Experiments with Mixtures: An Update and Bibliography

REFERENCES

• Becker , N. G. 1968 . Models for the response of a mixture . J. Roy. Statist. Soc., B , 30 : 349 – 358 .
   Google Scholar
• Becker , N. G. 1970 . Mixture designs for a model linear in the proportions . Biometrika , 57 : 329 – 338 .
   Web of Science ®Google Scholar
• Becker , N. G. 1978 . Models and designs for experiments with mixtures Submitted to Aust. J. of Statistics.
   Google Scholar
• Cornell , J. A. 1973 . Experiments with mixtures: A review . Technometrics , 15 : 437 – 455 .
   Web of Science ®Google Scholar
• Cornell , J. A. 1975 . Some comments on designs for Cox's mixture polynomial . Technometrics , 17 : 25 – 35 .
   Web of Science ®Google Scholar
• Cornell , J. A. 1977 . Weighted versus unweighted estimates using Scheffe's mixture model for symmetrical error variance patterns . Technometrics , 19 : 237 – 247 .
   Web of Science ®Google Scholar
• Cornell , J. A. and Good , I. J. 1970 . The mixture problem for categorized components . J. Amer. Statist. Assoc. , 65 : 339 – 355 .
   Web of Science ®Google Scholar
• Cornell , J. A. and Ott , L. 1975 . The use of gradients to aid in the interpretation of mixture response surfaces . Technometrics , 17 : 409 – 424 .
   Web of Science ®Google Scholar
• Cornell , J. A. and Gorman , J. W. 1978 . On the detection of an additive blending component in multicomponent mixtures . Biometrics , 34 : 251 – 263 .
   Web of Science ®Google Scholar
• Cornell , J. A. and Khuri , A. I. 1978 . Obtaining constant prediction variance on concentric triangles for ternary mixture systems Fla. Ag. Exp. Sta. J. Series No. 1086. To appear in Technometrics.
   Google Scholar
• Cox , D. R. 1971 . A note on polynomial response functions for mixtures . Biometrika , 58 : 155 – 159 .
   Web of Science ®Google Scholar
• Donelson , D. H. and Wilson , J. T. 1960 . Effect of the relative quantity of flour fractions on cake quality . Cereal Chemistry , 37 : 241 – 262 .
   Web of Science ®Google Scholar
• Draper , N. R. and Lawrence , W. E. 1965 . Mixture designs for three factors . J. Roy. Statist. Soc., B , 27 : 450 – 465 .
   Google Scholar
• Draper , N. R. and Lawrence , W. E. 1965 . Mixture designs for four factors . J. Roy. Statist. Soc., B , 27 : 473 – 478 .
   Google Scholar
• Draper , N. R. and St. John , R. C. 1977 . A mixtures model with inverse terms . Technometrics , 19 : 37 – 46 .
   Web of Science ®Google Scholar
• Draper , N. R. and St. John , R. C. 1977 . Designs in three and four components for mixtures models with inverse terms . Technometrics , 19 : 117 – 130 .
   Web of Science ®Google Scholar
• Galil , Z. and Kiefer , J. 1977 . Comparison of Box-Draper and D-optimum designs for experiments with mixtures . Technometrics , 19 : 441 – 444 .
   Web of Science ®Google Scholar
• Galil , Z. and Kiefer , J. 1977 . Comparison of simplex designs for quadratic mixture models . Technometrics , 19 : 445 – 453 .
   Web of Science ®Google Scholar
• Gorman , J. W. and Hinman , J. E. 1962 . Simplex-lattice designs for multi-component systems . Technometrics , 4 : 463 – 487 .
   Web of Science ®Google Scholar
• Hahn , G. J. , Meeker , W. Q. and Feder , P. I. 1976 . The evaluation and comparison of experimental designs for fitting regression relationships . J. Quality Technology , 8 : 140 – 157 .
   Google Scholar
• Hare , L. B. Designs for mixture experiments involving process variables . Presented at the Annual Meeting of the American Statistical Association . August 1977 , Chicago , Illinois .
   Google Scholar
• Kissell , L. T. 1967 . Optimization of white layer cake formulations by a multiple-factor experimental design . Cereal Chemistry , 44 : 253 – 268 .
   Web of Science ®Google Scholar
• Kissell , L. T. and Marshall , B. D. 1962 . Multifactor responses of cake quality to basic ingredient ratios . Cereal Chemistry , 39 : 16 – 30 .
