A good way to improve any procedure is to conduct an experiment. For each experimental run, JMP’s custom designer determines which brand to use, how long to cook each bag in the microwave and what power setting to use. Each run involves popping one bag of corn. After popping a bag, enter the total number of kernels and the number of popped kernels into the appropriate row of a JMP data table. After doing all the experimental runs, use JMP’s model fitting capabilities to do the data analysis. Then, you can use JMP’s profiling tools to determine the optimal settings of popping time, power level, and brand.
The first step is to select DOE > Custom Design. Then, define the responses and factors.
Custom Design Responses Panel
1.
To rename the Y response, double-click the name and type “Number Popped.” Since you want to increase the number of popped kernels, leave the goal at Maximize.
2.
To add the second response (total number of kernels), click Add Response and choose None from the menu that appears. JMP labels this response Y2 by default.
3.
Double-click Y2 and type “Total Kernels” to rename it.
Renamed Responses with Specified Goals
In the Factors panel, add Brand as a two-level categorical factor:
1.
Click Add Factor and select Categorical > 2 Level.
3.
To rename the default levels (L1 and L2), click the level names and type Top Secret and Wilbur.
Add Time as a two-level continuous factor:
4.
Click Add Factor and select Continuous.
6.
Likewise, to rename the default levels (–1 and 1) as 3 and 5, click the current level name and type in the new value.
Add Power as a two-level continuous factor:
7.
Click Add Factor and select Continuous.
9.
Rename the default levels (currently named -1 and 1) as 5 and 10 by clicking the current name and typing. The completed Factors panel looks like Renamed Factors with Specified Values.
Renamed Factors with Specified Values
10.
Click Continue.
2.
Click the Add Constraint button twice, once for each of the known constraints.
3.
Complete the information, as shown to the right in Defining Factor Constraints. These constraints tell the Custom Designer to avoid combinations of Power and Time that sum to less than 10 and more than 13. Be sure to change <= to >= in the second constraint.
The area inside the parallelogram, illustrated on the left in Defining Factor Constraints, is the allowable region for the runs. You can see that popping for 5 minutes at a power of 10 is not allowed and neither is popping for 3 minutes at a power of 5.
Defining Factor Constraints
1.
Click Interactions in the Model panel and select 2nd. JMP adds two-factor interactions to the model as shown to the left in Add Interaction and Power Terms to the Model.
2.
Click Powers and select 2nd to add quadratic effects of the continuous factors, Power and Time.
Add Interaction and Power Terms to the Model
The Design Generation panel in Model and Design Generation Panels shows the minimum number of runs needed to perform the experiment with the effects you’ve added to the model. You can use that minimum or the default number of runs, or you can specify your own number of runs as long as that number is more than the minimum. JMP has no restrictions on the number of runs you request. For this example, use the default number of runs, 16. Click Make Design to continue.
Model and Design Generation Panels
When you click Make Design, JMP generates and displays a design, as shown on the left in Design and Output Options Section of Custom Designer. Note that because JMP uses a random seed to generate custom designs and there is no unique optimal design for this problem, your table may be different than the one shown here. You can see in the table that the custom design requires 8 runs using each brand of popcorn.
Now click Make Table in the Output Options section.
Design and Output Options Section of Custom Designer
The resulting data table (JMP Data Table of Design Runs Generated by Custom Designer) shows the order in which you should do the experimental runs and provides columns for you to enter the number of popped and total kernels. Note that the design matrix is updated to match the order of runs, the Time and Power values, and the Number Popped and Total Kernels columns are added.
Tip: Note that optionally, before clicking Make Table in the Output Options, you could select Sort Left to Right in the Run Order menu to have JMP present the results in the data table according to the brand. We have conducted this experiment for you and placed the results, called Popcorn DOE Results.jmp, in the sample data folder installed with JMP. These results have the columns sorted from left to right.
JMP Data Table of Design Runs Generated by Custom Designer
Results of the Popcorn DOE Experiment
After the experiment is finished and the number of popped kernels and total kernels have been entered into the data table, it is time to analyze the data. The design data table has a script, labeled Model, that shows in the top left panel of the table. When you created the design, a standard least squares analysis was stored in the Model script with the data table.
1.
Click the red triangle for Model and select Run Script.
The default fitting personality in the model dialog is Standard Least Squares. One assumption of standard least squares is that your responses are normally distributed. But because you are modeling the proportion of popped kernels it is more appropriate to assume that your responses come from a binomial distribution. You can use this assumption by changing to a generalized linear model.
2.
Change the Personality to Generalized Linear Model, Distribution to Binomial, and Link Function to Logit, as shown in Fitting the Model.
Fitting the Model
3.
Click Run.
4.
Scroll down to view the Effect Tests table (Investigating p-Values) and look in the column labeled Prob>Chisq. This column lists p-values. A low p-value (a value less than 0.05) indicates that results are statistically significant. There are asterisks that identify the low p-values. You can therefore conclude that, in this experiment, all the model effects except for Time*Time are highly significant. You have confirmed that there is a strong relationship between popping time (Time), microwave setting (Power), popcorn brand (Brand), and the proportion of popped kernels.
Investigating p-Values
1.
Choose Profilers > Profiler from the red triangle menu on the Generalized Linear Model Fit title bar. The Prediction Profiler is shown at the bottom of the report. The Prediction Profiler shows the Prediction Profiler for the popcorn experiment. Prediction traces are displayed for each factor.
The Prediction Profiler
Moving the Time Value from 4 to Near 5
As Time increases and decreases, the curved Brand and Power prediction traces shift their slope and maximum/minimum values. The substantial slope shift tells you there is an interaction (synergistic effect) between Time and Brand and Time and Power.
Furthermore, the steepness of a prediction trace reveals a factor’s importance. Because the prediction trace for Time is steeper than that for Brand or Power for the values shown in Moving the Time Value from 4 to Near 5, you can predict that cooking time is more important than the brand of popcorn or the microwave power setting.
4.
Click the red triangle icon in the Prediction Profiler title bar and select Maximize Desirability. JMP automatically adjusts the graph to display the optimal settings at which the most kernels will be popped (The Most Desirable Settings).
The Most Desirable Settings