Abstract
In this paper, blocking in response surface for fitting first order model incorporating neighbour effects has been investigated. The conditions for orthogonal estimation of the parameters of the model have been obtained. A method of constructing designs which ensures the constancy of variance of the parameter estimates of the model has also been given.
Highlights
Response Surface Methodology (RSM) is used to explore the relationship between one or more response variable and a set of experimental variables or factors with an objective to optimize the response.Let there be v independent variables denoted by x1, x2,xv and the response variables be y and there are N observations
The response from a particular plot may not be the actual response from the plot but may be the joint effect of the treatment combination applied to same plot and the treatment combination applied to the neighbouring plots
It is important to study the response surface in the presence of neighbour effects which would result in more precise estimation of the parameters of the response surface model
Summary
Response Surface Methodology (RSM) is used to explore the relationship between one or more response variable and a set of experimental variables or factors with an objective to optimize the response. The work on RSM is done assuming observations to be independent and no effect of neighbouring units. Sarika et al [4] studied second order response surface model with neighbour effects and the rotatability conditions were derived. Jaggi et al [5] studied response surface model incorporating neighbour effects and the same has been illustrated. It is generally assumed that the experimental trials are carried out under homogeneous conditions. This assumption may not be valid in every experimental situation. We focus on the methodology for blocking in first order response surface model incorporating neighbour effects. 2. First Order Response Surface Methodology with Block Effects and Incorporating Neighbour Effects
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