Hi all,
When creating Functional DoE's - Is there a specific additional "guidance" on selecting the number of runs compared to regular DoE's?
Any thoughts or experiences with this?
Best
Florian
Hi @Florian_Vogt ,
It is going to be very hard to do power analysis because you would be using a response that is the functional principal component score. How would you know what that score means before you have done the experiment? You probably would not even know the number of principal components. Maybe if they have a good amount of useful prior data this might be possible.
Perhaps you could think about a simple (non-functional, scalar) response as a proxy in order to do power analysis. That could work but it will only tell you about the power to detect that response, and not the power to detect changes to the functional response.
Even with simple responses, power analysis is hard to do because you often don't have good estimates of the noise prior to the experiment. I know a lot of customers that are big users of DOE that never use power analysis.
As-many-runs-as-you-can-afford is probably the best advice.
Also, looking at the trade-offs with number of runs vs effect correlation and aliasing is useful for any DOE. The number of effects that you can estimate will be a function of the number of runs, of course. And that is true for functional and non-functional DOE.
If your customer wants to find out more about design evaluation I would recommend the Goos & Jones book for very thorough discussion of this topic. (No mention of functional DOE in that book though as it was a few years before FDE).
I hope that helps,
Phil
Thanks @Phil_Kay , that helps a lot.
I think the question also aimed a little bit towards "do I need more runs for FDOE compared to standard DOE". So from your answer I conclude this can only be said based on practical experience in a certain experimental situation maybe (which is then out of our SE-expertise).
Thanks a lot!
If I was forced to answer to that question, I would say that you might require fewer runs for FDOE as there should be more information in a functional response. But you might also give the standard statistician answer: "it depends..."
It will depend on lots of other things.
One important point is how well your functional response sampling captures the functional behaviour. That is, have you measured the functional response at the best time points (if it is a time-dependent function, for example)?
