An Empirical Study of Second Order Rotatable Designs under Tri-Diagonal Correlated Structure of Errors using Incomplete Block Designs

Abstract

In this paper, an empirical study of second order rotatable designs under tri-diagonal correlated structure of errors using incomplete block designs like pairwise balanced designs (PBD) and symmetrical unequal block arrangements (SUBA) with two unequal block sizes are suggested. Further we study the variance function of the estimated response for different values of tri-diagonal correlated coefficient (ρ) and distance from center (d) for 6≤v≤15 (vnumber of factors)).

Evaluating Measure of Modified Rotatability for Second Degree Polynomial Design Using Balanced Incomplete Block Designs

“…Victorbabu and Vasundharadevi [5], Victorbabu et al [6], Victorbabu [7], Victorbabu et al [8], Victorbabu and Vasundharadevi [9,10], Victorbabu and Surekha [11], Victorbabu and Surekha [12], Victorbabu and Chiranjeevi [13], Chiranjeevi and Victorbabu [14], Victorbabu and Surekha [15], Victorbabu and Jyostna [16] and so on. Some work contributed on tri-diagonal, intra-class correlated structure of errors on second order rotatable designs (SORD) by Rajyalakshmi and Victorbabu [17][18][19]. Raghavendraswamy and Victorbabu [20] studied SORD under tri-diagonal correlated structure of errors using a pair of SUBA with two unequal block sizes.…”

A Study of Second Order Slope Rotatable Designs under Intra-class Correlated Structure of Errors Using Partially Balanced Incomplete Block Type Designs

“…Rajyalakshmi and Victorbabu [16,17,18] constructed SOSRD under intra-class correlation structure of errors using central composite designs (CCD), symmetrical unequal block arrangements (SUBA) with two unequal block sizes and BIBD respectively. Rajyalakshmi and Victorbabu [19,20] constructed SOSRD under intraclass correlation structure of errors using SUBA with two unequal block sizes and BIBD respectively. Sulochana and Victorbabu [21,22] studied SOSRD under intra-class correlated structure of errors using a pair of BIBD and a pair of SUBA with two unequal block sizes respectively.…”

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

“…Robust second order rotatable designs (RSORD) were introduced and studied by Das [5,6,7]. Rajyalakshmi and Victorbabu [8] studied rotatability for second order response surface designs under tri-diagonal correlation structure of errors using incomplete block designs (IBD), Victorbabu and Chiranjeevi [9] examined measure of degree of rotatability for second order response surface designs using symmetrical unequal block arrangements (SUBA) with two unequal block sizes .…”

“…In this paper, following the works of Victorbabu and Narasimham [10,11], Victorbabu and Narayanarao [12], Das [14], Rajyalakshmi [15], Rajyalakshmi and Victorbabu [8,16,17,18,19,20] here a study of slope rotatability for second order response surface designs under tri-diagonal correlation structure of errors using a pair of SUBA with two unequal block sizes is studied. Further we study the variance function of the estimated slopes 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.…”

“…On simplification of (2.16) using (2.9) and (2.10) leads to [8,16,17,18,19,20], here a study on slope rotatability for second order response surface designs under tri-diagonal correlation structure of errors using a pair of SUBA with two unequal block sizes is studied. Let ρ be the correlation errors of any two observations.…”