Optimizing Desirability With Uncontrolled Factor

[#1]

I am looking for advice on how to automate maximizing the desirability of a process profile when I am locking one of the factors and having the others optimize around it. My process has an uncontrolled factor, so I need to adapt to what it's doing per unit I measure. My desired response can generally be achieved by adjusting the controlled factors, but the desirability situation is unique per value of the uncontrolled factor. 

Does anyone have a method or script I could use to feed JMP a column of this uncontrolled factor, and then adjacent columns that are the controlled factors will display their optimized value per row? It would be great if the estimated response was also a column in this table. 

[#2]

Hi @V1N0V3R1T4S,

It's difficult to help you with limited context about your project.
You seem to be concerned about optimization of your response regarding several factors, with one uncontrolled (numerical continuous ?) factor. Can this factor vary during the experiment ? Or is it fixed to an uncontrolled value during the experiment ? What is this source of variation ?

As you have no control about this factor, you may not be interested into knowing how this factor influence your mean response(s), but more likely how much variation it can cause on the response(s). You could try to set up this factor as a random main effect in your model, thanks to the "Attribute" role in the Fit Model platform : Construct Model Effects

Then, using this Mixed model, the Profiler can help you optimize the response mean without using this uncontrolled factor as a fixed effect.

There may be other more suitable option, if you can provide more info and an anonymized dataset it can greatly help understand your situation.

Hope this first answer might help you,

[#3]

Hey Victor and Statman, 

It will take some time to anonymize my data set.... I will try to describe the situation in better detail before I do that. 

My experiment:

Reponse: Y - attribute of a part being built during the test.

3 Controlled Continuous Factors: CX1, CX2, CX3

1 Uncontrolled (Ambient Environmental) Continuous Factor: UX4 

I designed an experiment around the CXi, and knew ahead of time that UX4 drifts in a somewhat predictable way over the course of a day, so if I timed by tests correctly I could capture close-to-repeatable values of it, to give its domain some sense of regularity. 

I then built what appears to be a fairly well behaved model using the factors, to see how they effect the response Y. Y does have  a target value I am trying to achieve per unit built. 

What seems to be the case is that my optimized values for the CXi are dependent on the value of UX4, so the scheme I am trying to implement as we go to make a part is: measure UX4, feed that value into the profiler, and then maximize the desirability of the CXi with the UX4 value fixed. The operator will then set their tools to the optimized CXi values before building the part.

What I would like then, is to automate this optimization per arbitrary value of UX4. I would like to have a data table where I provide a column of UX4, and then the other columns in the data table will be auto-filled with the optimized values of the CXi, and the predicted value of Y associated with those factor settings.

Does that add some clarity to my request? 

[#4]

I have the same problem Victor has in that you have provided a very limited amount of context for your query.  I would guess, Victor is on the right track.  One way to handle the uncontrolled factor would be treat the uncontrolled factor as a covariate.  This is essentially what Victor is suggesting.  This will ultimately result in a mixed model (both fixed and random effects in the model).

[#5]

Hey Statman, 

I've added my reply under Victor's post, let me know if additional details would be helpful in explaining my situation. 

Thanks!

[#6]

Your proposal seems reasonable.  This is the typical way covariates are accounted for.  The other option is to design the process robust to UX4.