1. Optimisation

2. Optimisation
Simplex
Steepest ascent

3. Response surface for an experimental system
Optimum U1 U2
At the outset of an experimental study the location of the optimum is not known.

4. Optimisation by Simplex search I
Optimum U1 U2 1 3 2 4
Starting simplex and the first move from the poor conditions

5. Optimisation by Simplex search II
Optimum U1 U2 1 3 2 4 5 6 7 9 11 10 8 12
Progression of the simplex towards the optimum conditions.

6. First order response surface and path of steepest ascent.
Region of fitted first order response surface

7. Response Surface Modelling (RSM)

8. Central Composite Design
Three parts: 1.
Factorial or reduced factorial design Estimate of main effects and interactions 2.
At least one center point experiment Possible to reveal curvature and estimate the experimental error 3.
Experiments  on the variable axes Possible to estimate quadratic terms

9. Central composite rotatable design for two variables

10. Central composite rotatable design for three variables
Number of experiments: = 18