This example shows how to create a design when you have not yet collected data, but have a guess for the unknown parameters. In this example, you model the fractional yield (Observed Yield) of an intermediate product in a chemical reaction. The fractional yield is a function of reaction time and temperature. See Box and Draper (1987).
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The columns for the predictors, Reaction Temperature and Reaction Time, have the Coding, Design Role, and Factor Changes properties. To see these properties, click in the Columns panel. They tell JMP how to treat these predictors when constructing a design. For information about how to save these column properties, see the Column Properties topic.
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The Observed Yield column will contain response data obtained by running the experiment.
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The Yield Model column contains the formula that relates the predictors to the response, Observed Yield. Click in the Columns panel to see the formula. The formula is nonlinear in the parameters t1 and t3.
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Select DOE > Special Purpose > Nonlinear Design.
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Click OK.
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In this example, the values 510 and 540 for Reaction Temperature and 0.1 and 0.3 for Reaction Time were specified using the Coding column property. Alternatively, you can specify a reasonable range of values directly in the Factors outline.
These new values represent a reasonable range of parameter values for the experimental situation. The default values were constructed based on the initial parameter values that were specified in the definition of the prediction formula. For information about constructing formulas, see Formula Editor in the Using JMP book.
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Click Make Design.
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Click Make Table.
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Figure 22.3 Design Table
Your design should be similar to the one shown in Figure 22.3. The runs might be in a different order, and the values for Reaction Temperature and Reaction Time, and consequently those computed for Yield Model, can be slightly different. Notice that values appear in the Yield Model column because the column contains the formula for the model. Also notice that the table contains a Model script that you can use to fit a nonlinear model to your observations.
Now that you have created your design table, run your experiment, and record the responses in the Observed Yield column. The data table Reaction Kinetics.jmp, found in the Design Experiment folder contains observed results for the design.
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Select Graph > Graph Builder.
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Figure 22.4 Design Settings
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Click Done.
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Figure 22.5 Design Settings with Density Contours
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Select Analyze > Specialized Modeling > Nonlinear.
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Click OK.
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Click Go in the Control Panel.
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Click the Nonlinear Fit red triangle menu and select Profilers > Profiler.
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To maximize the yield, click the Prediction Profiler red triangle menu and select Optimization and Desirability > Maximize Desirability.
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Figure 22.6 Time and Temperature Settings for Maximum Yield