This example, adapted from Cornell (1990), comes from an experiment to optimize the texture of fish patties. The data is in Fish The columns Mullet, Sheepshead, and Croaker represent what proportion of the patty came from that fish type. The column Temperature represents the oven temperature used to bake the patties. The column Rating is the response and is a measure of texture acceptability, where higher is better. A response surface model was fit to the data and the prediction formula was stored in the column Predicted Rating.
To launch the Mixture Profiler, select Graph > Mixture Profiler. Assign Predicted Rating to Y, Prediction Formula and click OK. The output should appear as in Initial Output for Mixture Profiler..
Initial Output for Mixture Profiler.
The manufacturer wants the rating to be at least 5. Use the slider control for Predicted Rating to move the contour close to 5. Alternatively, you can enter 5 in the Contour edit box to bring the contour to a value of 5. Contour Showing a Predicted Rating of 5 shows the resulting contour.
Contour Showing a Predicted Rating of 5
The Up Dots shown in Contour Showing a Predicted Rating of 5 represent the direction of increasing Predicted Rating. Enter 5 in the Lo Limit edit box. The resulting shaded region shown in Contour Shading Showing Predicted Rating of 5 or More. represents factor combinations that will yield a rating less than 5. To produce patties with at least a rating of 5, the manufacturer can set the factors values anywhere in the feasible (unshaded) region.
The feasible region represents the factor combinations predicted to yield a rating of 5 or more. Notice the region has small proportions of Croaker (<10%), mid to low proportions of Mullet (<70%) and mid to high proportions of Sheepshead (>30%).
Contour Shading Showing Predicted Rating of 5 or More.
Up to this point the fourth factor, Temperature, has been held at 400 degrees. Move the slide control for Temperature and watch the feasible region change.
This example uses data from Five Factor There are five continuous factors (x1x5), one categorical factor (Type), and three responses, Y1, Y2 and Y3. A response surface model is fit to each response and the prediction equations are saved in Y1 Predicted, Y2 Predicted and Y3 Predicted.
Launch the Mixture Profiler and assign the three prediction formula columns to the Y, Prediction Formula role, then click OK. Enter 3 in the Contour edit box for Y3 Predicted so the contour shows on the plot. The output appears in Initial Output Window for Five Factor Mixture.
Initial Output Window for Five Factor Mixture
All the factors appear at the top of the window. The mixture factors have low and high limits, which were entered previously as a Column Property. See the Using JMP book for more information about entering column properties. Alternatively, you can enter the low and high limits directly by entering them in the Lo Limit and Hi Limit boxes.
The on-axis factors, x1, x2 and x3, have radio buttons selected.
The categorical factor, Type, has a radio button, but it cannot be assigned to the plot. The current value for Type is L1, which is listed immediately to the right of the Current X box. The Current X box for Type uses a 0 to represent L1.
A manufacturer desires to hold Y1 less than 1, hold Y2 greater than 8 and hold Y3 between 4 and 5, with a target of 4.5. Furthermore, the low and high limits on the factors need to be respected. The Mixture Profiler can help you investigate the response surface and find optimal factor settings.
Start by entering the response constraints into the Lo Limit and Hi Limit boxes, as shown in Response Limits and Shading. Colored shading appears on the plot and designates unfeasible regions. The feasible region remains white (unshaded). Use the Response slider controls to position the contours in the feasible region.
Response Limits and Shading
Feasible Region Enlarged
Use the slider controls or Contour edit boxes for Y1 Predicted to maximize the red contour within the feasible region. Keep in mind the Up Dots show direction of increasing predicted response.
Use the slider controls or Contour edit boxes for Y2 Predicted to minimize the green contour within the unshaded region.
Enter 4.5 in the Contour edit box for Y3 Predicted to bring the blue contour to the target value.
Factor Settings
As shown in Factor Settings, the optimal factor settings can be read from the Current X boxes.
The factor values above hold for the current settings of x4, x5 and Type. Select Factor Settings > Remember Settings from the Mixture Profiler red triangle menu to save the current settings. The settings are appended to the bottom of the report window and appear as shown below.
Remembered Settings
With the current settings saved, you can now change the values of x4, x5 and Type to see what happens to the feasible region. You can compare the factor settings and response values for each level of Type by referring to the Remembered Settings report.