DOE for Patient Satisfaction

This was not my industry, but I will say it is certainly possible to conduct DOE's where the final assessment of the results takes weeks, or months to get.   In the electronics industry, the impact to the final device yields may take months to see after the design takes place.

In your case, I am more concerned as to whether you will have the discrimination on the Survey data to see the impacts.  If current patient satisfaction is 90%, and success would be measured as 96%, it is going to take a large numbers of patients to find that difference.

Also, you need to make sure the factors are controllable so that the DOE settings are solid, and make sense when the analysis is done.   There is no reason DOE's can't be done, though, if they are well thought out in advance of the data collection.