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This module helps to find optimum values of technological or other (independent) variables, using observations of some output (dependent or response) variable obtained experimentally. Assumptions are that a) the optimum independent variables settings (e.g. temperature, pressure, drying time) correspond to minimum or maximum of the dependent variable mean, b) dependent variable values were observed for various settings of independent variables, c) minimum or maximum of the dependent variable mean exists and is not very far from experimental settings tried. The Response surface module fits a model through the experimental data – complete Taylor polynomial of second order and tries to find its extremum by looking for a stationary point (a point with zero first partial derivatives). When extremum (minimum or maximum) exists, its estimate and confidence interval are given in the protocol. When the optimized model has no extremum, stationary point corresponds to a saddle point and no optimum setting for independent variables can be found. Optimum independent variables setting can be located outside of experimental region, the estimate is less reliable in such case however.

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Task: Find optimal process parameters

Temperature Pressure Power Cons.
50 110 89.15
50 130 88.75
50 150 89.25
55 110 86.14
... ... ...

Response Surface Optimization

Protocol Text Output:
Optimization of Quadratic Response Surface    
Task name : Optim1    
Independent variable: Temperature    
Dependent variable: Power Input    
No. of variables : 2    
No of data : 15    
Degrees of freedom : 8    
Type of the stationary point : Minimum    
Stationary point X0 CI Lower bound CI Upper bound
Column 1 60.06733711 57.2344181 62.90025611
Column 2 128.3637814 115.4868087 141.240754
Value estimate in X0 : 84.7934742    
Confidence interval : 85.09194377    
Mean error : 0.118050794    
Residual sum of squares (RSS) : 0.311794286    
Residual variance : 0.02227102    
Condition number kappa : 19.03088768    
Correlation coefficient : 0.995943235    
Determinant : 1.024524982    

Graphical Output:
Response Surface Optimization

Reconstruction of the response "curve" for 1 parameter.
Response Surface Optimization

Examples of 3D-quadratic surfaces for 2-parameter (factor) optimization
Response Surface Optimization
Response Surface Optimization
Response Surface Optimization
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