In this paper, a study on second order slope rotatable designs under intra-class correlation structure of errors using pairwise balanced designs is suggested. Further, the variance function of the estimated slopes for different values of intra-class correlated coefficient ‘ ’ for 6 ≤ v ≤ 15 (v- number of factors) are studied.

In this paper, a study of second order slope rotatable designs under intra-class correlated structure of errors using partially balanced incomplete block type designs is suggested. Further, we study the variance function of the estimated slopes for different values of intra-class correlated coefficient ( ) and distance from centre (d) for 6 ≤ v ≤ 12 (number of factors) are also suggested. We note the new method sometimes leads to designs with fewer number of design points.

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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.

In this paper, measure of slope rotatability for second order response surface designs using symmetrical unequal block arrangements with two unequal block sizes under tri-diagonal correlation error structure is suggested and illustrated with examples.