How to cite this paper
Limmun, W., Chomtee, B & Borkowski, J. (2019). Constructing model robust mixture designs via weighted G-optimality criterion.International Journal of Industrial Engineering Computations , 10(4), 473-490.
Refrences
Atkinson, A. C., Donev A. N., & Tobias, R. D. (2007). Optimum Experimental Designs, with SAS. Oxford University Press Inc.
Anderson-Cook, C. M., Borror, C. M., & Jones, B. (2009). Graphical tool for assessing the sensitivity of response designs to model misspecification. Technometrics, 51(1), 75-87.
Borkowski, J. J. (2003). Using genetic algorithm to generate small exact response surface designs. Journal of Probability and Statistical Science, 1(1), 65-88.
Borkowski, J. J., Chomtee, B., & Turk, P. (2010). Using Weak and Strong Heredity to Generate Weighted Design Optimality Criteria for Response Surface Designs. Journal of Statistical Theory and Applications, 10(2), 163-192.
Borkowski, J. J., & Piepel, G. F. (2009). Uniform designs for highly constrained mixture experiments. Journal of Quality Technology, 41(1), 1-13.
Chipman, H. A. (1996) Bayesian variable selection with related predictors. The Canadian Journal of Statistics, 24(1), 17-36.
Chung, P. J., Goldfarb, H., & Montgomery, D. C. (2007). Optimal designs for mixture-process experiments with control and noise variables. Journal of Quality Technology, 39(3), 179-190.
Cornell, J. A. (2002) Experiments with Mixtures : Designs, Models, and the Analysis of Mixture Data. (3rd edition). John Wiley & Sons, Inc.
Drain, D., Carlyle, W. M., Montgomery, D. C., Borror, C., & Anderson-Cook, C. (2004). A genetic algorithm hybrid for constructing optimal response surface designs. Quality and Reliability Engineering International, 20(7), 637-650.
DuMouchel, W., & Jones, B. (1994). A simple Bayesian modification of D-optimal design to reduce dependence on an assumed model. Technometrics, 36(1), 37-47.
Emmett, M., Goos, P., & Stillman. E. C. (2011). A weighted prediction-based selection criterion for response surface designs. Quality and Reliability Engineering International, 27(5), 719–729.
Engelbrecht, A.P. (2002). Computational Intelligence: An Introduction. John Wiley & Sons, Inc.
Goldberg, D. E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley.
Goldfarb, H. B., Anderson-Cook, C. M., Borror, C. M., & Montgomery, D. C. (2004). Fraction of design space plots for assessing mixture and mixture-process designs. Journal of Quality Technology , 36(2), 169-179.
Goldfarb, H. B., Borro, C. M., Montgomery, D. C., & Anderson-Cook, C. M. (2005). Using genetic algorithms to generate mixture-process experimental designs involving control and noise variables. Journal of Quality Technology, 37(1), 60-74.
Haupt, R. L., & Haupt, S. E. (2004). Practical Genetic Algorithms. John Wiley & Sons, Inc.
Heredia-Langner, A., Carlyle, W. M., Montgomery, D. C., Borror, C. M., & Runger, G. C. (2003). Genetic algorithms for the construction of D-optimal designs. Journal of Quality Technology, 35(1), 28-46.
Heredia-Langner, A., Montgomery, D. C., Carlyle, W. M., & Borror, C. M. (2004). Model-robust optimal designs: a genetic algorithm approach. Journal of Quality Technology, 36(3), 263-279.
Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. MIT Press.
Kiefer, J. (1959). Optimum experimental designs. Journal of the Royal Statistical Society, Series B, 21(2), 272-304.
Kiefer, J., & Wolfowitz, J. (1959). Optimum design in regression problems. Annals of Mathematical Statistics, 30(2), 271-294.
Kiefer, J., & Wolfowitz, J. (1960). The equivalence of two extremum problems. Canadian Journal of Mathematics, 12(3), 363-366.
Kinnear, K. E. (1994). Advances in Genetic Programming. MIT Press.
Li, W., & Nachtsheim, C. J. (2000). Model-robust factorial designs. Technometrics, 42(4), 345-352.
Limmun, W., Borkowski, J. J., & Chomtee, B. (2013). Using a Genetic Algorithm to Generate D-optimal Designs for Mixture Experiments. Quality and Reliability Engineering International, 29(7), 1055-1068.
