Response Surface Methodology (RSM) has applications in Chemical, Physical, Meteorological, Industrial and Biological fields. The estimation of slope response surface occurs frequently in practical situations for the experimenter. The rates of change of the response surface, like rates of change in the yield of crop to various fertilizers, to estimate the rates of change in chemical experiments etc. are of interest. If the fit of second order response is inadequate for the design points, we continue the experiment so as to fit a third order response surface. Higher order response surface designs are sometimes needed in Industrial and Meteorological applications. Gardiner et al. [9] introduced third order rotatable designs for exploring response surface. Anjaneyulu et al. [2] constructed third order slope rotatable designs using doubly balanced incomplete block designs. Anjaneyulu et al. [1] introduced third order slope rotatable designs using central composite type design points. Babu et al. [11] studied modified construction of third order slope rotatable designs using central composite designs. Babu et al. [12] constructed TOSRD using BIBD. In view of wide applicability of third order models in RSM and importance of slope rotatability, here we made an attempt to construct TOSRD using Pairwise Balanced Designs.

third order slope rotatable design, pairwise balanced designs.

Received: August 24, 2021; Accepted: October 23, 2021; Published: November 15, 2021

How to cite this article: P. Seshu Babu and A. V. Dattatreya Rao, On third order slope rotatable designs using pairwise balanced designs, Far East Journal of Theoretical Statistics 63(1) (2021), 29-37. DOI: 10.17654/TS063010029

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] G. V. S. R. Anjaneyulu, A. V. Dattatreya Rao and V. L. Narasimham, Third order slope rotatable designs, Journal of Indian Society for Probability and Statistics 5 (2001), 75-79.
[2] G. V. S. R. Anjaneyulu, A. V. Dattatreya rao and V. L. Narasimham, Construction of third order slope rotatable designs, Gujarat Statistical Review 21&22 (1994-1995), 49-53.
[3] G. E. P. Box and J. S. Hunter, Multifactor experimental designs for exploring response surfaces, Ann. Math. Statist. 28 (1957), 195-241.
[4] M. N. Das, Construction of rotatable designs from factorial designs, Journal of Indian Society for Agriculture Statistics 13 (1961), 329-194.
[5] M. N. Das and V. L. Narasimham, Construction of rotatable designs through balanced incomplete block designs, Ann. Math. Statist. 33 (1962), 1421-1439.
[6] N. R. Draper, A Third order rotatable designs in three dimensions, Ann. Math. Statist. 31 (1960a), 865-874.
[7] N. R. Draper, A Third order rotatable designs in four dimensions, Ann. Math. Statist. 31 (1960b), 875-877.
[8] N. R. Draper, Centre points in second order response surface designs, Technometrics 24 (1982), 127-133.
[9] D. A. Gardiner, A. H. E. Grandage and R. J. Hader, Third order rotatable designs for exploring response surface, Ann. Math. Statist. 30 (1959), 1082-1096.
[10] R. J. Hader and S. H. Park, Slope rotatable central composite design, Technometrics 20 (1978), 413-417.
[11] P. Seshu Babu, A. V. Dattatreya Rao and G. V. S. R. Anjaneyulu, Modified construction of third order slope rotatable designs using central composite design, ANU Journal of Physical Science III(1&2) (2011), 1-12.
[12] P. Seshu Babu, A. V. Dattatreya Rao and K. Srinivas, Construction of third order slope rotatable designs using BIBD, International Journal of Scientific and Innovative Research (IJSIRM) 3 (2015), 149-152.
[13] B. Re Victor Babu and V. L. Narasimham, Construction of second order slope rotatable designs through incomplete block designs with unequal block sizes, Pakistan J. Statist. 6(3) (1990), 65-73.