3D-Responses for Measure of Second Order Rotatability Using a Pair of Dissimilar Incomplete Block Designs
Victorbabu B. Re.
Department of Statistics, Acharya Nagarjuna University, Guntur-522 510, India.
Surekha Ch. V. V. S.
Department of Statistics, Acharya Nagarjuna University, Guntur-522 510, India.
Siva Parvathi M.
*
Department of Statistics, Acharya Nagarjuna University, Guntur-522 510, India.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a comprehensive methodology for assessing the measure of rotatability for response surface design in second-order through the use of suitably chosen pairs of dissimilar incomplete block designs. The proposed framework incorporates multiple combinations of block structures, including symmetrically unequal block arrangements (SUBA) with two unequal block sizes combined with balanced incomplete block designs (BIBD), pairwise balanced designs (PBD) combined with BIBD, and PBD combined with SUBA with two unequal block sizes. By integrating these complementary block designs, the study aims to generate second-order designs that achieve improved precision and enhanced rotatability properties. To demonstrate the applicability of the method, several worked examples are constructed, highlighting the steps involved in deriving the design points and computing the corresponding measures of rotatability. Furthermore, three-dimensional response surface plots are provided to visually examine the geometric and variance characteristics of the resulting designs. These graphical representations support the interpretation of the theoretical results and illustrate the advantages of the proposed approach in constructing efficient rotatable second-order designs.
Keywords: Response Surface Methodology (RSM), block designs, second order, rotatability