Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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ON SECOND ORDER SLOPE ROTATABLE DESIGNS - A REVIEW

  • Victorbabu, B. Re. (Department of Statistics, Acharya Nagarjuna University)
  • Published : 2007.09.30
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Abstract

In this paper, a review on second order slope rotatable designs (SOSRD) is studied. Further, different methods of constructions of SOSRD like slope rotatable central composite designs (SRCCD), SOSRD using balanced incomplete block designs (BIBD), SOSRD using pairwise balanced designs (PBD), SOSRD using partially balanced incomplete block type designs (PBIBD) and SOSRD using symmetrical unequal block arrangements (SUBA) with two unequal block sizes are examined in detail. A table is provided where for a range of different values of v (v stands for number of factors) the design points needed by different methods are compared. The optimum SOSRD with minimum number of design points for each factor is suggested for $2{\leq}v{\leq}16$.

Keywords

References

  1. ANJENEYULU, G. V. S. R., DATTATREYARAO, A. V. AND NARASIMHAM, V. L. (1993). 'Embedding in second order slope rotatable designs', Reports of Statistical Application Research, Union of Japanese Scientists and Engineers, 40, 1-11
  2. ANJENEYULU, G. V. S.R., DATTATREYARAO, A. V. AND NARASIMHAM, V. L. (1998) 'Group divisible second order slope rotatable designs', Gujarat Statistical Review, 25, 3-8
  3. ANJENEYULU, G. V. S. R., DATTATREYARAO, A. V. AND NARASIMHAM, V. L. (2005). 'On four level second order slope rotatable designs', Assam Statistical Review, 19, 1-2
  4. ANJENEYULU, G. V. S. R., NAGHABHUSHANAM, P. AND NARASIMHAM, V. L. (2002). 'Construction of variance sum group divisible second order slope rotatable designs' , Statistical Methods, 4, 122-131
  5. ANJENEYULU, G. V. S. R., VARMA, D. N. AND NARASIMHAM, V. L. (1997). 'A note on second order slope rotatable designs over all directions', Communications in StatisticsTheory and Methods, 26,1477-1479 https://doi.org/10.1080/03610929708831994
  6. Box, G. E. P. AND HUNTER, J. S. (1957). 'Multifactor experimental designs for exploring response surfaces', Annals of Mathematical Statistics, 28, 195-241 https://doi.org/10.1214/aoms/1177707047
  7. DAS, R. N. (2003). 'Slope rot at ability with correlated errors', Calcutta Statistical Association Bulletin, 54, 57-70 https://doi.org/10.1177/0008068320030105
  8. HADER, R. J. AND PARK, S. H. (1978). 'Slope-rotatable central composite designs', Technometrics, 20, 413-417 https://doi.org/10.2307/1267641
  9. JANG, D. H. AND PARK, S. H. (1993). 'A measure and a graphical method for evaluating slope rot at ability in response surface designs', Communications in Statistics- Theory and Methods, 22, 1849-1863 https://doi.org/10.1080/03610929308831120
  10. MUKERJEE, R. AND HUDA, S. (1985). 'Minimax second-and third-order designs to estimate the slope of a response surface', Biometrika, 72, 173-178 https://doi.org/10.1093/biomet/72.1.173
  11. PARK, S. H. (1987). 'A class of multi factor designs for estimating the slope of response surfaces', Technometrics, 29, 449-453 https://doi.org/10.2307/1269456
  12. PARK, S. H. AND KIM, J. I. (1988). 'Slope rotatable designs for estimating the slope of response surfaces in experiments with mixtures', Journal of the Korean Statistical Society, 17, 121-133
  13. PARK, S. H. AND KIM, H. J. (1992). 'A measure of slope rot at ability for second order response surface experimental designs', Journal of Applied Statistics, 19, 391-404 https://doi.org/10.1080/02664769200000035
  14. RAGHAVARAO, D. (1962). 'Symmetrical unequal block arrangements with two unequal block sizes', Annals of Mathematical Statistics, 33, 620-633 https://doi.org/10.1214/aoms/1177704586
  15. RAGHAVARAO, D. (1971). Constructions and Combinatorial Problems in Design of Experiments, John Wiley & Sons, New York
  16. VICTORBABU, B. RE. (2000). 'Second order slope rotatable designs over all directions using balanced incomplete block designs with unequal block sizes', Statistical Methods, 2, 136-140
  17. VICTORBABU, B. RE. (2002a). 'A note on the construction of four and six level second order slope rotatable designs', Statistical Methods, 4, 11-20
  18. VICTORBABU, B. RE. (2002b). 'Construction of second order slope rotatable designs using symmetrical unequal block arrangements with two unequal block sizes', Journal of the Korean Statistical Society, 31, 153-161
  19. VICTORBABU, B. RE. (2002c). 'Augmented second order rotatable designs as second order slope rotatable designs using BIBD', Proceedings of Andhra Pradesh Akademi of Sciences, 6, 61-62
  20. VICTORBABU, B. RE. (2002d). 'Second order slope rotatable designs with equi-spaced levels', Proceedings of Andhra Pradesh Akademi of Sciences, 6, 211-214
  21. VICTORBABU, B. RE. (2003). 'On second order slope rotatable designs using incomplete block designs', Journal of the Kerala Statistical Association, 14, 19-25
