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

REFERENCES

• Chernoff , H. “Metric Considerations in Cluster Analysis,” . Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1: Theory of Statistics) . Berkeley , CA : University of California Press. .
   Google Scholar
• Cornell , J. A. 1981 . Experiments With Mixtures New York : John Wiley. .
   Google Scholar
• Daniel , C. and Wood , F. S. 1980 . Fitting Equations to Data, , 2nd ed. New York : John Wiley. .
   Google Scholar
• Draper , N. R. and Smith , H. 1966 . Applied Regression Analysis New York : John Wiley. .
   Google Scholar
• Dykstra , O. 1971 . “The Augmentation of Experimental Data to Maximize | X'X |,” . Technometrics , 13 : 682 – 688 .
   Web of Science ®Google Scholar
• Everitt , B. 1974 . Cluster Analysis London : Heineman Educational. .
   Google Scholar
• Everitt , B. 1979 . “Unresolved Problems in Cluster Analysis,” . Biometrics , 35 : 169 – 181 .
   Web of Science ®Google Scholar
• Hoel , P. G. 1965 . “Minimax Designs in Two Dimensional Regression,” . Annals of Mathematical Statistics , 36 : 1097 – 1106 .
   Google Scholar
• Kempthorne , O. 1977 . “Why Randomise?” . Journal of Statistical Planning and Inference , 1 : 1 – 25 .
   Web of Science ®Google Scholar
• Kendall , M. G. and Stuart , A. 1968 . The Advanced Theory of Statistics (Vol. 3: Design and Analysis and Time Series), , 2nd ed. London : Charles W. Griffin. .
   Google Scholar
• Kennard , R. W. and Stone , L. A. 1969 . “Computer Aided Design of Experiments,” . Technometrics , 11 : 137 – 148 .
   Web of Science ®Google Scholar
• Kiefer , J. 1959 . “Optimum Experimental Designs” . Journal of the Royal Statistical Society , 21 : 272 – 319 . (with discussion), Ser. B
   Google Scholar
• Lumelsky , V. J. 1982 . “A Combined Algorithm for Weighting the Variables and Clustering in the Clustering Problem,” . Pattern Recognition , 15 : 53 – 60 .
   Google Scholar
• Mardia , K. V. 1977 . “Mahalanobis Distances and Angles,”. ” . In Multivariate Analysis—IV Edited by: Krishnaiah , P. R. 495 – 511 . Amsterdam : North-Holland. .
   Google Scholar
• Mardia , K. V. , Kent , J. T. and Bibby , J. M. 1979 . Multivariate Analysis London : Academic Press. .
   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
• Mitchell , T. J. 1974 . “An Algorithm for the Construction of D-Optimal Experimental Designs,” . Technometrics , 16 : 203 – 210 .
   Web of Science ®Google Scholar
• Scheffé , H. 1958 . “Experiments With Mixtures,” . Journal of the Royal Statistical Society , 20 : 344 – 360 . Ser. B
   Google Scholar
• Scoltock , J. 1982 . “A Survey of the Literature of Cluster Analysis,” . The Computer Journal , 25 : 130 – 134 .
   Web of Science ®Google Scholar
• Searle , S. R. 1971 . Linear Models New York : John Wiley. .
   Google Scholar
• Smith , K. 1918 . “On the Standard Deviations and Interpolated Values of an Observed Polynomial Function and Its Constants and the Guidance They Give Towards a Proper Choice of the Distribution of Observations,” . Biometrika , 12 : 1 – 85 .
   Google Scholar
• Snee , R. D. 1981 . “Developing Blending Models for Gasoline and Other Mixtures,” . Technometrics , 23 : 119 – 130 .
   Web of Science ®Google Scholar
• Stigler , S. M. 1971 . “Optimum Experimental Design for Polynomial Regression,” . Journal of the American Statistical Association , 66 : 311 – 318 .
   Web of Science ®Google Scholar
• Wynn , H. P. 1970 . “The Sequential Generation of D-Optimum Experimental Designs,” . Annals of Mathematical Statistics , 41 : 1655 – 1664 .
   Google Scholar
• Zemroch , P. J. 1981a . “Algorithm AS 166, Generation of Polynomial Contrasts for Incomplete Factorial Designs With Quantitative Levels,” . Applied Statistics , 30 : 325 – 333 .
   Google Scholar
• Zemroch , P. J. 1981b . “Algorithm AS 167, Screening Algorithm for Experimental Designs With Quantitative Levels,” . Applied Statistics , 30 : 334 – 339 .
   Google Scholar