The ratings follow a 0 – 20 scale, where 0 is the worst and 20 is the best. Rating, the variable consisting of the experts’ ratings, is the response of interest. You want to identify the wine-related factors that maximize the response.
Because each rater tastes eight wines, Rater is a blocking factor with eight runs per block. For this experiment, only these five raters are of concern. You are not interested in generalizing to a larger population of raters.
The factors and their levels appear in Process Factors and Levels for Wine Tasting Experiment. Note that all of these factors are categorical. The factors and their levels are also given in the factor table Wine Factors.jmp in the Design Experiment folder of Sample Data.
1.
Select DOE > Custom Design.
2.
Double-click Y under Response Name and type Rating.
Completed Responses and Factors Outlines shows the completed Responses outline.
1.
First, add the blocking factor, Rater. Click Add Factor > Blocking > 8 runs per block.
2.
Type Rater over the default Name of X1.
3.
Click Add Factor > Categorical > 2 Level.
4.
Type Variety over the default Name of X2.
6.
Click Add Factor > Categorical > 4 Level.
7.
Type Field over the default Name of X3.
9.
Click Add Factor > Categorical > 2 Level.
10.
Type De-Stem over the default Name of X4.
12.
Type 6 next to Add N Factors, and then click Add Factor > Categorical > 2 Level.
Yeast (Cultured and Wild)
Temperature (High and Low)
Press (Hard and Soft)
Barrel Age (New and Two Years)
Barrel Seasoning (Air and Kiln)
Filtering (No and Yes)
Completed Responses and Factors Outlines
14.
Click Continue.
2.
Select Help > Sample Data Library and open Design Experiment/Wine Factors.jmp.
Model Outline
The Alias Terms outline specifies the effects to be shown in the Alias Matrix, which appears later. See Alias Matrix. The Alias Matrix shows the aliasing relationships between the Model terms and the effects listed in the Alias Terms outline. Open the Alias Terms outline node to verify that all two-factor interactions are listed.
Partial View of the Alias Terms Outline
3.
5.
6.
1.
Under Number of Runs, type 40 in the User Specified box.
2.
Click Make Design.
Design for Wine Experiment
Color Map on Correlations
The only red in Color Map on Correlations is on the main diagonal. The color indicates absolute correlations of one, reflecting that each term is perfectly correlated with itself. It follows that no main effect is completely confounded with any two-way interaction. In fact, the absolute values of the correlations of main effects with two-way interactions are fairly low. This means that estimates of main effects might be only slightly biased by the presence of active two-way interactions.
Partial View of Alias Matrix
For example, consider the model effect Barrel Seasoning. If Variety*Press is active, then the expected value of the estimate for the Barrel Seasoning effect differs from an unbiased estimate of that effect. The amount by which it differs is equal to 0.4 times the effect of Variety*Press. Therefore, what appears to be a significant Barrel Seasoning estimated effect could in reality be a significant Variety*Press effect.
Design Diagnostics Outline
Specify the order of runs in your data table using the Output Options panel. The default selection, Randomize within Blocks, is appropriate for this example. Simply click Make Table.
Custom Design Table
Now you are ready to run your experiment, gather the Rating data, and insert the results in the Rating column of your Custom Design table.
1.
Select Help > Sample Data Library and open Design Experiment/Wine Data.jmp.
The Wine Data.jmp table is exactly the same as the Custom Design table shown in Custom Design Table, except that it contains your recorded experimental results.
2.
Select Run Script from the red triangle to the left of the Model script.
Fit Model Dialog for Wine Experiment
Notice that Rater, the blocking factor, is added as a fixed effect, rather than as a random block effect. This is appropriate because the five raters were specifically chosen and are not a random sample from a larger population.
3.
Click Run.
Partial Model Fit Results
2.
Click Remove.
Profiler for Reduced Model shows the Prediction Profiler. Recall that you specified a response goal of Maximize, with lower and upper limits of 0 and 20. Setting these limits caused a Response Limits column property to be saved to the Rating column in the Custom Design table. The Prediction Profiler uses the Response Limits information to construct a Desirability function, which appears in the right-most plot in the top row in Profiler for Reduced Model. The bottom row displays Desirability traces.
The first six plots in the top row show traces of the predicted model. For each factor, the line in the plot shows how Rating varies when all other factors are set at the values defined by the red dashed vertical lines. By default, the profiler appears with categorical factors set at their low settings. By varying the settings for the factors, you can see how the predicted Rating for wines changes. Notice that a confidence interval is given for the mean predicted Rating.
Observe that Rater is not included among the factors shown in the profiler. This is because Rater is a block variable. You included Rater to explain variation, but Rater is not of direct interest in terms of optimizing process factor settings. The predicted Rating for a wine with the given settings is the average of the predicted ratings for that wine by all raters.
Profiler for Reduced Model
A Factor Settings window appears with columns for all of the factors, including Rater. The box under Rater and next to Show is not checked. This indicates that Rater is not shown in the Prediction Profiler.
2.
Check the box under Rater in the row corresponding to Show.
3.
Deselect the box under Rater in the row corresponding to Lock Factor Setting.
4.
Profiler for Reduced Model Showing Rater
Prediction Profiler with Factor Settings Optimized
A column called Pred Formula Rating is added to the data table. Note that one of the runs, row 33, was given the maximum rating of 20 by Rater 5. The predicted rating for that run by Rater 5 is 19.550. But the row 33 trial was run at the optimal settings. The predicted value of 19.925 given for these settings in the Prediction Profiler is obtained by averaging the predicted ratings for that run over all five raters.
When you maximized desirability, you learned that the optimal rating is achieved with the Dijon variety of grapes. See Prediction Profiler with Factor Settings Optimized. Your manager points out that it would be cost-prohibitive to replant the fields that are growing Bernard grapes with young Dijon vines. Therefore, you need to find optimal process settings and the predicted rating for Bernard grapes.
1.
In the Variety plot of the Prediction Profiler, drag the red dashed vertical line to Bernard.
3.
Select Lock Factor Setting and click OK.
Prediction Profiler with Optimal Settings for Bernard Variety