How many experiments should be run at the center point

To fit a quadratic model, it is necessary to run at least one experiment at the center point, otherwise the X X matrix will be singular and cannot be inverted to give a least squares fit. Although the property of rotatability is obtained with only one experiment at the center, there is a lot to be gained if more than one such experiment is run  

When linear and second order interaction models are determined from a two-level design, the estimate of the constant term will be an alias in which the true intercept fig is confounded with all square coefficients. 

Experiments at the center point will give an estimate, ig, of the true intercept Bg. The observed difference hg - y(0) will estimate the sum of the square coefficients 

To separate the aliased square coefficients, it will be necessary to run experiments on more than two levels so that the curvatures in different directions can be discerned. This is accomplished by the experiments in the axial points. 

From the above it is evident how a step-wise strategy can be used  

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