Using Genetic Algorithms to Generate Mixture-Process Experimental Designs Involving Control and Noise Variables

References

• Borkowski, J. J. (2003). “Using a Genetic Algorithm to Generate Small Exact Response Surface Designs”. Journal of Probability and Statistical Science 1, pp. 65–88.
   Google Scholar
• Borror, C. M.; Montgomery, D. C.; and Myers, R. H. (2002). “Evaluation of Statistical Designs for Experiments Involving Noise Variables”. Journal of Quality Technology 34, pp. 54–70.
   Web of Science ®Google Scholar
• Cook, R. D. and Nachtsheim, C. J. (1980). “A Comparison of Algorithms for Constructing Exact D-Optimal Designs”. Technometrics 22, pp. 315–324.
   Web of Science ®Google Scholar
• Cornell, J. A. (2002). Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data, 3rd ed. John Wiley & Sons, New York, NY.
   Google Scholar
• Cornell, J. A. (1995). “Fitting Models to Data from Mixture Experiments Containing Other Factors”. Journal of Quality Technology 27, pp. 13–33.
   Web of Science ®Google Scholar
• Cornell, J. A. and Gorman, J. W. (1984). “Fractional Design Plans for Process Variables in Mixture Experiments”. Journal of Quality Technology 16, pp. 20–38.
   Web of Science ®Google Scholar
• Dykstra, O. (1971). “The Augmentation of Experimental Data to Mazimize |X'X|”. Technometrics 3, pp. 682–688.
   Google Scholar
• Goldfarb, H. B.; Borror, C. M.; and Montgomery, D. C. (2003). “Mixture-Process Variable Experiments with Noise Variables”. Journal of Quality Technology 35, pp. 393–405.
   Web of Science ®Google Scholar
• Goldfarb, H. B.; Borror, C. M.; Montgomery, D. C.; and Anderson-Cook, C. M. (2004). “Evaluating Mixture-Process Designs with Control and Noise Variables”. Journal of Quality Technology 36, pp. 245–262.
   Web of Science ®Google Scholar
• Hamada, M.; Martz, H. F.; Reese, C. S.; and Wilson, A. G. (2001). “Finding Near-Optimal Bayesian Experimental Designs via Genetic Algorithms”. The American Statistician 55, pp. 175–181.
   Web of Science ®Google Scholar
• Heredia-Langner, A.; Carlyle, W. M.; Montgomery, D. C.; Borror, C. M.; and Runger, G. C. (2003). “Genetic Algorithms for the Construction of D-Optimal Designs”. Journal of Quality Technology 35, pp. 28–46.
   Web of Science ®Google Scholar
• Heredia-Langner, A.; Montgomery, D. C.; Carlyle, W. M.; and Borror, C. M. (2004). “Model-Robust Designs: A Genetic Algorithm Approach”. Journal of Quality Technology 36, pp. 263–279.
   Web of Science ®Google Scholar
• Johnson, M. E. and Nachtsheim, C. J. (1995). “Some Guidelines for Constructing Exact D-Optimal Designs on Convex Design Spaces”. Technometrics 3, pp. 271–277.
   Google Scholar
• Lucas, J. M. (1994). “How to Achieve a Robust Process Using Response Surface Methodology”. Journal of Quality Technology 26, pp. 248–260.
   Web of Science ®Google Scholar
• Mukerjee, R. and Huda, S. (1985). “Minimax Second and Third Order Designs to Estimate the Slope of a Response Surface”. Biometrika 72, pp. 173–178.
   Web of Science ®Google Scholar
• Murty, V. N. and Studden, W. J. (1972). “Optimal Designs for Estimating the Slope of a Polynomial Regression”. Journal of the American Statistical Association 67, pp. 869–873.
   Web of Science ®Google Scholar
• Meyer, R. K. and Nachtsheim, C. J. (1995). “The Coordinate-Exchange Algorithm for Constructing Exact Optimal Experimental Designs”. Technometrics 1, pp. 60–69.
   Google Scholar
• Myers R. H.; Khuri, A. I.; and Vining, G. (1992). “Response Surface Alternatives to the Taguchi Robust Parameter Design Approach”. American Statistician 46, pp. 131–139.
   Web of Science ®Google Scholar
• Myers R. H. and Lahoda, S. J. (1975). “A Generalization of the Response Surface Mean Square Error Criterion with a Specific Application to the Slope”. Technometrics 17, pp. 481–486.
   Web of Science ®Google Scholar
• Myers, R. H. and Montgomery, D. C. (2002). Response Surface Methodology, 2nd ed. John Wiley & Sons, New York, NY.
   Google Scholar
• Piepel, G. F. and Cornell, J. A. (1985). “Models for Mixture Experiments When the Response Depends on the Total Amount”. Technometrics 27, pp. 219–227.
   Web of Science ®Google Scholar
• Piepel, G. F. and Cornell, J. A. (1987). “Designs for Mixture-Amount Experiments”. Journal of Quality Technology 26, pp. 177–196.
   Web of Science ®Google Scholar
• Stat-Ease, Inc. (2003). Design-Expert Version 6.07. Minneapolis, MN.
   Google Scholar
• Steiner, S. H., and Hamada, M. (1997). “Making Mixtures Robust to Noise and Mixing Measurement Errors”. Journal of Quality Technology 29, pp. 441–450.
   Web of Science ®Google Scholar
• St. John, R. C. and Draper, N. R. (1975). “D-Optimality for Regression Designs: A Review”. Technometrics 1, pp. 15–23.
   Google Scholar
• Taguchi, G. (1986). Introduction to Quality Engineering. Quality Resources, White Plains, NJ.
   Google Scholar
• Taguchi, G. (1987). System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Cost. Quality Resources, White Plains, NJ.
   Google Scholar
• Taguchi, G. and Wu, Y. (1985). Introduction to Off-Line Quality Control. Central Japan Quality Control Association (available from American Supplier Institute, Dearborn, MI).
   Google Scholar
• Wynn, H. P. (1970). “The Sequential Generation of D-optimum Experimental Designs”. Annals of Mathematical Statistics 41, pp. 1655–1664.
   Google Scholar