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How to design such a experiment?

MartinY

Martin Here:

A typical cementitious adhesive formulation looks like this:

cement: 30%

MC: 0.4%

Filler: 69.6%

Water% 22%

I have three types of MC: MC#1,MC#2,MC#3; two types of fillers: Filler #1, Filler #2. I want to study the adhesion of adhesive under below conditions:

MC (fixed at 0.4%) as categorical factor MC#1~MC#3

Fillers as mixture with the sum of filler#1 and filler#2 equals 69.6 (filler#1 could be from 10% to 90% of 69.6; filler#2 then will be 90% to 10%).

Finally, I want to insert water % as a process factor: water level could be ranged from a% to b%, depending on the consistancy required.

Could this be done? Basically, it is categorical factors combined with mixture factors with extra process factor.

Thanks!

Martin

Accepted answers

Phil_Kay

You can add mixture factors in Custom Design. These are just another type of factor like Continuous and Categorical.

cwillden

Adding onto @Phil_Kay's answer, I would usually try to formulate my model for a mixture design the following way:

1. Specify a model for just the mixture components. Don't add quadratic terms, but for non-linear blends add 2-factor interactions or even 3-way interactions if you're so inclined.

2. Specify a model for the process variables only - done as usual.

3. Construct a combined model mixture model + process variable model + (mixture model x process variable model). The last part is crossing all the terms of the mixture model with the process variable model.

As a simple example, let's say you have 3 mixture components X1, X2, X3, and 2 process variables Z1, Z2. My model from step 1 might include terms X1, X2, X3, X1*X2, X1*X3, X2*X3. My model for step 2 might include terms Z1, Z2, Z1*Z2. The combined model would have terms X1, X2, X3, X1*X2, X1*X3, X2*X3, Z1, Z2, Z1*Z2, X1*Z1, X2*Z1, X3*Z1, X1*Z2, X2*Z2, X3*Z2, X1*Z1*Z2, X2*Z1*Z2, X3*Z1*Z2,...,X2*X3*Z1*Z2.

It's usually ok to trim back on the crossed model portion. For example, I could eliminate all the interactions of (X[i]*X[j]) with (Z[1]*Z[2]). Obviously these combined models can really explode in the number of model terms.

There's a good example of doing this in the DOE guide in Help > Books > Design of Experiments Guide on page 170 (for JMP 13). You can search "Mixture Design with Nonmixture Factors" in the document to find the section.

All comments

cwillden

Hi @MartinY,

I want to make sure I understand your situation properly. The ratios you defined are for those 3 components before adding water, correct? They sum to 100%, so I just want to make sure. Is the water % really just a dilution effect? Also, are you keeping all the ratios of cement, MC, and Filler (combined Filler 1 and 2) fixed at the stated ratios? It seems like the only ratios that are varying are the ratios of Filler 1 to Filler 2, right?

If all of that is correct, here is what I would suggest:

Forget about mixture effects. If you really only have Filler 1 and Filler 2 mixture components, then you can just do a Filler 1% effect that ranges from 10-90%, and obviously Filler 2% is just 100%-Filler 1%. Mixture effects are only necessary when you have 3+ components that are being varied in their ratios.
In Custom Design, set up your factors like so:

I just guessed on a range for Water. Obviously, you can put whatever percentages you want there. I probably should have stayed consistent with proportions or percentages for the last 2 factors, but you can do what you want.

From here, you just construct your desired model from these factors, determine how many runs you want to do, etc. You can choose to add 2-way interactions, squared terms for Filler 1 Ratio and Water, and even a 3-way interaction if you desired.

MartinY

Hi Cwillden:

Thanks for taking time answer my question.

Your design suits my question perfectly. I certainly will try your design in my incoming project.

I am curious to know how to blend categorical factors with mixture. for instance, in my question, suppose I have three fillers ( #1, #2,#3) that is added up to fixed percentage, I want to vary two of them. In this case, we have to face mixture design seriously. Do you have any idea of how this can be done?

Thanks

Martin

Phil_Kay

You can add mixture factors in Custom Design. These are just another type of factor like Continuous and Categorical.

cwillden

Adding onto @Phil_Kay's answer, I would usually try to formulate my model for a mixture design the following way:

1. Specify a model for just the mixture components. Don't add quadratic terms, but for non-linear blends add 2-factor interactions or even 3-way interactions if you're so inclined.

2. Specify a model for the process variables only - done as usual.

MartinY

Hi Willden:

Thanks for your very detailed explanation, I get the concept now.

Regards

Martin