DOE Costom Design with standard factors or with Mixture Factors?

[#1]

I am facing the following problem:

I have a bunch of factors that are ingredients of a solution:

Ingredient A (2 - 20%)

Ingredient B (0 - 4%)

Ingredient C (5 - 20%)

whereas behind Ingredient B and C a selection of categorial Ingredients exists.

Further, I have several process factors:

Pressure 200 - 400

Runs 2 - 4

Responses:

Stability

Costs

Aim of that DOE is to find out which is the best formulation with corresponding process factors with highest stability and lowest costs

At first, I though about a standard Screening Model, with subsequent RSM:

Ingredient A - continious

Amount Ingredient B - continious

Selection of Ingredients B - 4 step categoric

Amount of Ingreident C - continious

Selection of Ingredient C - 2 step categoric

Pressure - continious

Runs - continious

with a screening model maybe a selection of Ingredient B and C could be eliminated, before proceeding with RSM

Second, I thought about the following setup:

Ingredient A - mixture

Ingredient B - mixture

Ingredient C - mixture

Selection of Ingredient B - categoric 4 step

Selection of Ingredient C - categoric 2 step

Pressure - continious

Runs - continious

I am wondering, if I am with teh second design as flexible as with the first design in terms of augment designs...

Further, I am wondering how I can analyse interacttions of Pressure, Runs, selection of Ingredient B and Selection of Ingredient C with the mixture?

Thank you,

Jasmin  

[#2]

A few questions that need answers in order to start setting up this experiment. You list 3 ingredients in your mixture, A, B, and C, with their ranges. However, those three ingredients cannot add to 100%. What are the other ingredients? Are they going to be varied? Will they all be held constant? As it stands those ingredients do not look like a mixture. 

Also, what is the process factor Runs? With a name like that it implies that you are going to conduct that trial multiple times. Is that the case? If so, then why would that be a factor?

Finally, you will need to be aware that the different types of B and C factors, each at 4 levels will cause this to be a VERY large experiment. Categorical factors will always make the experiment much larger as there are no "tricks" to try and save some runs.

Ultimately, you can indeed mix process variables with the mixture ingredients in a single design. The model gets more complicated and can take some time to understand. I would recommend that you do some research on these "mixture-process designs and models" as they are called. The subject is a bit lengthy for a forum like this. In fact, you might also want to learn a bit more about mixture experiments and the corresponding mixture models because they are fit and interpreted differently than the "classical" models. JMP can handle all of this, but the more knowledge you have, the better you will be able to use JMP.

[#3]

Hi Dan,

thanks for replying.

---

@Dan_Obermiller wrote:

A few questions that need answers in order to start setting up this experiment. You list 3 ingredients in your mixture, A, B, and C, with their ranges. However, those three ingredients cannot add to 100%. What are the other ingredients? Are they going to be varied? Will they all be held constant? As it stands those ingredients do not look like a mixture. 

Correct, I forgot to add ingredient D which can vary 10-100% and acts as a "filler" to 100%

---

Also, what is the process factor Runs? With a name like that it implies that you are going to conduct that trial multiple times. Is that the case? If so, then why would that be a factor?

"Runs" could also be called "passes" --> the product has to pass the processing device seveal times (2 - 4 times) in oder to reach the desired product quality/stabilty

---

Ultimately, you can indeed mix process variables with the mixture ingredients in a single design. The model gets more complicated and can take some time to understand. I would recommend that you do some research on these "mixture-process designs and models" as they are called. The subject is a bit lengthy for a forum like this. In fact, you might also want to learn a bit more about mixture experiments and the corresponding mixture models because they are fit and interpreted differently than the "classical" models. JMP can handle all of this, but the more knowledge you have, the better you will be able to use JMP.

---

Thank you. Are there jmp tutorials recarding "mixture-process designs and models"?

Jasmin

[#4]

As Dan suggests, it would help if you researched mixture designs.  The definitive author on mixture designs is Cornell (Cornell, John (1990) “Experiments with Mixtures, Designs, Models, and the Analysis” Wiley (ISBN:047152221X).  There are also many papers on the topic including one written by Dan (Tips on JMPing into Mixture Experimentation).  One Cornell paper "Embedding Mixture Experiments Inside Factorial Experiments", JQT, Vol. 22, No. 4, October 1990 may be useful.

There are also Mastering JMP tutorials as well:

https://community.jmp.com/t5/Mastering-JMP/Designing-Mixture-Experiments-Part-2/ta-p/549335

[#5]

Thank you for the extra information. Since you have ingredient D which is a filler, that implies that you are not interested in really "quantifying" it's effect. (Note: you don't really quantify effects in a mixture experiment. You can't say that increasing A will increase the response because increasing A will simultaneously decrease B, C, and D. This rules out "effects". Instead you are just interested in modeling the response.

If you treat D as a filler, then you can put the mixture ingredients A, B, and C as continuous factors with their ranges. This will take you out of the realm of mixtures. D would just "float" to complete the mixture. and not appear as a factor. Add all of the other factors as you have them right now and build the model that you want to estimate. Ingredient D will not appear anywhere, but that is okay since it is just a filler.

You may not want to do this. In some situations people really do want to see all of the mixture ingredients in the model, and/or not believe something is a filler. But if this works for you, then this would be the easiest approach for you to take. If this does not work for you, then you will be forced to treat this as a mixture-process design. @statman has pointed you towards Cornell's book, which is still the best book on mixture experimentation and includes a chapter on mixture-process designs. The JMP resources are also very good and very applied. At one time there was a JMP mixture course that you MIGHT be able to access that has a lesson on mixture-process designs. I'm not sure how you can access it, but you could start by contacting your JMP sales person to ask about it.