a simple mixture DoE problem

[#1]

I am a chemist working with cementitious formulations.

Below is an example:

Ingredient	%
OPC	30
Sand	54.38
CAC	15
retarder	0.12
accelerator	0.2
additive	0.3
Total	100

I am only interested in three ingredients: CAC; retarder, and accelerator. I want to vary them as below:

                        Low          high

CAC:              10%          15%

retarder:          0.07%      0.14%

accelerator      0.10%       0.2%

however, in order to varies three ingredients listed above, I have to drag another ingredient, sand, to absorb the changes to make sure CAC+retarder+accelerator+sand=const.

then a 3 ingredients design becomes a 4 ingredients design.

Is there any way I can only work with the 3 ingredients I am interested in?

Thanks

[#2 · Accepted solution]

It seems that including sand in the design would be an advantage, because then JMP would tell you the proportion of sand needed.

Once you open Custom Design and define the three (or four) ingredients, click the red triangle at the top and select Advanced Options > Mixture Sum. You can define the amount that the ingredients in the study make up in the entire formulation. In your case, it seems like that would be 1 minus the proportion of OPC and additive.

(Note that JMP uses proportions (0-1), not percentages (0%-100%).

[#3 · Accepted solution]

Thanks for your answer.

I am investigating setting and hydration behavior of two cementious materials, so cements, retarder, accelerators are the main factors, sand as a filler should not have big impact

on the setting behavior of cementious materials.

So it is purely to comply with the mixture design constraint that sand is included to take up the slack, it is very inefficient.

also the % of sand is so big that by reducing or increasing it would not make it a significant factor.

[#4 · Accepted solution]

Hello,

For any mixture design the total of all ingredients must add to 100% as  you are finding by having to add sand.  If your goal is to have a mixture of the three ingredients listed then you will need to adjust their percentages accordingly so that any combination adds up to 1 or 100%.  See the link below for an example that I believe fits your needs.  

JMP Chemical Mixture

[#5]

Thanks for your suggestion.

sometimes I could manage to adjust the % of  ingredients that are revelant  to 1 or 100%,  majority of times, like the above case, when I combine large quantity ingredient,like cement and small quanitity additives, like retarder/accelerator, it virtually impossible to do that. The variation of cement % would be too small to make a difference from the chemistry point of view.

[#6]

Yes.  Whilst you inherently have a mixture, you don't need to treat it as a mixture from a DOE perspective.

Traditional designs have a rectangular symmetry, meaning that you need to be able to vary the factors independently of each other.  For a strict mixture problem that is not possible, since the sum of the components has to add to 100%.  So mixture designs are intended to accommodate this constraint during the design and analysis.  But you have a filler component (sand) that takes up the slack - and if that is something that is not of interest then there is no reason why you can't build a traditional design based on the 3 factors you identified.

[#7]

I used to do that, vary all the ingredients by whatever % I like, adjust sand % to make the whole formulation added up to 100%.

But the analysis would be based on factorical design, I still think RSM analysis is superior to factorical analysis for formulation, correct me if I am wrong.

Also is it  plain wrong to do factorical design for this case, since sand % IS changed during the process?  even though I believe sand is not a significant factor.

Thanks for sharing your idea.