Fraction of design space plots for examining model robustness

Journal of Quality Technology

Volumn 37, Issue 3, 2005, Pages 223-235

  Ozol Godfrey, Ayca ^a   Anderson Cook, Christine M ^b   Montgomery, Douglas C ^c,d  

^a WYETH RESEARCH   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c ARIZONA STATE UNIVERSITY   (United States)

^d Department of Industrial Engineering ^*  (United States)

Author keywords

Alphabetical Optimality Criteria; FDS Plot; Mixture Experiments; Model Reduction; Response Surface Designs; Scaled Prediction Variance

Indexed keywords

APPROXIMATION THEORY; DATA REDUCTION; GRAPHIC METHODS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; POLYNOMIALS; ROBUSTNESS (CONTROL SYSTEMS);

ALPHABETICAL OPTIMALITY CRITERIA; FDS PLOT; MIXTURE EXPERIMENTS; MODEL REDUCTION; RESPONSE SURFACE DESIGN; SCALED PREDICTION VARIANCE;

SYSTEMS ANALYSIS;

EID: 22544471551     PISSN: 00224065     EISSN: None     Source Type: Journal    
DOI: 10.1080/00224065.2005.11980323     Document Type: Article

References (36)

1. ANDREA-RENDON, J.; MONTGOMERY, D. C.; and KOLLIER, D. W. (1997). "Design of Mixture Experiments Using Bayesian D-Optimality". Journal of Quality Technology 29, pp. 451-463.
2. ANDREWS, D. F. (1971). "Sequentially Designed Experiments for Screening out Bad Models with F Tests". Biometrika 58, pp. 427-432.
3. ATKINSON, A. C. and FEDEROV, V. V. (1975). "The Design of Experiments for Discriminating Between Two Rival Models" . Biometrika 62, pp. 57-70.
4. BINGHAM, D. R. and LI, W. (2002). "A Class of Optimal Robust Parameter Designs". Journal of Quality Technology 34, pp. 244-259.
5. BORKOWSKI, J. J. and VALEROSO, E. S. (2001). "Comparison of Design Optimality Criteria of Reduced Models for Response Surface Designs in the Hypercube". Technometrics 43, pp. 468-477.
6. BOX, G. E. P. and DRAPER, N. R. (1974). "On Minimum-Point Second-Order Designs". Technometrics 16, pp. 613-616.
7. BOX, G. E. P. and DRAPER, N. R. (1987). Empirical Model Building and Response Surfaces. John Wiley & Sons, New York, NY.
8. BOX, G. E. P. and HILL, W. J. (1967). "Discrimination among Mechanical Models". Technometrics 9, pp. 57-71.
9. BOX, G. E. P. and WILSON, K. B. (1951). "On the Experimental Attainment of Optimum Conditions". Journal of the Royal Statistical Society, Series B, 13, pp. 1-45.
10. CHENG, S-W. and WU, C. F. J. (2001). "Factor Screening and Response Surface Exploration". Statistica Sinica 11, pp. 553-604.
11. CHIPMAN, H. (1996). "Bayesian Variable Selection with Related Predictors". The Canadian Journal of Statistics 24, pp. 17-36.
12. COOK, R. D. and NACHTSHEIM, C. J. (1982). "Model-Robust, Linear Optimal Designs". Technometrics 24, pp. 49-54.
13. CORNELL, J. A. (1986). "A Comparison Between Two Ten-Point Designs for Studying Three-Component Mixture Systems". Journal of Quality Technology 18, pp. 1-15.
14. CORNELL, J. A. (2002). Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data. 3rd ed. John Wiley & Sons, New York, NY.
15. COX, D. R. (1961). "Tests of Separate Families of Hypotheses". Proceedings Fourth Berkeley Symposium 1, pp. 105-123.
16. DRAPER, N. R. (1985). "Small Composite Designs". Technometrica 27, pp. 173-180.
17. DUMOUCHEL, W. and JONES, B. (1994). "A Simple Bayesian Modification of D-Optimal Designs to Reduce Dependence on an Assumed Model". Technometrics 36, pp. 37-47.
18. GIOVANNITTI-JENSEN, A. and MYERS, R. H. (1989). "Graphical Assessment of the Prediction Capability of Response Surface Designs". Technometrics 31, pp.159-171.
19. GOLDFARB, H. B.; ANDERSON-COOK, C. M.; BORROR, C. M.; and MONTGOMERY, D. C. (2004). "Fraction of Design Space Plots to Assess the Prediction Capability of Mixture and Mixture-Process Designs". Journal of Quality Technology 36, pp. 169-179.
20. GOLDFARB, H. B.; BORROR, C. M.; MONTGOMERY, D. C.; and ANDERSON-COOK, C. M. (2004). "Three-Dimensional Variance Dispersion Graphs for Mixture-Process Experiments". Journal of Quality Technology 36, pp. 109-124.
21. HARTLEY, H. O. (1959). "Smallest Composite Designs for Quadratic Response Surfaces". Biometrics 15, pp. 611-624.
22. HEREDIA-LANGNER, A.; MONTGOMERY, D. C.; CARLYLE, W. M.; and BORROR, C. M. (2004). "Model-Robust Optimal Designs: A Genetic Algorithm Approach". Journal of Quality Technology 36, pp. 263-279.
23. HILL, P. D. H. (1978). "A Review of Experimental Design Procedures for Regression Model Discrimination". Technometrics 20, pp. 15-21.
24. HOKE, A. T. (1974). "Economical Second-Order Designs Based on Irregular Fractions of the 3rd Factorial". Technometrics 16, pp. 375-384.
25. HUNTER, W. G. and REINER, A. M. (1965). "Designs for Discriminating Between Two Rival Models". Technometrics 7, pp. 307-323.
26. KHURI, A. I.; KIM, H. J.; and UM, Y. (1996). "Quantile Plots of the Prediction Variance for Response Surface Designs". Computational Statistics & Data Analysis 22, pp. 395-407.
27. LI, C. and NACHTSHEIM, C. J. (2000). "Model-Robust Factorial Designs". Technometrics 42, pp. 345-352.
28. MONTGOMERY, D. C. (2001). Design and Analysis of Experiments. 5th ed. John Wiley & Sons, New York, NY.
29. MYERS, R. H. and MONTGOMERY, D. C. (2002). Response Surface Methodology: Process and Product Optimization Using Designed Experiments. 2nd ed. John Wiley & Sons, New York, NY.
30. NOTZ, W. (1982). "Minimal Second-Order Designs". Journal of Statistical Planning and Inference 6, pp. 47-58.
31. PLACKETT, R. L. and BURMAN, J. P. (1946). "The Design of Optimum Multifactorial Experiments". Biometrika 33, pp. 305-325.
32. ROTH, P. M. (1965). Design of Experiments for Discriminating among Rival Models. Ph.D. Thesis, Princeton University.
33. SCHEFFÉ, H. (1958). "Experiments with Mixtures". Journal of the Royal Statistical Society, Series B, 20, pp. 344-360.
34. VINING, G. G. and MYERS, R. H. (1991). "A Graphical Approach for Evaluating Response Surface Designs in Terms of the Mean Squared Error of Prediction". Technometrics 33, pp. 315-326.
35. WU, C.-F. (1981). "On the Robustness and Efficiency of Some Randomized Designs". The Annals of Statistics 9, pp. 1168-1177.
36. ZAHRAN, A. R.; ANDERSON-COOK, C. M.; and MYERS, R. H. (2003). "Fraction of Design Space to Assess Prediction Capability of Response Surface Designs". Journal of Quality Technology 35, pp. 377-386.