Factor Constraints: Multiplication

[#1]

Hi everyone.

I am pretty new with JMP so pardon m eif the question sounds silly to you.

We are trying to set up a custom experimental design, in which we want to optimize a continuous response, working with 5 continuous factors, one discrete factor and two constants.
While we want to explore the effect of the factors on the response, we have parallely developed a relationship within the factors: for this reason we would like to use it to set contraints on the allowed levels, before creating the DOE.

After reading through the precious suggestions from this amazing community, we are using the Disallowed Combination Script, to meet this goal.

A bit more into details, here is the constraint:

[X1 * (X2 / X3) * C1 * ((C2 / X4) + 1) * D1 * (195.08 / 9) < 4.01] & [X1 * (X2 / X3) * C1 * ((C2 / X4) + 1) * Z1 * (195.08 / 9) < 0.1]
(where Xi are the factors, Ci the constants and D1 is the discrete factor).


Our problem is that the treatment do not seem to respect the constraints: many of the treatments suggested by the JMP are above the limit value. It also seems to me that the Specify Linear Constraints option works only for linear combinations of the factors, and not for their products (such as in our case)

Am I missing something here? Or do you have any suggestion on how to reformulate the DoE to make it less complicated?
I hope the question is clear and not too silly.
Sorry for the very long message: I will patiently wait for your input, and can gladly provide more info when needed.

Thanks a lot in advance to whoever might take the time to read this post and, in the meantime, I wish you a pleasant day.

Kind Regards,
A

[#2]

Hi @agiacomo,

Welcome in the Community !

You can read more about Factor Constraints in the article from @Jed_Campbell :Demystifying Factor Constraints

I'm a bit surprised by the complexity of your constraint, as it seems you already have a precise idea about the relationships between factors. What is your objective ? Are you willing to create a useful model, approximating the "true" relationship between factors, or are you more interested in validating a physical equation/model ?

1. In the first case, unless runs are not physically feasible without this complex constraint, I would remove this constraint (or simplify it), to have a broader experimental space available which can help model the relationships and increase inference space.
2. If you're more interested in validating a physical equation/model, you could create a datatable with the constraint formula, and generate values for the different factors based on the equation and the available range.

You might also be interested in the Candidate Set approach if the Disallowed combinations option doesn't work as you intend to.

Here is presentation by Chris Gotwalt on how to use it : Candidate Set Designs: Tailoring DOE Constraints to the Problem (2021-EU-30MP-784) 

Using a candidate set approach through these steps could help you respect your constraint:

1. Create your candidate set, a datatable for all your factors and formula uniform distributions (with the limits you have set for continuous factors X1 to X5) or random integer (from min to max for your numeric discrete factors) with a large number of rows (1000+ might be a good start).
2. Using a data filter on this datatable, exclude points that do not respect your constraint.
3. Use the Custom design platform on your candidate set datatable, use "Select Covariate Factors" and select your factors.
4. Specify your model and the number of runs in your design. You can check "Allow covariate rows to be repeated" if the runs can be replicated in your experimental setup.
5. You should obtain a design that do respect your constraint.

Hope this answer will help you,

[#3]

Hi Victor,

First of all sorry for my late interaction: we had some troubled week and only now I had the time to sit and read your answer.

Secondly: thanks really a lot for your kind and detailed reply!
Being new to JMP, I was afraid this set of costraints could be a bit pretentious or, as you rightfully said, that the model we are trying to evaluate was a bit too convoluted.
Just to elaborate further, the model/costraints were obtained in another department, and we wanted to test whether this applies also with our setup. 

I will try the solutions you suggested ASAP, and will immediately jump (or better said JMP, ahah) into the presentation you attached to the message. 
I will come back to this post in any case, either to close the matter or to kindly ask for further support, if anybody has time to do so.

Once again, thanks really a lot for your help: it is really invaluable!

Kind Regards,
Alessio