The following example, adapted from Meyer et al. (1996) and Box, Hunter, and Hunter (1978), shows a five-factor reactor example.
Previously, the screening designer was used to investigate the effects of five factors on the percent reaction of a chemical process (see Screening Designs). The factors (Feed Rate, Catalyst, Stir Rate, Temperature, and Concentration) are all two-level continuous factors. The next example studies the same system using a full factorial design.
1.
Select DOE > Full Factorial Design.
3.
In the sample data folder (installed with JMP), open Reactor Response.jmp found in the Design Experiment folder.
5.
In the sample data folder (installed with JMP), open Reactor Factors.jmp found in the Design Experiment folder.
Full Factorial Example Response and Factors Panels
6.
Click Continue to see the Output Options panel. In the Output Options panel, select Sort Left to Right from the Run Order menu, as shown to the right. This command defines the order of runs as they will be in the final JMP design table.
7.
Click Make Table.
The design data table (Partial Listing of Reactor 32 Runs.jmp from the Sample Data Folder) contains a run for every combination of high and low values for the five variables, which covers all combinations of five factors with two levels each. Since there are five variables, there are 25=32 runs. Initially, the table has an empty Y column named Percent Reacted for entering response values when the experiment is complete.
To see the completed experiment and continue this example, open Reactor 32 Runs.jmp found in the Design Experiment sample data folder.
Partial Listing of Reactor 32 Runs.jmp from the Sample Data Folder
1.
Select Analyze > Distribution.
2.
Highlight Percent Reacted and click Y, Columns. Then click OK.
Distribution of Response Variable for Reactor Data
4.
Click the red triangle icon next to the Fit Model script and select Run Script. The stepwise analysis begins with the Stepwise Regression Control panel shown in Stepwise Control Panel.
5.
Select P-value Threshold from the Stopping Rule list.
Stepwise Control Panel
Starting Model For Stepwise Process
10.
Model After Mixed Stepwise Regression
11.
Click the Make Model button in the Stepwise Regression Control panel. The Model Specification window that appears is automatically set up with the appropriate effects (Fitting a Prediction Model).
Fitting a Prediction Model
12.
Click Run to see the analysis for a candidate prediction model (Actual by Predicted Plot and Prediction Parameter Estimates Table).
The figure on the left in Actual by Predicted Plot and Prediction Parameter Estimates Table shows the actual by predicted plot for the model. The predicted model covers a range of predictions from 40% to 95% reacted. The size of the random noise as measured by the RMSE is only 3.3311%, which is more than an order of magnitude smaller than the range of predictions. This is strong evidence that the model has good predictive capability.
The figure on the right in Actual by Predicted Plot and Prediction Parameter Estimates Table shows a table of model coefficients and their standard errors (labeled Parameter Estimates). All effects selected by the stepwise process are highly significant.
Actual by Predicted Plot and Prediction Parameter Estimates Table
Viewing the Profiler shows the profiler’s initial display. The Prediction Profiler is discussed in more detail in the chapter Response Surface Designs, and in the Multivariate Methods book.
Viewing the Profiler
Viewing the Prediction Profiles at the Optimum Settings
The goal is to maximize Percent Reacted. The reaction is unfeasible economically unless the Percent Reacted is above 90%. Percent Reacted increases from 65.5 at the center of the factor ranges to a predicted maximum of 95.875 ± 2.96 at the most desirable settings. The best settings of all three factors are at the ends of their ranges. Future experiments could investigate what happens as you continue moving further in this direction.