   Web of Science ®Google Scholar
• Kurotori , I. S. 1966 . Experiments with mixtures of components having lower bounds . Industrial Quality Control , 22 : 592 – 596 .
   Google Scholar
• Laake , P. 1975 . On the optimal allocation of observations in experiments with mixtures . Scandinavian J. of Statist. , 2 : 153 – 157 .
   Google Scholar
• Lambrakis , D. P. 1969 . Experiments with mixtures: Estimated regression function of the multiple-lattice design . J. Roy. Statist. Soc., B , 31 : 276 – 284 .
   Google Scholar
• Li , J. C. 1971 . Design of experiments with mixtures and independent variable factors , Ph.D. dissertation New Brunswick , N.J. : Dept. of Statistics, Rutgers Univ. .
   Google Scholar
• Marquardt , D. W. and Snee , R. D. 1974 . Test statistics for mixture models . Technometrics , 16 : 533 – 537 .
   Web of Science ®Google Scholar
• McLean , R. A. and Anderson , V. L. 1966 . Extreme vertices design of mixture experiments . Technometrics , 8 : 447 – 454 .
   Web of Science ®Google Scholar
• Murty , J. S. and Das , M. N. 1968 . Design and analysis of experiments with mixtures . Ann. Math. Statist. , 39 : 1517 – 1539 .
   Google Scholar
• Narcy , J. P. and Renaud , J. 1972 . Use of simplex experimental designs in detergent formulation . J. American Oil Chemist's Soc. , 49 : 598 – 608 .
   Web of Science ®Google Scholar
• Nigam , A. K. 1973 . Multifactor mixture experiments . J. Roy. Statist. Soc., B , 35 : 51 – 66 .
   Google Scholar
• Paku , G. A. , Manson , A. R. and Nelson , L. A. 1971 . Minimum bias estimation in the mixture problem , Raleigh , N.C. : North Carolina State Univ. Inst, of Statistics Mimeo . Series No. 757
   Google Scholar
• Park , S. H. 1978 . Selecting contrasts among parameters in Scheffe's mixture models: Screening components and model reduction . Technometrics , 20 : 273 – 279 .
   Web of Science ®Google Scholar
• Saxena , S. K. and Nigam , A. K. 1973 . Symmetric-simplex block designs for mixtures . J. Roy. Statist. Soc., B , 35 : 466 – 472 .
   Google Scholar
• Saxena , S. K. and Nigam , A. K. 1977 . Restricted exploration of mixtures by symmetric-simplex designs . Technometrics , 19 : 47 – 52 .
   Web of Science ®Google Scholar
• ScheffÉ , H. 1958 . Experiments with mixtures . J. Roy. Statist. Soc., B , 20 : 344 – 360 .
   Google Scholar
• ScheffÉ , H. 1963 . The simplex-centroid design for experiments with mixtures . J. Roy. Statist. Soc., B , 25 : 235 – 263 .
   Google Scholar
• Snee , R. D. 1973 . Techniques for the analysis of mixture data . Technometrics , 15 : 517 – 528 .
   Web of Science ®Google Scholar
• Snee , R. D. 1975 . Experimental designs for quadratic models in constrained mixture spaces . Technometrics , 17 : 149 – 159 .
   Web of Science ®Google Scholar
• Snee , R. D. 1975 . Discussion of Cornell and Ott (1975) . Technometrics , 17 : 425 – 430 .
   Web of Science ®Google Scholar
• Snee , R. D. and Marquardt , D. W. 1974 . Extreme vertices designs for linear mixture models . Technometrics , 16 : 399 – 408 .
   Web of Science ®Google Scholar
• Snee , R. D. and Marquardt , D. W. 1976 . Screening concepts and designs for experiments with mixtures . Technometrics , 18 : 19 – 29 .
   Web of Science ®Google Scholar
• Thompson , W. O. and Myers , R. H. 1968 . Response surface designs for experiments with mixtures . Technometrics , 10 : 739 – 756 .
   Web of Science ®Google Scholar
• Van Schalkwyk , D. J. 1971 . On the design of mixture experiments , Ph.D. Dissertation London , , England : Univ. of London .
   Google Scholar
• Watson , G. S. 1969 . Linear regression on proportions . Biometrics , 25 : 585 – 588 .
