Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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A MEASURE OF ROBUST ROTATABILITY FOR SECOND ORDER RESPONSE SURFACE DESIGNS

  • Published : 2007.12.31
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Abstract

In Response Surface Methodology (RSM), rotatability is a natural and highly desirable property. For second order general correlated regression model, the concept of robust rotatability was introduced by Das (1997). In this paper a new measure of robust rotatability for second order response surface designs with correlated errors is developed and illustrated with an example. A comparison is made between the newly developed measure with the previously suggested measure by Das (1999).

Keywords

References

  1. BISCHOFF, W. (1992). 'On exact D-optimal designs for regression models with correlated observations', Annals of the Institute of Statistical Mathematics, 44, 229-238 https://doi.org/10.1007/BF00058638
  2. BISCHOFF, W. (1995). 'Determinant formulas with applications to designing when the observations are correlated', Annals of the Institute of Statistical Mathematics, 47, 385-399 https://doi.org/10.1007/BF00773469
  3. Box, G. E. P. AND DRAPER, N. R. (2007). Response Surfaces, Mixtures, and Ridge Analyses, 2nd ed., John Wiley & Sons, New York
  4. Box, G. E. P. AND HUNTER, J. S. (1957). 'Multi-factor experimental designs for exploring response surfaces', Annals of Mathematical Statistics, 28, 195-241 https://doi.org/10.1214/aoms/1177707047
  5. DAS, R. N. (1997). 'Robust second order rotatable designs: Part-I (RSORD)', Calcutta Statistical Association Bulletin, 47, 199-214 https://doi.org/10.1177/0008068319970306
  6. DAS, R. N. (1999). 'Robust second order rotatable designs : Part-II (RSORD)', Calcutta Statistical Association Bulletin, 49, 65-76 https://doi.org/10.1177/0008068319990106
  7. DAS, R. N. (2003a). 'Slope rotatability with correlated errors', Calcutta Statistical Association Bulletin, 54, 57-70 https://doi.org/10.1177/0008068320030105
  8. DAS, R. N. (2003b). 'Robust second order rotatable designs: Part-III (RSORD)', Journal of the Indian Society of Agricultural Statistics, 56, 117-130
  9. DAS, R. N. (2004). 'Construction and analysis of robust second order rotatable designs', Journal of Statistical Theory and Applications, 3, 325-343
  10. DAS, R. N. AND PARK, S. H. (2006). 'Slope rotatability over all directions with correlated errors', Applied Stochastic Models in Business and Industry, 22,445-457 https://doi.org/10.1002/asmb.655
  11. DRAPER, N. R. AND GUTTMAN, I. (1988). 'An index of rotatability', Technometrics, 30, 105-111 https://doi.org/10.2307/1270326
  12. DRAPER, N. R. AND PUKELSHEIM, F. (1990). 'Another look at rotatability' , Technometrics, 32, 195-202 https://doi.org/10.2307/1268863
  13. FLEMING, W. (1977). Functions of Several Variables, 2nd ed., Springer-Verlag, New York
  14. GENNINGS, C., CHINCHILLI, V. M. AND CARTER, W. H. JR.(1989). 'Response surface analysis with correlated data: A nonlinear model approach', Journal of the American Statistical Association, 84, 805-809 https://doi.org/10.2307/2289670
  15. HADER, R. J. AND PARK, S. H. (1978). 'Slope-rotatable central composite designs', Technometrics, 20, 413-417 https://doi.org/10.2307/1267641
  16. KHURI, A. I. (1988). 'A measure ofrotatability for response-surface designs', Technometrics, 30,95-104 https://doi.org/10.2307/1270325
  17. KHURI, A. I. AND CORNELL, J. A. (1996). Response Surface, Marcel Dekker, New York
  18. KIEFER, J. AND WYNN, H. P. (1981). 'Optimum balanced block and latin square designs for correlated observations', The Annals of Statistics, 9, 737-757 https://doi.org/10.1214/aos/1176345515
  19. KIEFER, J. AND WYNN, H. P. (1984). 'Optimum and minimax exact treatment designs for one-dimensional autoregressive error processes', The Annals of Statistics, 12, 431-450 https://doi.org/10.1214/aos/1176346498
  20. KIM, H. J. AND PARK, S. H. (2006). 'Slope rotatability of icosahedron and dodecahedron designs', Journal of the Korean Statistical Society, 35, 25-36
  21. MUKHOPADHYAY, A. C., BAGCHI, S. B. AND DAS, R. N.(2002). 'Improvement of quality of a system using regression designs', Calcutta Statistical Association Bulletin, 53, 225-232 https://doi.org/10.1177/0008068320020305
  22. MYERS, R. H., KHURI, A. I. AND CARTER, W. H. JR. (1989). 'Response surface methodology: 1966-1988', Technometrics, 31, 137-157 https://doi.org/10.2307/1268813
  23. 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
  24. PANDA, R. N. AND DAS, R. N. (1994). 'First order rotatable designs with correlated errors (FORDWCE)' , Calcutta Statistical Association Bulletin, 44, 83-101 https://doi.org/10.1177/0008068319940107
  25. PARK, S. H. (1987). 'A class of multifactor designs for estimating the slope of response surfaces', Technometrics, 29, 449-453 https://doi.org/10.2307/1269456
  26. PARK, S. H., KANG, H.-S. AND KANG, K.-H. (2003). 'Measures for stability of slope estimation on the second order response surface and equally-stable slope rotatability' , Journal of the Korean Statistical Society, 32, 337-357
  27. PARK, S. H., LIM, J. H. AND BABA, Y. (1993). 'A measure of rotatability for second order response surface designs', Annals of the Institute of Statistical Mathematics, 45, 655-664 https://doi.org/10.1007/BF00774779
  28. PUKELSHEIM, F. (1993). Optimal Experimental Design, John Wiley & Sons, New York