Simplex sum rotatable design

Local optimum area is often reached when doing nongradient simplex optimization. In such a situation, a researcher wants to model the optimum mathematically. Due to the fact that an optimum is in principle either a maximal or minimal response value and that it corresponds to a curved surface geometrically, it may as a rule be approximated by a second-order model. 

To reach a second-order model by a mathematical theory of experiment, designs of second order experiments may be applied, as described in sects. 2.3.2, 2.3.3 and 2.3.4. Noncomposite designs such as simplex sum rotatable designs (SSRD) pentagonal or hexagonal types (k=2) with central points are analyzed in this case (Figs. 2.57 and 2.58.). 

Reference [56] states that these are the smallest second-order rotatable designs, with a smaller number of trials than central composite rotatable designs. Of special use are designs that are made by vertices of hexagons with central points n0 l Fig. 2.58. 

This kind of design may easily be split into two blocks of the type three vertex triangles +n0/2 of central points. As a special feature of this design we consider the property that factor X requires five and factor X2 three levels of variation. This property is particularly important for practical application since the number of variation levels is often limited. 

The associated SSRD design matrix for k=2 is given in Table 2.221. 

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Design points 4 to 8 were determined in accord with formula (2.182). Trials 9 and 10 are additional ones for the SSRD design. The simplex sum rotatable design is given in Table 2.227. 

Box, G.E.P., and Behnken, D.W. (1960a), Simplex-Sum Designs A Class of Second Order Rotatable Designs Derivable from those of First Order, Ann. Math. Statist., 31, 838-864. 

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