Extrapolating a Mixture Design
Note
The intrepid analyst can follow the example below to extrapolate a mixture model.
Take an existing design, with reasonable models and that shows a region beyond the range studied could be better. The plot below shows that less TEC might drive the system to a more desirable outcome.
Open the original design. Write down the number of rows in the design. Go to the Coefficients Table and write down (ctrl+A to select all, ctrl+C to copy it, then paste it into an outside spreadsheet) the terms present in the model. We must match these models in the extrapolated design.
Go back to the Design node.
Go to File => Export to File… to save the design as flat file data.
Go to File => New Design… and click Yes when asked to use previous information.
Switch the design to Historical Data. Type in the number of rows recorded above.
Change the components to be extrapolated. For this example the lower range of TEC was reduced to 2.
Click Next(s) and then Finish without making any further changes.
Go to File => Import from File… to bring the old design back.
The old design can be copied and then pasted into the Historical Data design as well.
Fit the models for the expanded component ranges. Standard analysis methods, should give the same model estimate, but check the results from the coefficients table above. Make sure the new models for each response match the original models term for term. (Short Cut: look at the model graphs, if they look the same keep going.)
Extrapolated solutions can now be identified.
Go to Numerical Optimization and click the options button (see below). Turn on the option to “Include Standard Error Models”.
Turning this option on creates new StdErr responses. Set the Goal(s) for the StdErr response(s) to be “in range”, and delete the lower limit. This restricts the extrapolation to have a confidence band around the prediction that is no wider than what it is at the worst run.
Set the goals for the critical responses and move to the Solutions tab, and then onto the Graphs tab.
The line for the original design limits was manually added, but it allows for a look at solutions beyond the limits of the original mixture design.
To improve the models even further augment the design, and add runs to the new region.
Save this design.
Go to Design Tools, Augment Design, Augment to open the optimal augment dialog.
