SOME NEW SECOND ORDER ROTATABLE DESIGNS BASED ON BALANCED INCOMPLETE BLOCK DESIGN

Abstract

The purpose of this study was to construct some new second order rotatable designs using balanced incomplete block designs. The study of rotatable designs is mainly concerned with the estimation of absolute response in designs and analysis of experiments. Second order rotatable designs in three, four, five, six and a generalization in k-factors (k>6) were constructed. The optimality criteria for these designs were also determined. To construct a second order rotatable design a BIBD v,b, s, r,  was considered and a combination of points with unknown constants was taken and associated with 2k factorial combinations of factors each at  1 levels to make level codes equidistant. This factorial combination form the set of points s(a, a,...,a) and s(b,b,...,o) .All such combinations form a design. Second order rotatable designs were obtained in three, four, five and six dimensions and finally a generalization (v=k) of the design in k-dimensions was obtained by derivation. An incidence matrix of BIBD was chosen suitably to satisfy the moment conditions of rotatability. In conclusion, some new second order rotatable designs in three, four, five and six factors and their generalization in k factors were obtained through balanced incomplete block designs and their optimalities determined