Abstract
ABSTRACT:
In RSM, it is generally assumed that the observations are independent and there is no overlap effects from the neighbouring units. But in situations where the units are placed linearly side by side, there is a chance to have overlap effects/neighbour effects from the adjoining experiments units. For example, in field experiments if a chemical spray is applied to one plot, it may spread over to the nearby plots due to wind. Hence, the response from a particular plot may be afected by effects from the adjacent plots and this efect has to be included in the model while fitting RSM. In this paper, first and second order response surface models with diferential effects from adjoining left and right neighbouring units has been considered and the conditions for the model with diferential neighbour effects to be rotatable have been obtained. Method of obtaining designs satisfying the derived conditions has been described. An illustration to show the impact of including neighbour effects in the model on the parameter estimates has also been given using a simulated data set. These designs result in more precise estimates of the parameters of the response surface model.
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