess (1978). Definition of a prediction model for determination of the effect of processing and compositional parameters on the textural characteristics of fabricated shrimp. Journal of Food Science, Vol. 43, pp. 1165-1171.
255. Steiner, S. H. and M. Hamada (1997). Making mixtures robust to noise and mixing measurement errors. Journal of Quality Technology, Vol. 29, pp. 441-450.
256. St. John, R. C. (1984). Experiments with mixtures, ill-conditioning, and ridge regression. Journal of Quality Technology, Vol. 16, pp. 81-96.
257. Tait, J. C, D. L. Mandolesi, and H. E. C. Rummens (1984). Viscosity of melts in the sodium borosilicate system. Physics and Chemistry of Glasses, Vol. 25, pp. 100-104.
258. Thompson, D. R. (1981). Designing mixture experiments- a review. Transactions ASAE, Vol. 24, pp. 1077-1086.
259. Thompson, W. O. and R. H. Myers (1968). Response surface designs for experiments with mixtures. Technometrics, Vol. 10, pp. 739-756.
260. Tiede, M. L. (1981). How to use SAS for ANOVA of mixture problems. Proceedings of the Sixth Annual SAS Users Group International Conference, SAS Institute, Inc., Cary, NC.
261. Uranisi, H. (1964). Optimum design for the special cubic regression on the q-simplex. Mathematical Reports, Vol. 1, pp. 7-12. General Education Department, Kyushu University.
262. Van Schalkwyk, D. J. (1971). On the design of mixture experiments. Unpublished Ph. D. dissertation, University of London, England.
263. Vining, G. G., J. A. Cornell, and R. H. Myers (1993). A graphical approach for evaluating mixture designs. Applied Statistics, Vol. 42, pp. 127-138.
264. Vuchkov, I. N., H. A. Yonchev, D. L. Damgaliev, V. K. Tsochev, and T. D. Dikova (1978). Catalogue of Sequentially Generated Designs. Department of Automation Higher Institute of Chemical Technology, Sofia, Bulgaria (in Bulgarian and English).
265. Vuchkov, I. N. and H. A. Yonchev (1979). Design and analysis of experiments for the investigation of properties of mixtures and alloys. Technika, Sofia, Bulgaria (in Bulgarian).
266. Vuchkov, I. N., D. L. Damgaliev, and H. A. Yonchev (1981). Sequentially generated second-order quasi D-optimal designs for experiments with mixture and process variables. Technometrics, Vol. 23, pp. 233-238.
267. Vuchkov, I. N., H. A. Yonchev, and D. L. Damgaliev (1983). Continuous D-optimal designs for experiments with mixture and process variables. Mathematische Operations-forschung und Statistik, Series Statistics, Vol. 14, pp. 33-51.
268. Wagner, T. O. and J. W. Gorman (1962). The lattice method for design of experiments with fuels and lubricants. Application of Statistics and Computers to Fuel and Lubricant Research Problems. Department of the Army, San Antonio, TX, pp. 123-145.
269. Wagner, T. O. and J. W. Gorman (1963). Fuels, lubricants, engines, and experimental design. Transactions of the Society of Automotive Engineers, Vol. 196, pp. 684-701.
270. Watson, G. S. (1969). Linear regression on proportions. Biometrics, Vol. 25, pp. 585-588.
271. Welch, W. J. (1982). Branch-and-bound search for experimental designs based on D-optimality and other criteria. Technometrics, Vol. 24, pp. 41-48.
272. Welch, W. J (1983). A mean squared error criterion for the design of experiments. Biometrika, Vol. 70, pp. 205-213.
273. Welch, W. J. (1984). Computer-aided design of experiments for response estimation. Technometrics, Vol. 26, 217-224.
274. Welch, W. J. (1985). ACED: algorithms for the construction of experimental designs. The American Statistician, Vol. 39, p. 146.
275. Weyland, J. W., C. H. P. Bruins, and D. A. Doornbos (1984). Use of three-dimensional minimum a-plots for optimization of mobile phase composition for RP-HPLC separation of sulfonamides. Journal of Chromatographic Science, Vol. 22, pp. 31-39.
276. Wheeler, R. E. (1972). Efficient experimental design. Joint statistical meetings of the American Statistical Association, IMS and Biometric Society, Montreal, Canada, August, 1972.
277. Williams, N. A. and G. L. Amidon (1984). Excess free energy approach to the estimation of solubility in mixed solvent systems. I: Theory. Journal of Pharmaceutical Sciences, Vol. 73, pp. 9-13. II: Ethanol-water mixtures. Journal of Pharmaceutical Sciences, Vol 73. pp. 14-18. III: Ethanol-propylene glycol-water mixtures Journal of Pharmaceutical Sciences, Vol. 73, pp. 18-23.
278. Wright, A. J. (1981). The analysis of yield-density relationships in binary mixtures using inverse polynomials. Journal of Agricultural Science, Cambridge, Vol. 96, pp. 561-567.
279. Wynn, H. R. (1970). The sequential generation of D-optimum experimental designs. Annals of Mathematical Statistics, Vol. 41, pp. 1655-1664.
280. Ying-nan, G. (1981). A computing method of the number of lateral sides and the coordinates of vertices of a mixture convex-polyhedron having lower and upper bounds. Journal of Northeast Institute of Technology, Vol. 28, pp. 13-22 (in Chinese).
281. Ying-nan, G. (1983). On some optimalities of simplex-centroid design. Technical Report #5, Department of Management Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan.
282. Ying-nan, G. (1984). A branch-constructing algorithm for extreme vertices of the mixture convex polyhedron and a modified CONSIM algorithm. Acta Mathematicae Applicatae Sinica, Vol. 7, pp. 340-346 (in Chinese).
283. Ying-nan, G. (1985). A branch-boundary algorithm of various dimension bound faces for the mixture convex hyper-polyhedron. Journal of Northeast Institute of Technology, Vol. 2, pp. 71-76 (in Chinese).
284. Ying-nan, G. (1987). Division design for mixture convex polyhedra. Acta Mathematicae Applicatae Sinica, Vol. 10, pp. 68-73 (in Chinese).
285. Yonchev, H. A. (1982). Optimization of multicomponent systems. Technika, Sofia, Bulgaria (in Bulgarian).
286. Yonchev, H, A. (1985). Optimization of processes and compositions in petroleum processing industry. Technika, Sofia, Bulgaria (in Bulgarian).
287. Zemroch, P. J. (1986). Cluster analysis as an experimental design generator with application to gasoline blending experiments. Technometrics, Vol. 28, pp. 39-49.
288. Zhu, W. Y, C. Hu, and W. Chen (1986). The mixture models with logarithmic terms and their D-optimality. Chinese Journal of Applied Probability and Statistics, Vol. 2, pp. 322-333 (in Chinese).
289. N-optimal designs for mixtures regression models with logarithmic terms. Acta Mathematicae Applicatae Sinica, Vol. 3, pp. 26-36 (in Chinese).
290. N-optimal designs in five and six components for mixture models with logarithmic terms.. Acta Mathematicae Applicatae Sinica, Vol. 3, pp. 317-329 (in Chinese).