The MathWorks. (2016). Matlab high performance numeric computation software. The MathWorks, Inc.
Michalewicz, Z. (1992). Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag.
Morgan, J. P., & Wang, X. (2010). Weighted Optimality in Designed Experimentation. Journal of the American Statistical Association, 105(492), 1566-1580.
Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2009). Response Surface Methodology : Process AND Product Optimization Using Designed Experiments. (3rd edition). John Wiley & Sons, Inc.
Ozol-Godfrey, A., Anderson-Cook, C.M., & Montgomery, D.C. (2005). Fraction of design space plots for examining model robustness. Journal of Quality Technology, 37(3), 223-235.
Park, Y., Montgomery, D. C., Fowler, J. W., & Borror, C. M. (2006). Cost-constrained G-efficient response surface designs for cuboidal regions. Quality and Reliability Engineering International, 22(2), 121-139.
Rodriguez, M., Montgomery, D.C., & Borror, C. M. (2009). Generating Experimental Designs Involving Control and Noise Variables using Genetic Algorithms. Quality and Reliability Engineering International, 25(8), 1045-1065.
SAS Institute. (2012). SAS QC 14.1 user’s guide, Version 9. SAS Institute Inc.
Smith, W. F. (2005). Experimental Design for Formulation. The American Statistical Association and the Society for Industrial and Applied Mathematics.
Smucker, B. J., Del Castillo, E., & Rosenberger, J. L. (2011). Exchange Algorithms for Constructing Model-Robust Experimental Designs. Journal of Quality Technology, 43(1), 1-15.
Snee, R. D. (1979). Experimental design for mixture systems with multicomponent constraints. Communications in Statistics-Theory and Methods, 8(4), 303-326.
Snee, R. D., & Rayner, A. A. (1982). Assessing the accuracy of mixture model regression calculations. Journal of Quality Technology , 14(2), 67-79.
Stallings, J. W. & Morgan, J. P. (2015). General weighted optimality of designed experiments. Biometrika, 102(4), 925-935.
Wheeler, R. E. (1972). Efficient experimental design. Annual Meeting of the American Statistical Association, Canada, August, 1972.
Zaharn, A., Anderson-Cook, C. M., & Myers, R. M. (2003). Faction of design space to assess prediction capability of response surface designs. Journal of Quality Technology, 35(4), 377-386.
Anderson-Cook, C. M., Borror, C. M., & Jones, B. (2009). Graphical tool for assessing the sensitivity of response designs to model misspecification. Technometrics, 51(1), 75-87.
Borkowski, J. J. (2003). Using genetic algorithm to generate small exact response surface designs. Journal of Probability and Statistical Science, 1(1), 65-88.
Borkowski, J. J., Chomtee, B., & Turk, P. (2010). Using Weak and Strong Heredity to Generate Weighted Design Optimality Criteria for Response Surface Designs. Journal of Statistical Theory and Applications, 10(2), 163-192.
Borkowski, J. J., & Piepel, G. F. (2009). Uniform designs for highly constrained mixture experiments. Journal of Quality Technology, 41(1), 1-13.
Chipman, H. A. (1996) Bayesian variable selection with related predictors. The Canadian Journal of Statistics, 24(1), 17-36.
Chung, P. J., Goldfarb, H., & Montgomery, D. C. (2007). Optimal designs for mixture-process experiments with control and noise variables. Journal of Quality Technology, 39(3), 179-190.
Cornell, J. A. (2002) Experiments with Mixtures : Designs, Models, and the Analysis of Mixture Data. (3rd edition). John Wiley & Sons, Inc.
Drain, D., Carlyle, W. M., Montgomery, D. C., Borror, C., & Anderson-Cook, C. (2004). A genetic algorithm hybrid for constructing optimal response surface designs. Quality and Reliability Engineering International, 20(7), 637-650.
DuMouchel, W., & Jones, B. (1994). A simple Bayesian modification of D-optimal design to reduce dependence on an assumed model. Technometrics, 36(1), 37-47.
Emmett, M., Goos, P., & Stillman. E. C. (2011). A weighted prediction-based selection criterion for response surface designs. Quality and Reliability Engineering International, 27(5), 719–729.
Engelbrecht, A.P. (2002). Computational Intelligence: An Introduction. John Wiley & Sons, Inc.
