Example of a response optimization experiment for a factorial design
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You are an engineer assigned to optimize the responses from a chemical reaction experiment. You have determined that three factors - reaction time, reaction temperature, and type of catalyst - affect the yield and cost of the process. You want to find the factor settings that maximize the yield and minimize the cost of the process.

You do not need to analyze these factorial design models. The worksheet contains the models for the response optimizer.

1    Open the worksheet FACTOPT.MTW.

2    Choose Stat > DOE > Factorial > Response Optimizer.

3    For the cost, under Goal, choose Minimize.

4    For the yield, under Goal, choose Maximize.

5    Click Setup. Complete the Lower, Target, and Upper columns of the table as shown below:

Response

Lower

Target

Upper

Cost

 

28

35

Yield

35

45

 

 

6    Click OK in each dialog box.

Session Window Output

Response Optimization: Cost, Yield

 

 

Parameters

 

Response  Goal     Lower  Target  Upper  Weight  Importance

Cost      Minimum             28     35       1           1

Yield     Maximum     35      45              1           1

 

 

Solution

 

                                      Cost    Yield     Composite

Solution  Time     Temp  Catalyst      Fit      Fit  Desirability

1         46.3636  150   A         28.9132  44.8282      0.924449

 

 

Multiple Response Prediction

 

Variable  Setting

Time      46.3636

Temp      150

Catalyst  A

 

 

Response     Fit  SE Fit       95% CI            95% PI

Cost      28.913   0.228  (28.374, 29.452)  (27.899, 29.928)

Yield     44.828   0.240  (44.262, 45.395)  (43.762, 45.894)

Graph Window Output

Interpreting the results

The individual desirabilities appear on the response optimization plot. The desirability for Yield is 0.98282 and the individual desirability for Cost is 0.86954. The composite desirability for both of these two variables is 0.924449.

To obtain this desirability, you would set the factor levels at the values shown under Solution in the Session window. That is, time would be set at 46.3636, temperature at 150, and you would use catalyst A.

If you want to try to improve this initial solution, you can use the plot. Move the red vertical bars to change the factor settings and see how the individual desirabilities and the composite desirability change. Click Predict on the graph to calculate the response values for the new solution.  

The response optimizer uses model equations. Ensure that your models are adequate before you interpret the results.