DOE - How to handle uncontrolled factors directly affected by other factors using custom DOE

[#1]

I am fairly novice to this stuff so I will define the situation. Please share your thoughts on the situation.

I have two factors (Inputs A, B) that individually and directly affect factors C and D (Measurements). Increasing either A, or B leads to an increase in C and D. The issue is that currently, I am trying to decouple the benefits of A and B from C and D. I attempted an RSM DOE where I left C and D as uncontrolled factors. JMP added a few more runs and my hope was I would get enough variation in these for the model to generate appropriately. Unfortunately, after filling in the factors with the C and D measurements, I evaluated the design and got this variance profile. So I believe I was unsuccessful in this attempt.

How does one model factors that are directly influenced by other factors?

[#2]

It sounds to me like your 'factors C and D' are what are called co-variates in JMP. You might want to take a look here for some additional insight. Handling Covariates When Designing Experiments 

[#3]

Okay, that is a route I was researching. Glad to be reaffirmed this may be the direction to go. Thanks!

[#4]

Sorry, I'm a bit confused by the terminology you are using.  Perhaps you can clarify.  You note that A & B are input variables (X's).  I am confused by what you are calling C & D?  Are these response variables (Y's) or input variables?  You are calling them measurements?

If they are input variables that you are not willing to control (for several reasons) then they are noise variables.  If they are measurable noise variables, then indeed these could be considered covariates as Pete suggests.  If they are input variables and they are correlated with A&B, then you have multicollinearity issues.  There is no mathematical way to remove collinearity issues.  You have to use SME to choose how to handle these collinear factors.  Options can include removing some of the collinear terms from the model or combining factors that are collinear into one combined factor.

[#5]

Oh, excellent point. A and B are both inputs (Factors) I have physical control over by adjusting concentrations. This in turn has an impact on C and D which are measurements I can take of the solution after mixing. C and D are both properties known to affect this process and therefore, they themselves are factors. I can either control for C and D by adjusting concentrations of A and B, or control A and B but allow C and D to remain uncontrolled. They are inherently tied together.

I absolutely see your point though. I could actually model C and D as a response from A and B. 

Do you think this falls more under a collinearity issue?

Both components (A and B) are different, but have the same effects on C & D. My hope was that I could use combinations of the two, to determine if the components themselves inherently improve the process, or if it is their common properties (C and D) on the solution that are driving the improvement.

From a OFAT standpoint, I would probably hold C and D constant by adjusting A and B. If the results were comparable, I would rule A and B as insignificant and C and D and the main factors.

A1 + B1 = C + D

A2 + B2 = C + D

A3 + B3 = C + D

I am trying to move toward more statistical approaches to these experiments though.

Thanks for your help so far!

[#6]

I must admit that talking in generalities about a specific situation is very challenging if not impossible.  Not enough context is provided.

"I could actually model C and D as a response from A and B."  That is your experiment. C & D are response variables to the factors A & B (at least that is your explanation).  Since C & D cannot be explicitly controlled/managed they are not factors.  I would call those in-process y's (Y=f(y)).  Think hierarchy of effects. (Y=f(C,D)=g(A,B))

Your OFAT statement makes no sense.  You can't hold C&D constant, you manipulate A&B to manage C&D.

Additional issues are uncontrolled variables you are not taking into account (measurement errors, variation in the raw materials, ambient conditions, processing variables, etc.)