A step-wise strategy is possible

At the outset of an exploratory study of a new synthetic procedure, the roles played by the various variables are not known. Under these conditions we are not primarily interested in very precise measures of the influence of the variables, but rather in obtaining information whether or not they are influencing, and for the influencing variables, the magnitude and the direction of their influence. In such cases, an approximation of the response surface by a plane will give sufficient information, i.e. 

The parameters in this model measure the slope of the plane and, hence, the sensitivity of the response to variations in the variable settings. 

In such cases it is possible to analyze three variables in four runs, up to seven variables in eight runs, up to fifteen variables in sixteen runs etc. 

This will provide us with a first check of which variables are influencing the response. It is then always possible to run a complementary set of new experiments to augment the model by cross-product terms to allow for an analysis of interaction effects, i.e. 

Fortunately, in many cases it will not be necessary to investigate interaction effects between all variables initially considered. After the first series of experiments and evaluation of the linear model, some variables often turn out to have a minor or even negligible linear influence. Such variables rarely show strong interaction effects with other variables. Interaction effects are more likely to be encountered between variables which also have strong linear influence. Of course, this is not fool-proof, but it offers a means of simplifying the problem, and will therfore lead to a reduction of the number of additional experimental runs. 

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