First Order Rotatable Designs Incorporating Neighbour Effects

Abstract

In response surface analysis, it is generally assumed that the observations are independent and there is no effect of neighbouring units. But under the situation when the units are placed linearly with no gaps, the experimental units may experience neighbour or overlap effects from neighbouring units. Hence, for proper specification it is important to include the neighbour effects in the model. First order response surface mode! with neighbour effects from immediate left and right neighbouring units has been considered here and the conditions have been derived for the orthogonal estimation of coefficients of this model. The variance of estimated response has also been obtained and conditions for first order response surface model with neighbour effects to be rotatable have been obtained. A method of obtaining designs satisfying the derived conditions has been proposed. A first order rotatable design with neighbour effects using half replicate of \(2^3\) has also been given.