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Animated Quantile Plots for Evaluating Response Surface Designs

반응표면실험계획을 평가하기 위한 동적분위수그림

  • Received : 20100100
  • Accepted : 20100300
  • Published : 2010.04.30

Abstract

The traditional methods for evaluating response surface designs are alphabetic optimality criteria. These single-number criteria such as D-, A-, G- and V-optimality do not completely reflect the prediction variance characteristics of the design in question. Alternatives to single-numbers summaries include graphical displays of the prediction variance across the design regions. We can suggest the animated quantile plots as the animation of the quantile plots and use these animated quantile plots for comparing and evaluating response surface designs.

반응표면실험계획들을 평가하기 위한 방법으로서 전형적인 방법이 알파벳최적화이다. 그러나 이러한 알파벳최적화(D-, A-, G-, V-최적화 등)는 하나의 수치이므로 그 유용성에도 불구하고 반응표면실험계획들이 갖는 추정반응값 분산의 분포에 대한 정보에 한계를 갖는다. 이를 극복하고자 하는 대안으로서 그래픽 방법들이 있는데 우리는 그 중에 분위수그림을 애니메이션화한 동적분위수그림을 제안할 수 있고 이 동적분위수그림을 이용하여 반응표면실험계획들이 갖는 추정반응값분산의 분포를 서로 비교, 평가할 수 있다.

Keywords

References

  1. Anderson-Cook, C. M., Borror, C. M. and Montgomery, D. C. (2009). Response surface design evaluation and comparison, Journal of Statistical Planning and Inference, 139, 629-641. https://doi.org/10.1016/j.jspi.2008.04.004
  2. Giovannitti-Jensen, A. and Myers, R. H. (1989). Graphical assessment of the prediction capability of response surface designs, Technometrics, 31, 159-171. https://doi.org/10.2307/1268814
  3. Jang, D. and Park, S. (1993). A measure and a graphical method for evaluating slope rotatability in response surface designs, Communications in Statistics-Theory and Methods, 22, 1849-1863. https://doi.org/10.1080/03610929308831120
  4. Khuri, A. I. (1997). Quantile dispersion graphs for analysis of variance estimates of variance components, Journal of Applied Statistics, 24, 711-722. https://doi.org/10.1080/02664769723440
  5. Khuri, A. I., Kim, H. J. and Um, Y. (1996). Quantile plots of the prediction variance for response surface designs, Computational Statistics and Data Analysis, 22, 395-407. https://doi.org/10.1016/0167-9473(95)00058-5
  6. Khuri, A. I. and Lee, J. (1998). A graphical approach for evaluating and comparing designs for nonlinear models, Computational Statistics and Data Analysis, 27, 433-443. https://doi.org/10.1016/S0167-9473(98)00016-4
  7. Kim, H., Um, Y. and Khuri, A. I. (1996). Quantile plots of the average slope variance for response surface designs, Communications in Statistics-Simulation and Computation, 25, 995-1014. https://doi.org/10.1080/03610919608813355
  8. Lee, J. and Khuri, A. I. (1999). Graphical technique for comparing designs for random models, Journal of Applied Statistics, 26, 933-947. https://doi.org/10.1080/02664769921945
  9. Lee, J. and Khuri, A. I. (2000). Quantile dispersion graphs for the comparison of designs for a random two-way model, Journal of Statistical Planning and Inference, 91, 123-137. https://doi.org/10.1016/S0378-3758(00)00135-X
  10. Mukhopadhyay, S. and Khuri, A. I. (2008). Comparison of designs for multivariate generalized linear models, Journal of Statistical Planning and Inference, 138, 169-183. https://doi.org/10.1016/j.jspi.2007.05.014
  11. Myers, R. H. and Montgomery, D. C. (2002). Response Surface Methodology: Process and Product Optimization using Designed Experiments, 2nd ed., Wiley, New York.
  12. Ozol-Godfrey, A., Anderson-Cook, C. M. and Robinson, T. J. (2007). Fraction of design space plots for generalized linear models, Journal of Statistical Planning and Inference, 138, 203-219. https://doi.org/10.1016/j.jspi.2007.05.011
  13. Robinson, K. S. and Khuri, A. I. (2003). Quantile dispersion graphs for evaluating and comparing designs for logistic regression models, Computational Statistics and Data Analysis, 43, 47-62. https://doi.org/10.1016/S0167-9473(02)00182-2
  14. Zahran, A., Anderson-Cook, C. M. and Myers, R. H. (2003). Fraction of design space to assess the prediction capability of response surface designs, Journal of Quality Technology, 35, 377-386.

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