   PubMed Web of Science ®Google Scholar
• Wheeler , R. E. Efficient experimental design . Presented at the Annual. Meeting of the American Statistical Association . August 1972 , Montreal , Canada.
   Google Scholar
• Wynn , H. P. 1970 . The sequential generation of D-optimum experimental designs . Ann. Math. Statist. , 41 : 1655 – 1664 .
   Google Scholar
• Becker , N. G. 1969 . Regression problems when the predictor variables are proportions . J. Roy. Statis. Soc., B , 31 : 107 – 112 .
   Google Scholar
• Boyles , H. E. , Heimbach , N. and Fuld , M. 1965 . To improve a finish formulation . Soap and Chemical Specialties , 77–80 : 112 – 113 .
   Google Scholar
• Bownds , J. M. , Kurotori , T. S. and Cruise , D. R. 1965 . Notes on simplex models in the study of multi-component mixtures 1 – 40 . China Lake , California U.S. Naval Ordinance Test Station, NA VWEPS Report 8670, NOTS TP 3719, Copy 197, Jan.
   Google Scholar
• Box , G. E. P. and Gardiner , C. J. 1966 . Constrained designs–part I, First order designs , 1 – 14 . Madison , Wisconsin : Department of Statistics, Univ. of Wisconsin . Technical Report No. 89
   Google Scholar
• Clarinbold , P. J. 1955 . Use of the simplex design in the study of the joint action of related hormones . Biometrics , 11 : 174 – 185 .
   Web of Science ®Google Scholar
• Cornell , J. A. 1971 . Process variables in the mixture problem for categorized components . J. Amer. Statist. Assoc. , 66 : 42 – 48 .
   Web of Science ®Google Scholar
• Cruise , D. R. 1966 . Plotting the composition of mixtures on simplex coordinates . J. of Chemical Education , 43 : 30 – 33 .
   Web of Science ®Google Scholar
• Diamond , W. J. 1967 . Three dimensional models of extreme vertices designs for four component mixtures . Technometrics , 9 : 472 – 475 .
   Web of Science ®Google Scholar
• Drew , B. A. 1967 . Experiments with mixtures . The Minnesota Chemist , 19 : 4 – 9 .
   Google Scholar
• Farrand , E. A. 1969 . Starch damage and alpha-amylase as bases for mathematical models relating to flour-water absorption . Cereal Chemistry , 46 : 103 – 116 .
   Web of Science ®Google Scholar
• Gorman , J. W. 1966 . Discussion of extreme vertices design of mixture experiments by R. A. McLean and V. L. Anderson . Technometrics , 8 : 455 – 456 .
   Web of Science ®Google Scholar
• Gorman , J. W. 1966 . Fitting equations to mixture data with restraints on compositions. Research and Development Department, American Oil Company, Whiting, Indiana, 1–20. (1970) . J. Quality Technology , 2 : 186 – 194 .
   Google Scholar
• Hackler , W. C. , Kriegel , W. W. and Hader , R. J. 1956 . Effect of raw-material ratios on absorption of white-ware compositions . J. Amer. Ceramic Soc. , 39 : 20 – 25 .
   Web of Science ®Google Scholar
• Hare , L. B. 1974 . Mixture designs applied to food formulation . Food Technology , 28 : 50 – 62 .
   Web of Science ®Google Scholar
• Hare , L. B. and Brown , P. L. 1977 . Plotting response surface contours on a three-component mixture space . J. Quality Technology , 9 : 193 – 197 .
   Web of Science ®Google Scholar
• Henika , R. G. and Henselman , M. R. 1969 . Stable brew concentrate for whey cysteine breadmaking and methods . Cereal Science Today , 14 : 248 – 253 .
   Google Scholar
• Hewlett , P. S. 1969 . Measurement of the potencies of drug mixtures . Biometrics , 25 : 477 – 487 .
   PubMed Web of Science ®Google Scholar
• Hewlett , P. S. and Plackett , R. L. 1961 . “ Models for quantal responses to mixtures of two drugs ” . In Quantitative Methods in Pharmacology , 328 – 336 . Amsterdam : North Holland .
   Google Scholar
• John , P. W. M. and Gorman , J. W. Experiments with mixtures . Gordon Research Conference on Statistics in Chemistry and Chemical Engineering.
   Google Scholar
• Kentworthy , O. O. 1963 . Factorial experiments with mixtures using ratios . Industrial Quality Control , 19 : 24 – 26 .
