Construction 0f Group Divisible Variance – Sum Third Order Rotatable Design through Balanced Incomplete Block Designs

Abstract

In the study of rotatable designs, the variance of the estimated response at a point is a function of the distance of that point from a particular origin. Group divisible Rotatable Designs have been evolved by imposing conditions on the levels of factors in a rotatable design. In Group Divisible Third Order Rotatable Designs, the v-factors are split into two groups of p and (v-p) factors such that the variance of a response in each of the group from a suitable origin. The purpose of this study was to construct Group Divisible Variance-Sum Third Order Rotatable Designs using a balanced incomplete block designs. The objectives were, to construct a Group Divisible Third Order Rotatable Designs in four, five and its generalization in k-dimensions, to obtain a Variance-Sum Group Divisible Third Order Rotatable Designs in four and in five dimensions and to obtain (k-1) Group Divisible Third Order Rotatable Designs in four, five and its generalization in (k-1) dimensions by rotating designs for one group only. Considering a BIBD with parameters where and k=2, the v- factors are sub-divided into two groups of factors one of p-dimensions and the other dimensions. A set of design points generated through factorial combination was added to suitably chosen sets of points, where the unknown levels were determined from the generated design points so as to satisfy the moment conditions. The equations obtained were satisfied since there exists a non-negative solution forming a v-dimensional Group Divisible Third Order Rotatable Designs with their Variance-Sum being a function of the distances for the two groups respectively. In conclusion Group Divisible Variance-Sum Third Order Rotatable Designs was constructed through BIBDs. The Group Divisible Variance-Sum Third Order Rotatable Designs constructed in this study gave less number of design points than the corresponding rotatable designs constructed using BIBDs. Further, the number of normal equations for estimating the parameter estimates was reduced by adopting this method. Other methods on construction of Group Divisible Variance-Sum Third Order Rotatable Designs for k number of groups were recommended.