topic Re: DoE with fixed sum volume in Discussions

DoE with fixed sum volume

SIBH — Thu, 08 Jun 2023 21:05:57 GMT

I am working in formulation team and a very new to DoE. Need guidance for a DoE with below conditions:
there are 5 factors : P1 (%), P2 (%), P3 (%), P4 (%) and P5 (ppm)

P4 is used for volume make up & the equation is P4 = 100 - (P1+P2+P3)

P4 also has effect on Y (response).

P1, P2 and P3 have 2 level discrete values while P5 has 3 level discrete value.

Please see the image for reference:

My queries:

1. how to include P4 and keep the total (P1+P2+P3+P4)=100

2. Previously we tried to do DoE with only P1, P2, P3 and P5 and after designing, added P4 manually to resultant DoE table (i.e. P4= 100-(P1+P2+P3)) - is it recommended?

Much Thanks-
Simanti

Re: DoE with fixed sum volume

David_Burnham — Tue, 21 Sep 2021 10:04:41 GMT

The approach you have mentioned is known as a slack-variable approach. P4 takes the slack to make the total sum to a constant value. That can make sense, if P4 represents a bulk item (e.g. water) with other parameters being much smaller components.

What are describing is a mixture problem. Look under DOE>Classical and you will find options for mixture designs.

Re: DoE with fixed sum volume

statman — Tue, 21 Sep 2021 14:48:00 GMT

As David indicates you are in the Mixture design area of experimentation. These designs lack some of the common properties of orthogonality due to the factor constraints. For thorough treatise of the mixture design problem, read John Cornell, Experiments with Mixtures.

I am a bit confused by your factor description...P1-P3 & P5 are discrete? You indicate they are %, are there a limited number of % available? Usually mixture designs are for a small number of continuous variables where you are looking at the response surface contours to find best conditions. This, of course, after you have assessed these are indeed significant factors and you thoroughly understand noise. I will say it is a challenge to work with 5 mixture factors...your measurements systems will have to be very precise with effective resolution.

Re: DoE with fixed sum volume

SIBH — Wed, 22 Sep 2021 06:15:29 GMT

Thank you for your response.

To answer your doubt, yes, P1-P3 and P5 are fixed set of numbers, for example P5 will have only three values: 100, 200 and 300 and same is the case for P1-P3...(they are not ranges of numbers, rather discrete two values). P4 is used for volume make up (but it is not water, it is a chemical / reactive substance) and has larger volume / numbers than P1-P3 has and P4 has effect on Y (the outcome/response).