   Google Scholar
• Kissell , L. T. 1959 . A lean-formula cake method for varietal evaluation and research . Cereal Chemistry , 36 : 168 – 175 .
   Web of Science ®Google Scholar
• Krol , L. H. 1966 . Butadiene and isoprene rubber in giant tire trends . Rubber Chemistry and Technology , 39 : 452 – 459 .
   Google Scholar
• Lambrakis , D. P. 1968 . Estimated regression function of the {q, m} simplex-lattice design . Bull, of Hellenic Math. Soc., Athens, Greece , 9 : 13 – 19 .
   Google Scholar
• Lambrakis , D. P. 1968 . Experiments with mixtures: A generalization of the simplex-lattice design . J. Roy. Statist. Soc., B , 30 : 123 – 136 .
   Google Scholar
• Lambrakis , D. P. 1968 . Experiments with p-component mixtures . J. Roy. Statist. Soc., B , 30 : 137 – 144 .
   Google Scholar
• Lambrakis , D. P. 1969 . Experiments with mixtures: An alternative to the simplex-lattice design . J. Roy. Statist. Soc., B , 31 : 234 – 245 .
   Google Scholar
• Lee , H. H. and Warner , J. C. 1935 . The system biphenyl-bebenzyl-caphthalene. Nearly ideal binary and ternary systems . J. Amer. Chem. Soc. , 57 : 318 – 321 .
   Google Scholar
• Macdonald , I. A. and Bly , D. A. 1966 . Determination of optimal levels of several emulsifiers in cake mix shortenings . Cereal Chemistry , 43 : 571 – 584 .
   Web of Science ®Google Scholar
• Mendieta , E. J. , Linssen , H. N. and Doornbos , R. 1975 . Optimal designs for linear mixture models . Statist. Neerlandica , 29 : 145 – 150 .
   Google Scholar
• Myers , R. H. 1964 . Methods for estimating the composition of a three component liquid mixture . Technometrics , 6 : 343 – 356 .
   Web of Science ®Google Scholar
• Nigam , A. K. 1970 . Block designs for mixture experiments . Ann. Math. Statist. , 41 : 1861 – 1869 .
   Google Scholar
• Nigam , A. K. 1974 . Some designs and models for mixture experiments for the sequential exploration of response surfaces . J. Indian Soc. Agric. Statist. , 26 : 120 – 124 .
   Google Scholar
• Quenouille , M. H. 1953 . The Design and Analysis of Experiments. , 260 – 262 . New York : Hafner .
   Google Scholar
• Quenouille , M. H. 1959 . Experiments with mixtures . J. Rob. Statist. Soc., B , 21 : 201 – 202 .
   Google Scholar
• ScheffÉ , H. 1961 . Reply to Mr. Quenouille's comment about my paper on mixtures . J. Roy. Statist. Soc., B , 23 : 171 – 172 .
   Google Scholar
• Snee , R. D. 1971 . Design and analysis of mixture experiments . J. of Quality Technology , 3 : 159 – 169 .
   Google Scholar
• Uranisi , H. 1964 . Optimum design for the special cubic regression on the q-simplex . Mathematical Reports , 1 : 7 – 12 . General Education Department, Kyushu University
   Google Scholar
• Wagner , T. O. and Gorman , J. W. The lattice method for design of experiments with fuels and lubricants . Application of Statistics and Computers to Fuel and Lubricant Research Problems . pp. 123 – 145 . Proceedings of a symposium sponsored by the Office of the Chief of Ordinance, Dept. of the Army, San Antonio, Texas
   Google Scholar
• Wagner , T. O. and Gorman , J. W. 1963 . Fuels, lubricants, engines, and experimental design . Trans. of the Soc. of Automotive Engineers , 196 : 684 – 701 .
   Google Scholar
• Wilson , J. T. and Donelson , D. H. 1965 . Studies on the dynamics of cake baking, II. The interaction of chlorine and liquid in the formation of layer cake structure . Cereal Chemistry , 42 : 25 – 37 .
   Web of Science ®Google Scholar
• Womeldorph , D. E. 1966 . Estimation in the use of the X-ray fluorescence method and use of reference components in mixtures experimental designs , Ph.D. Dissertation Blacksburg , Virginia : Virginia Polytechnic Inst. .
   Google Scholar