Goldberg, D. E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley.
Goldfarb, H. B., Anderson-Cook, C. M., Borror, C. M., & Montgomery, D. C. (2004). Fraction of design space plots for assessing mixture and mixture-process designs. Journal of Quality Technology , 36(2), 169-179.
Goldfarb, H. B., Borro, C. M., Montgomery, D. C., & Anderson-Cook, C. M. (2005). Using genetic algorithms to generate mixture-process experimental designs involving control and noise variables. Journal of Quality Technology, 37(1), 60-74.
Haupt, R. L., & Haupt, S. E. (2004). Practical Genetic Algorithms. John Wiley & Sons, Inc.
Heredia-Langner, A., Carlyle, W. M., Montgomery, D. C., Borror, C. M., & Runger, G. C. (2003). Genetic algorithms for the construction of D-optimal designs. Journal of Quality Technology, 35(1), 28-46.
Heredia-Langner, A., Montgomery, D. C., Carlyle, W. M., & Borror, C. M. (2004). Model-robust optimal designs: a genetic algorithm approach. Journal of Quality Technology, 36(3), 263-279.
Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. MIT Press.
Kiefer, J. (1959). Optimum experimental designs. Journal of the Royal Statistical Society, Series B, 21(2), 272-304.
Kiefer, J., & Wolfowitz, J. (1959). Optimum design in regression problems. Annals of Mathematical Statistics, 30(2), 271-294.
Kiefer, J., & Wolfowitz, J. (1960). The equivalence of two extremum problems. Canadian Journal of Mathematics, 12(3), 363-366.
Kinnear, K. E. (1994). Advances in Genetic Programming. MIT Press.
Li, W., & Nachtsheim, C. J. (2000). Model-robust factorial designs. Technometrics, 42(4), 345-352.
Limmun, W., Borkowski, J. J., & Chomtee, B. (2013). Using a Genetic Algorithm to Generate D-optimal Designs for Mixture Experiments. Quality and Reliability Engineering International, 29(7), 1055-1068.
The MathWorks. (2016). Matlab high performance numeric computation software. The MathWorks, Inc.
Michalewicz, Z. (1992). Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag.
Morgan, J. P., & Wang, X. (2010). Weighted Optimality in Designed Experimentation. Journal of the American Statistical Association, 105(492), 1566-1580.
Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2009). Response Surface Methodology : Process AND Product Optimization Using Designed Experiments. (3rd edition). John Wiley & Sons, Inc.
Ozol-Godfrey, A., Anderson-Cook, C.M., & Montgomery, D.C. (2005). Fraction of design space plots for examining model robustness. Journal of Quality Technology, 37(3), 223-235.
Park, Y., Montgomery, D. C., Fowler, J. W., & Borror, C. M. (2006). Cost-constrained G-efficient response surface designs for cuboidal regions. Quality and Reliability Engineering International, 22(2), 121-139.
Rodriguez, M., Montgomery, D.C., & Borror, C. M. (2009). Generating Experimental Designs Involving Control and Noise Variables using Genetic Algorithms. Quality and Reliability Engineering International, 25(8), 1045-1065.
SAS Institute. (2012). SAS QC 14.1 user’s guide, Version 9. SAS Institute Inc.
Smith, W. F. (2005). Experimental Design for Formulation. The American Statistical Association and the Society for Industrial and Applied Mathematics.
Smucker, B. J., Del Castillo, E., & Rosenberger, J. L. (2011). Exchange Algorithms for Constructing Model-Robust Experimental Designs. Journal of Quality Technology, 43(1), 1-15.
Snee, R. D. (1979). Experimental design for mixture systems with multicomponent constraints. Communications in Statistics-Theory and Methods, 8(4), 303-326.
Snee, R. D., & Rayner, A. A. (1982). Assessing the accuracy of mixture model regression calculations. Journal of Quality Technology , 14(2), 67-79.
Stallings, J. W. & Morgan, J. P. (2015). General weighted optimality of designed experiments. Biometrika, 102(4), 925-935.
Wheeler, R. E. (1972). Efficient experimental design. Annual Meeting of the American Statistical Association, Canada, August, 1972.
Zaharn, A., Anderson-Cook, C. M., & Myers, R. M. (2003). Faction of design space to assess prediction capability of response surface designs. Journal of Quality Technology, 35(4), 377-386.