# Second Order Slope Rotatable Designs under Tri-diagonal Correlation Structure of Errors Using a Pair of Incomplete Block Designs

## Abstract

Box and Hunter [1] introduced the concept of rotatability for response surface designs. The concept of slope-rotatability was introduced by Hader and Park [2] as an analogous to rotatability property, which is an important design criterion for response surface design. Slope-rotatable design is that of which the variance of partial derivative is a function of distance from the design (d). Recently, a few measures of slope-rotatability for a given response surface design was introduced. In this paper, a new method of slope rotatability for second order response surface designs under tri-diagonal correlation structure of errors using a pair of symmetrical unequal block arrangements with two unequal block sizes is studied. Further, a study on the dependence of variance function of the second order response surface at different design points for different values of tri-diagonal correlation coefficient ρ which lies between -0.9 to 0.9 and the distance from centre (d) is suggested.

Keywords:
Response surface designs, slope rotatability, tri-diagonal correlation errors, symmetrical unequal block arrangements with two unequal block sizes.

## Article Details

How to Cite
Sulochana, B., & Victorbabu, B. R. (2020). Second Order Slope Rotatable Designs under Tri-diagonal Correlation Structure of Errors Using a Pair of Incomplete Block Designs. Asian Journal of Probability and Statistics, 6(4), 1-11. https://doi.org/10.9734/ajpas/2020/v6i430165
Section
Original Research Article

## References

Box GEP, Hunter JS. Multifactor exponential designs for exploring response surfaces. Annals of Mathematical Statistics. 1957;28:195-241.

Hader RJ, Park SH. Slope rotatable central composite designs. Technometrics. 1978;20:413-417.

Das MN, Narasimham VL. Construction of rotatable designs through balanced incomplete block designs. Annals of Mathematical Statistics. 1962;33:1421-1439.

Narasimham VL, Ramachandrarao P, Rao KN. Construction of second order rotatable designs through a pair of incomplete block designs. Journal of the Indian Society for Agricultural Statistics. 1983;35:36-4.

Das RN. Robust second order rotatable designs (part-I). Calcutta Statistical Association Bulletin. 1997;47:199-214.

Das RN. Robust second order rotatable designs (part-II). Calcutta Statistical Association Bulletin. 1999;49:65-78.

Das RN. Robust second order rotatable designs (part-III). Journal of the Indian Society for Agricultural Statistics. 2003a;56:117-130.

Rajyalakshmi K, Victorbabu B. Re. An empirical study of second order rotatable designs under tri-diagonal correlated structure of errors using incomplete block designs. Sri Lankan Journal of Statistics. 2014a;1:1-17.

Victorbabu B. Re, Chiranjeevi P. On measure of rotatability for second order response surface designs using symmetrical unequal block arrangements with two unequal block sizes. International Journal of Agricultural and Statistical Sciences. 2018;9:943-947.

Victorbabu B. Re, Narasimham VL. Construction of second order slope rotatable designs through balanced incomplete block designs. Communications in Statistics-Theory Methods. 1991a;20:2467-2478.

Victorbabu B. Re, Narasimham VL. Construction of second order slope rotatable designs through a pair of incomplete block designs. Journal of the Indian Society for Agricultural Statistics. 1991b;43:291-295.

Victorbabu B. Re, Narayanarao ESV. Construction of second order slope rotatable designs through a pair of symmetrical unequal block arrangements with two unequal block sizes. Journal of Current Sciences. 2006;9:943-947.

Victorbabu B. Re. On second order slope rotatable designs – A review. Journal of the Korean Statistical Society. 2007;36:373-386.

Das RN. Slope rotatability with correlated errors. Calcutta Statistical Association Bulletin. 2003b;54:58-70.

Rajyalakshmi K. Some contributions to second order rotatable and slope rotatable designs under different correlated error structures. Unpublished Ph.D. Thesis, Acharya Nagarjuna University, Guntur-522510, India; 2014.

Rajyalakshmi K, Victorbabu B. Re. An empirical study on robustness of slope rorarable central composite designs. Journal of Statistics. 2014b;21:1-14.

Rajyalakshmi K, Victorbabu B. Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using central composite designs. International Journal of Advanced Statistics and Probability. 2014c;2:70-76.

Rajyalakshmi K, Victorbabu B. Re. Construction of second order slope rotatable designs under tri-diagonal correlated error structure using pairwise balanced designs. International Journal of Agricultural and Statistical Sciences. 2015;11:1-7.

Rajyalakshmi K, Victorbabu B. Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using symmetrical unequal block arrangements with two unequal block arrangements. Journal of Statistics and Management Systems. 2018;21:201-205.

Rajyalakshmi K, Victorbabu B. Re. Construction of second order slope rotatable designs under tri-diagonal correlated structure of errors using balanced incomplete block designs. Thailand Statistician. 2019;17(1):104-117.

Sulochana B, Victorbabu B. Re. A study of second order slope rotatable designs under tri-diagonal correlated structure of errors using a pair of balanced incomplete block designs. Paper to be Presented at XXXIX ISPS Conference Held during 21-23, December 2019, at Department of Statistics, Utkal University, Bhubaneswar; 2019.

Raghavarao D. Constructions and combinatorial problems in design of experiments. John Wiley, New York; 1971.