  22. VICTORBABU, B. RE. (2006). 'A note on variance-sum group divisible second order slope rotatable designs using BIBD' , preprint
  23. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1990). 'Construction of second order slope rotatable designs through incomplete block designs with unequal block sizes', Pakistan Journal of Statistics, 6, 65-73
  24. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1991a). 'Construction of second order slope rotatable designs through balanced incomplete block designs', Communications in Statistics-Theory and Methods, 20, 2467-2478 https://doi.org/10.1080/03610929108830644
  25. VICTORBABUB. RE. AND NARASIMHAM, V. L. (1991b). 'Construction of second order slope rotatable designs through a pair of balanced incomplete block designs', Journal of the Indian Society of Agricultural Statistics, 43, 291-295
  26. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1993a). 'Construction of second order slope rotatable designs using pairwise balanced designs', Journal of the Indian Society of Agricultural Statistics, 45, 200-205
  27. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1993b). 'Classification and parameter bounds of second order slope rotatable designs', Reports of Statistical Application Research, Union of Japanese Scientists and Engineers, 40, 12-19
  28. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1993c). 'Construction of three level second order slope rotatable designs using balanced incomplete block designs', Pakistan Journal of Statistics, 9, 91-95
  29. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1994). 'A new type of slope rotatable central composite design', Journal of the Indian Society of Agricultural Statistics, 46, 315-317
  30. VICTORBABU, B. RE., NARAYANARAO, E. S. V. AND NARASIMHAM, V. L. (1994). 'Construction of second order slope rotatable designs with equi-spaced levels using incomplete block designs with unequal block sizes', Proceedings of the XV Indian Society for Probability and Statistics Conference, 21-23, December, M. S. University, Tirunelveli-627008, 116-119
  31. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1994&95). 'Augmented second order rotatable design as second order slope rotatable design', Gujarat Statistical Review, 21&22, 31-36
  32. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1995). 'A new method of construction of second order slope rotatable designs using a pair of incomplete block designs', Journal of Indian Society of Agricultural Statistics, 47, 273-277
  33. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1996). 'Construction of second order slope rotatable designs using partially balanced incomplete block type designs', Journal of Indian Society of Agricultural Statistics, 48, 159-164
  34. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1996&97). 'Construction of three level second order slope rotatable designs using incomplete block designs with unequal block sizes', Gujarat Statistical Review, 23&24, 29-36
  35. VICTORBABU, B. RE. NARAYANARAO, E. S. V. AND NARASIMHAM, V. L. (1996&1997). 'Construction of second order slope rotatable designs over all directions using incomplete block designs', Gujarat Statistical Review, 23&24, 45-49
  36. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (1997). 'Second order slope rotatable designs over all directions using partially balanced incomplete block type designs', Gujarat Statistical Review, 24, 27-30
  37. VICTORBABU, B. RE. AND NARASIMHAM, V. L. (2000-01). 'A new method of construction of second order slope rotatable designs', Journal of Indian Society for Probability and Statistics, 5, 75-79
  38. VICTORBABU, B. RE. AND SESHUBABU, P. (2005). 'Construction of four level second order slope rotatable designs using symmetrical unequal block arrangements with two unequal block sizes', Statistical Methods, 7, 149-156
  39. VICTORBABU, B. RE. AND VASUNDHARADEVI, V. (2003). 'On the efficiency of second order response surface designs for estimation of responses and slopes', Proceedings of Andhra Pradesh Akademi of Sciences, 7, 49-54
  40. VICTORBABU, B. RE. AND VASUNDHARADEVI, V. (2004a). 'On the efficiency of second order response surface designs for estimation of responses and slopes using balanced incomplete block designs', Statistical Methods, 6, 210-234
  41. VICTORBABU, B. RE. AND VASUNDHARADEVI, V. (2004b). 'Performance of second order response surface designs for estimation of responses and slopes using pairwise balanced designs', Proceedings of Andhra Pradesh Akademi of Sciences, 8, 223-230
  42. YING, L. H. PUKERSHEIM, F. AND DRAPER, N. R. (1995a). 'Slope rotatability over all directions designs', Journal of Applied Statistics, 22, 331-341 https://doi.org/10.1080/757584723
  43. YING, L. H. PUKERSHEIM, F. AND DRAPER, N. R. (1995b). 'Slope rot at ability over all directions designs for k $\geq$ 4', Journal of Applied Statistics, 22, 343-354 https://doi.org/10.1080/757584724