topic Re: Mixture design - specifying linear constraints in Discussions

Mixture design - specifying linear constraints

Mathej01 — Wed, 29 Nov 2023 14:40:13 GMT

I wanted to have mixture design or custom design with 5 raw materials (P1, P2, X, Y, Z). And in this design, sum of two of the same type of raw materials P1 & P2 should be between 0.2 and 0.4. I tried to use linear constraints. But JMP is saying that the constraints are wrong. What will be the right constraint for that? and is this possible to do? And is it possible to include the combined effect of P1 & P2?

Re: Mixture design - specifying linear constraints

Victor_G — Wed, 29 Nov 2023 12:30:30 GMT

Hi @Mathej01

I don't see why the constraints may not be possible to implement in the Custom design platform.

I was able to obtain a design with your specified constraints on P1 and P2 with the following linear constraints :

{1 * :P1 + 1 * :P2 <= 0.4, 1 * :P1 + 1 * :P2 >= 0.2}

Here is the screenshot of the platform :

Would these constraints work for your use case ?

Concerning the combined effects of P1 and P2, I would suggest keep the main effects of these factors in the model and add the interaction P1xP2.

Hope this first answer will help you,

Re: Mixture design - specifying linear constraints

Mathej01 — Wed, 29 Nov 2023 14:41:27 GMT

Hi Victor ,

Thanks for your reply. I guess, I have to add some more details to my questions.

I had specified the range of values for all my mixture factors. But only P1& P2 has a relation in terms of their sum should also lie between 0.2 and 0.4. Is it not possible? How can I do it correctly? By adding all of the as linear contraints?

Thanks in advance.

Re: Mixture design - specifying linear constraints

Victor_G — Wed, 29 Nov 2023 13:38:21 GMT

Hi @Mathej01,

It seems you have set-up your DoE correctly. Did you had any error messages ?
With the same configuration as yours, I can obtain a DoE table. If you have troubles, try using this script :

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Mixture, 0, 0.85, "P1", 0 ),
	Add Factor( Mixture, 0, 0.85, "P2", 0 ),
	Add Factor( Mixture, 0.15, 0.3, "O", 0 ), Add Factor( Mixture, 0, 0.65, "R", 0 ),
	Add Factor( Mixture, 0, 0.2, "A", 0 ), Set Random Seed( 476871027 ),
	Number of Starts( 25985 ), Add Constraint( [1 1 0 0 0 0.4, -1 -1 0 0 0 -0.2] ),
	Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
	Add Term( {5, 1} ), Set Sample Size( 15 ), Simulate Responses( 0 ),
	Save X Matrix( 0 ), Make Design, Set Run Order( Randomize ), Make Table}
)

Hope this will help you,

Re: Mixture design - specifying linear constraints

drdrf — Wed, 29 Nov 2023 13:57:29 GMT

Isn't the problem here that P1 must be between 0.2 and 0.4, P2 must be between 0.2 and 0.4 and also the sum of P1 and P2 must be between 0.2 and 0.4? This leaves only one possibility for P1 and P2, both being 0.2.

I think you wither need to allow the sum to go higher than 0.4 or allow the individual values of P1 and/or P2 to go below 0.2

Re: Mixture design - specifying linear constraints

Mathej01 — Wed, 29 Nov 2023 14:02:09 GMT

Thanks @Victor_G ,

Seems like I solved the issue. I made a mistake by giving values ranges (0.2, 0.4) for the factors P1 and P2 and also added a constraint for their sum. Now When I gave the value range as (0. 0.4) for both factors. It is working. Thank you.

Re: Mixture design - specifying linear constraints

Victor_G — Wed, 29 Nov 2023 14:11:37 GMT

Hi @drdrf,

P1 and P2 should not have their individual ranges fixed between 0,2 and 0,4 as their sum is already constrained between 0,2 and 0,4 so that leaves more than one option. Just as an example (but we could have more options and levels by specifying a more complex model):

You always have the possibility to check the constraints before launching the DoE by clicking on "Check constraints".

Re: Mixture design - specifying linear constraints

Victor_G — Wed, 29 Nov 2023 14:10:47 GMT

Yes, as you already have an upper and lower constraint for the sum of the two mixture factors P1 and P2, it's best to not specify any individual range and check the design proposed at the end, in order to avoid adding impossible or useless constraints.

Glad that it helped you !