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.

Slope Rotatable Central Composite Designs of Second Type

“…Sulochana and Victorbabu [27] studied SOSRD under intra-class correlated structure of errors using partially balanced incomplete block type designs. Sulochana and Victorbabu [28] studied SOSRD under tri-diagonal correlation structure of errors using a pair of incomplete block designs. Victorbabu and Jyostna [29] studied measure of modified slope rotatability for second order response surface designs.…”