Nested DOE with continous factors?

[#1]

In many examples of nested DOE categorical effects are used. Is nesting also possible with a continuous effect that is scaled? Example: suppose one has five emulgators and also the emulgator concentration is a factor; however the concentration range is different for each emulgator. Is it possible to design the experiment with a scaled continuous concentration at three levels -1 0 +1? 

[#2]

Hi @frankderuyck  !

I will repeat some of the options I was discussing with you outside of the JMP Community and add some details, so that it may start a discussion with other members and provide a discussion starter as well.

There may be several options with various difficulties and compromise for this situation :

1. You can use a categorical factor with levels High and Low, and specify in your model the interaction between concentration and emulgator type factors to take into consideration the difference in concentration numerical levels.
2. If you have a common concentration range for several emulgators, you can create one numerical continuous factor "concentration" and use the "disallowed combinations" to specify the available ranges for each emulgator, as well as specifying the interaction "concentration*emulgator type".
3. Finally (but I'm not entirely sure of the viability of this option), you can also keep one continuous factor concentration as a coded factor with two level (-1 and 1), and use different min and max concentrations values for each emulgators. It's like having a relative numerical scale for the concentration factors, where level min would be equivalent to x%, and level max would be equivalent to 100%. You would also have to include in the model the interaction terms between concentration and emulgator type factors. I'm not sure about this last option, but looking at a "relative" scale depending on the emulgator this may work.

EDIT: Following our discussion and with the paper you send me from Peter Goos about nested factors in DoE (link: https://lirias.kuleuven.be/retrieve/560302), it seems the example 4.2 looks similar to what you intend to do. It looks like the use of split-plot designs might help in keeping the link and hierarchy between the choice of emulgator type and its related concentration. Emulgator type would be a hard to change factor, and the concentration an easy to change factor.

I hope this will bring other members to jump in the conversation and provide feedbacks, guidance and advices.

All the best Frank,

[#3]

Indeed Victor, I will use this Split Plot approach with scaled nested continuous factor settings (as correctly you suggested!) and then recode the scaled settings to their real values. Thanks a lot! I look forward to any more feedback on this frequently encountered issue.

[#4]

HI @frankderuyck ,

The approach that you are proposing sounds good to me.

More generally you might also want to consider the candidate set design approach to deal with complex constraints. You might need to do this if your concentration factors were mixture factors, rather than continuous factors.

Phil