I have read one of the documents in the site (7 Component Mixture Design with Additional Constraints)
I have a similar problem; I have one mixture component (A) for which i have three different types (A1, A2 and A3). I have similar constraints to what include in your paper (min/max % of A as a whole). However i also want to evaluate mixtures with
* only A1 or A2 or A3 within total limits min/max for A
* a combination of A1+A2 or A1+A3 or A2+A3 within total min/max for A
Is there a way to put these constraints in JMP? I have found that the disallowed combination filter does not work for continous mixture factors so i dont really know how to do this.
I suppose a way around is to do 3 different designs (A1+A2) and (A1+A3) and (A2+A3) but i was wondering if there a way to do only 1 design with those constraints.
You should be able to apply a linear constraint to mixture designs (e.g. to make it so that the 3 "A" components cannot exceed 70% of the total mixture, set A1 + A2 + A3 < 0.7). You would just need to specify all 3 components. It gets a bit trickier if you want to make it so only 2 of the 3 are used in any mixture. One idea would be to only specify 2 generic "A" components and then include a categorical factor that specifies *which* substances are A1 and A2. Here's what I mean:
Thank you for your reply!
I saw a similar reply to yours in a different discussion. So I had a go at it in JMP. I put a few screens shots below to
clarify (factors, constraints, model and design).
The dummy variables (1&2) are only there as you said for the combination of component A (I want only two types of A at the same time in the mixture).
Then, i have also defined a "allowed combination of A" categorical variable where i have the 3 possible combinations of component A (A1+A2, A1+A3, A2+A3).
I have selected only main factors just for the sake of the exercise.
I get a design and yes, in this case, with the categorical value I can see which 2 A components I will put in the mixture. However, this design is not really telling me anything about how I have to combine the different quantities for A (1,2 or 3) for each experiment. For example, for run 1. I will only use A1 and A2 to a total of 33% but i dont get any information about how much of A1 or A2 I should put in that experiment.
Do you have any suggestion?
The intention in my suggestion was that Dummy 1 and Dummy 2 would correspond respectively to the first and second "A" component in the categorical factor Combination. So, row 1 indicates 0% A1 and 33% A2, row 4 is 36% A1 and 0% A2. Since you only have main effects, you're not going to get blends of Dummy 1 and Dummy 2 in your example. Add an interaction between Dummy1 and Dummy2 and you should see some blends.
Thank you again for your reply!
So Dummy1 is component A1 and Dummy2 is component A2
Then from that design table i get
A1 A2 A3 Combination
Run1 33% 0% 0% A1+A2
Run4 36% 0% 0% A1+A2
Run7 0% 35.64% 0% A2+A3
Run14 35.64% 0% 0% A1+A3
But when&how do I get to put some component A3 then?
in Run7 and A1 (0%) and
in Run14 as A2 (0%)?
Is this what you mean? or do I get this wrong?
Thank you for your reply!
Indeed, I can use your example as guidance (and I did). I put below, some of the screenshots to help the discussion.
In this case, i have 1 ingredient A with 3 different subtypes (A1, A2 and A3). If possible I would like to evaluate combinations of maximum 2 A ingredients (A1+A2, A1+A3, A2+A3) and obviously mixtures with only one type of A.
The total sum of ingredients in this case is only 44.34% (the other ingredients are not changed).Something similar to another of your examples.
I only put main factors in the model. I just wanted to know what I would get. In this case, for some reason, I only get mixtures with only 1 A ingredient (out of the 3 A ingredients that i have) . Do you know why we get this type of design?
Another question that I have (and this is more fundamental i believe) is about the correlations. From the correlations map, I would understand that this DOE is not great. Is that right? What can we do in general in this type of situations?
Similary, with the Power, I have the feeling that this is not great either? (Although I have to admit that I dont fully grasp the concept of power :-(
Again, what can we do in this type of situations?
Thank you again for any help!
The correlation of the estimates and the power are related. The correlation inflates the variance of the estimates. The inflated variance decreases the power.
This behavior (high correlation of estimates, low power) is characteristic of mixture designs because of the ever-present constraint that the components must sum to 1. This behavior is exacerbated by restricting the range of the component (not full 0-1 range) and by adding further constraints among the components.