The Augment Design Interface... 123 Replicate Design ... 124 Add Centerpoints ... 125 Fold Over ... 125 The Reactor Example Re-visited ... 126 Interface for D-Optimal Augmentation ... 126 Analyze the Augmented Design ... 130
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The Augment Design Interface
The augment design feature of JMP DOE gives the ability to modify an existing design data table. If you do not have an open JMP table when you select Augment Design from the DOE menu, or from the DOE tab on the JMP Starter, the File Open dialog for your computer appears as in Figure 9.1. Select a data set that you want to augment. For this example, use the Reactor 8 Runs.jmp data in the Design Experiment sample data folder. This table was generated previously in Chapter 4, “Screening Designs.”
Figure 9.1 File Open Dialog to Open
a Design Data Table
After the file opens, the dialogs in Figure 9.2 prompt you to identify the factors and responses you want to use for the augmented design.
Select the columns that are model factors and click OK. Then select the column or columns that are responses. When you click OK again, the dialog below appears with the list of factors and factor values that were saved with the design data table. Buttons on the dialog give four choices for
augmenting a design:
❿ Replicate
❿ Add Centerpoints
❿ Fold Over
❿ Augment
The next sections describe how to use these augment- ation choices.
Replicate Design
The Replicate button displays the dialog shown here. Enter the number of times to perform each run. Enter two (2) in the dialog text entry to specify that you want each run to appear twice
in the resulting design. This is the same as one replicate. Figure 9.3 shows the Reactor
data with one replicate.
Figure 9.3 Design With One Replicate
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Add Centerpoints
When you click Add Centerpoints, a dialog appears for you to enter the number of center- points you want. The table shown to the right is the design table for the reactor data with two center points
appended to the end of the table.
Fold Over
When you select Foldover and click Make Data Table, the JMP Table that results has an extra column called Block as shown in Figure 9.4. The first set of runs is block 1 and the new (foldover) runs are block 2.
Note: Adding centerpoints or replicating the design also generates an additional Block
column in the JMP Table.
The Reactor Example Re-visited
The factors in the previous section were from the reactor example in the Chapter 4,
“Screening Designs.” This section returns to that example, which had ambiguous results. To begin, open the Reactor 8 Runs.jmp table from the Design Experiment sample data folder (if it is not already open).
Interface for D-Optimal Augmentation
After you identify the factors and response and click OK, the Augment Design dialog shown to the right appears.
Now click Augment on this dialog to see the display shown in Figure 9.5.
This display is the same as the one for Custom Design, except that the only factor control is the Add Block Factor button. Click Add Block Factor to add a two-level block factor to the factors panel. The original runs are the first block level and the new runs that result from augmenting the design are the second level. Choosing this option means that the augment design algorithm will optimally block the new runs versus the original runs.
9 Augment Figure 9.5 Augment User Interface
To continue with the reactor analysis, choose 2nd from the Interactions popup menu as shown on the left in Figure 9.6, which adds all the two-factor interactions to the model. The minimum number of runs given the specified model is 16, as shown in the Design
Generation text edit box. You can increase this number by clicking in the box and typing a new number.
Figure 9.6 Augmented Model
When you click Make Design, the DOE facility computes D-optimally augmented factor settings, as shown in Figure 9.7.
9 Augment Figure 9.7 D-Optimally Augmented Factor Settings
Note: The resulting design is a function of an initial random number seed. To reproduce the exact factor settings table in Figure 9.7, (or the most recent design you generated), choose Set Random Seed from the popup menu on the Augment Design title bar. A dialog shows the most recently used random number. Click OK to use that number again, or Cancel to generate a design based on a new random number.
The dialog to the right shows the random number (1859832026) used to generate the runs in Figure 9.7.
Figure 9.8 is the data table data from the corresponding runs in the Reactor Example from Chapter 6, "Full Factorial Designs." The Reactor Augment Data.jmp sample data file contains these runs. The example analysis in the next section uses this data table. Figure 9.8 Completed Augmented Experiment
Analyze the Augmented Design
To start the analysis, run the Fit Model script stored as a table property with the data table. This table property contains the JSL commands that display the stepwise regression control panel shown in Figure 9.9. Click the check boxes for all the main effect terms.
Note: If you generate a data table using the design dialog, the table property automatically generated by the DOE facility is called Model and contains a standard least squares fit model script. This data table has a script written specifically to do a stepwise regression. The stepwise regression can then do a standard least squares model fit after selecting effects.
9 Augment Figure 9.9 Initial Stepwise Model
Click Go to see the stepwise regression process begin and continues until all terms are entered into the model that meet the Prob to Enter and Prob to Leave criteria in the Stepwise Regression Control panel. Figure 9.10 shows the result of this example analysis. Note that Feed Rate and Stir Rate are out of the model while the Temperature*Catalyst
Figure 9.10 Completed Stepwise Model
After Stepwise is finished, click Make Model on the Stepwise control panel to generate this reduced model, as shown in Figure 9.11. You can now fit the reduced model to do
additional diagnostic work, make predictions, and find the optimal factor settings. Figure 9.11 New Prediction Model Dialog
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The ANOVA and Lack of Fit Tests in Figure 9.12 indicate a highly significant regression model with no evidence of Lack of Fit.
Figure 9.12 Prediction Model Analysis of Variance and Lack of Fit Tests
The Scaled Estimates table in Figure 9.13 show that Catalyst has the largest main effect. However, the significant two-factor interactions are of the same order of magnitude as the main effects. This is the reason that the initial screening experiment, shown in Chapter 4, “Screening Designs,” had ambiguous results.
Figure 9.13 Prediction Model Estimates Plot
It is desirable to maximize the percent reaction. The prediction profile plot in
Figure 9.14 shows that maximum occurs at the high levels of Catalyst and Temperature
and the low level of Concentration. When you drag the prediction traces for each factor to their maximum settings, the estimate of Percent Reacted increases from 65.375 to 95.6635.
Figure 9.14 Maximum Percent Reacted
To summarize, compare the analysis of 16 runs with the analyses of reactor data from previous chapters:
❿ In Chapter 4, “Screening Designs,” the analysis of a screening design with only 8 runs produced a model with the five main effects and two interaction effects with
confounding. None of the factors effects were significant, although the Catalyst factor was large enough to encourage collecting data for further runs.
❿ Chapter 6, “Full Factorial Designs,” a full factorial of the five two-level reactor factors, 32 runs, was first subjected to a stepwise regression. This approach identified three main effects (Catalyst, Temperature, and Concentration) and two interactions
(Temperature*Catalyst, Contentration*Temperature) as significant effects.
❿ By using a D-optimal augmentation of 8 runs to produce 8 additional runs, a stepwise analysis returned the same results as the analysis of 32 runs. The bottom line is that only half as many runs yielded the same information. Thus, using an iterative approach to DOE can save time and money.
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