Great Curvature Domain of the Response Surface Sequential Experimental Planning

Investigation of the Great Curvature Domain of the Response Surface Sequential Experimental Planning 

It is clear that we can thus determine a way to the extreme point of the response surface curvature. At the same time, it is not difficult to observe that the ABCDE way is not a gradient. Despite its triviality, this method can be extended to more complex dependences (more than two variables) if we make amendments. It is important to note that each displacement required by this procedure is accomplished through an experiment here the length of displacement is an apparently random variable since we cannot compute this value because we do not have any analytical or numerical expression of the response function. The response value is available at the end of the experiments. 

The example shown above, introduces the necessity for a statistical investigation of the response surface near its great curvature domain. We can establish the proximity of the great curvature domain of the response surface by means of more complementary experiments in the centre of the experimental plan (xj = 0,X2 = 0.Xij = 0). In these conditions, we can compute y, which, together with Pq (computed by the expression recommended for a factorial experiment 

It is well known that the domains of the great curvature of the response surface are characterized by non-linear variable relationships. The most frequently used state of these relationships corresponds to a two-degree polynomial. Thus, to express the response surface using a two-degree polynomial, we must have an experimental plan which considers one factor and a minimum of three different values. A complete factorial 3 experiment requires a great number of experiments (N = 3 k = 3 N = 27 k = 4 N = 81). It is obvious that the reduction of the number of experiments is a major need here. We can consequently reduce the number of experiments if we accept the use of a composition plan (sequential 

An increase in the number of experiments in the centre of the experimental plan (ng). 

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