DOE for a single component with different sources & levels

[#1]

I am trying to optimize the maltodextrin component of a formulation. There are 3 different maltodextrins I would like to assess (different suppliers - categorical), and I would like to run each at 3 concentrations/levels.

It doesn't make sense to put the 3 different maltodextrin options as different factors, because they will never be used together - the idea is to choose the best one. I could do 3 separate one-factor DOEs, but this seems inefficient. 

Is there a good design to simultaneously assess which maltodextrin is the best and which concentration is the best?

Thanks!

[#2]

@thaumi .  Welcome to the JMP community.  There are multiple options to achieve what you may want.  Just to make sure, you are not interested in understanding causal structure, you are just trying to "pick the winner", correct.  I can offer some of my thoughts/questions, but I admit I'm a devout determinist, so I apologize in advance:

1. If you are trying to determine which supplier is the best, I'm not sure DOE would be my recommended data collection strategy.  Why, because I'm not sure how you would represent the supplier as a "level" with the likely within supplier variation.  I might suggest a nested sampling plan where you take multiple samples of multiple concentrations and maybe even nest a layer for measurement precision.

2. How confident are you in the measurement system? 

3. Are the concentrations the same for all suppliers?

4. How many samples of "materials" would you need to have a degree of confidence that those samples represent the variability in the processes?

[#3]

@statman raises some good points for you to consider. I was probably being too naive (or assuming too much), but your problem description led me to think you had two factors. One is Supplier, which is a 3-level categorical variable. The other factor is Concentration which should probably be continuous (you only specify the number of levels based on the model you want to fit -- quadratic effects require 3 levels). Given this, I thought the model would be: Supplier, Concentration, Supplier*Concentration, Concentration*Concentration and MAYBE Supplier*Concentration*Concentration.

There are LOTS of assumptions in my thinking, so please be very thoughtful about what you are trying to do and why. Thinking about and answering @statman's questions will certainly help you out.

[#4]

Hi @statman. Thanks for your quick & thoughtful response. Yes, I am just trying to pick a winner as opposed to determining causality.

1) I don't believe that within-supplier variability is actually a major concern in this case. This experiment will use highly purified chemicals that come with CoAs certifying lot dextrose equivalents (DE), which is the actual parameter we care about between suppliers. We know from past work there is very low variation surrounding these dextrose equivalents between different lots from the same supplier. But yes, I am also not sure if a DOE is the correct approach here, which is the reason for my question

2) We have well-established and robust measurement systems with low variability and have quantified and assessed these in the past - again, not a major concern for us in this case. 

3) The maltodextrin itself is "pure" regardless of supplier, but as mentioned above, they will have different DE values. The plan is to dissolve different amounts of each type to different concentrations, and ultimately to assess both source & concentration on our final product. 

4) Good question. Typically for a non-DOE experiment, we will process things in triplicate, and as long as our variation is low, leave it at this. Obviously with DOEs this is not always the case. But as mentioned above, I am not that concerned about a high level of within-source variability.

Thanks again for your time!

[#5]

I won't argue with the CoA and how they sample the material to obtain this, but doesn't the CoA list an actual DE value? And isn't that value from a continuous measurement scale?
In this case, why not make the factors DE and Concentration. It seems that both are actually continuous variables and it would be nice to know the best combination? This could be modeled if you ran a 3^2 factorial. Otherwise you could optimize concentration within each DE value and then compare those "best" conditions from each DE.

[#6]

To add a couple additional questions/thoughts to supplement @Dan_Obermiller and @statman 's thoughts...and harkening back to my days as a supplier quality manager...there are many non-statistical criteria that go into supplier selection especially when you say you are looking for the 'best'...whatever that means...

1. Cost (price).

2. Long term variation from a quality/composition point of view.

3. Lead time. This is important if one of your organization's goals are minimizing work in process inventory, single piece flow process design, and just general good Lean practices.

4. Minimum order quantity restrictions?

5. On time delivery performance.

6. Confidence/risk in assured supply. For example...in this COVID world...will the supplier have to shut down for pandemic reasons?

My experience unfortunately was that the criteria above almost always overwhelmed whatever engineering/scientific recommendations that were learned or observed in performance testing/evaluation. I hope your organization is different?

[#7]

@P_Bartell thank you for these points - definitely all important considerations. 

In this case, I am trying to look at differences caused by a characteristic of the maltodextrin itself (the dextrose equivalents/DE). It's hugely important to a few different aspects of our process (and, as you mentioned below - there are many different outcomes to balance). I just said "different suppliers" as a shorthand to indicate categorical levels (because different suppliers do make the different DE products), but  think I learned a lesson in this post about trying to simplify things but making them more complicated as a result.

I appreciate the input!