Use of Simplex Regular Plan for Experimental Research

Question (ii) is certainly the most crucial. A possible answer to this question will be developed in the next section. The research has to begin with a small or local plan of experiments in order to describe the first movements from the starting point when the first point of these previously planned experiments has been completed, the most non-favourable experiment will be rejected and it will be replaced by another experiment thus we obtain, the displacement of the local group of experiments. 

For a process with k factors, an abstract presentation of this procedure can be given as follows  

We define a regular simplex plan as an assembly of k+1 equidistant points for k= 1, the simplex is a segment for k= 2, it is a triangle for k= 3, we are faced with a regular tetrahedron, etc. Each simplex has a geometric centre placed at one point. 

When we replace the point rejected out of the group, in order to maintain a number of k-rl points, the next point wUl be the mirror image of the rejected point relative to the opposite face of the simplex. 

After the replacement of the rejected point, the simplex is rebuilt with a new geometric centre only the experiments corresponding to the new point can be carried out to start the procedure (displacement and elimination) over again. 

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