Simplex lattice screening designs

The efficiency of screening experiment designs depends on the form of experimental domain. If this domain suits a total simplex (0 X 1 i=l, 2. q), then a design of experiments with (2q+l) design points-trials is recommended. In that case design of experiments includes q-pure components (Xpl.O), of centroid simplex (X = q for all i=l, 2. q) and q-internal points with coordinates  

It should be said that q-responses of pure components makes determination of regression coefficients of linear model possible, while q-internal and central points serve to estimate the nonlinearity of the response surface. It is useful to include in the mentioned designs of experiments q-points of null effects in this form  

The elasticity of a rocket propellant was measured as the system response. An analysis of Fig. 3.3 indicates that all three components of the composition have large effects and that the response surface is greatly curved or nonlinear. Besides, the greatest response values were obtained dose to the centroid. Large response values also occurred for lower Xi levels and for X3 values between 0.33 and 0.67. Graphic interpretation of the simplex screening experiment may be compared to the response surface contour plots of the same example, Fig. 3.4. 

It is evident that graphic interpretation of the simplex screening experiment offers a robust idea about the form of the response surface. It is therefore not recommended to replace the response surface contour plot with a graphic interpretation of the simplex screening experiment. 

It should be pointed out that to obtain a second-order model we have to do 66 trials, or 10 with pure components, 45 of binary composition, 10 internal points and one centroid point. However, the 21 compositions out of 31 mixtures from a screening experiment are simultaneously a part of the design of 66 design points for a second-order model. This shows that even in mixture experiments we may deal with the principle of upgrading/augmenting a design of experiments. 

---