Hello @YanivD ,

Please find below my thoughts:

Generically, in an attempt to better understand the relationship amongst the factors, usually I would go with a sequential design of experiment approach, using at the beginning 2-level fractional factorial designs with "bold" (most apart as possible) level settings and tight control of the experimental noise (using different noise strategies, such as randomization, mapping noise factors, holding them constant or even better using them as factors, etc) in order to surface the vital few effects and then using them to progress with the experimentation.

If you are not close to you objective, to save some runs I would start with foldover designs, Res III, to understand the effects size for each factor and their interactions than once you are satisfied with the variation generated in the response you can foldover the design to increase the resolution and start dealing with the confoundings, screening out the non active factors and interactions, then move on with your inference space towards the optimal point. At the very beginning I would not run replicates, instead I would screen out the factors based on the sparsity of effects, using Daniel plots, to understand about the statistical significance and once you are close to your objective (with much fewer factors to deal with) you can use RSM methods to better model the surface near the optimum point, replicates to improve predictions, etc

Now, about your case, could you please provide more info, are those 10 suppliers supplying the same product and you need to choose one of them? Do you know whether the process factors and its noise would impact the performance of each supplier? Do you know if there is any quantity that could help you predict if a supplier would be better than the other? (this would help to reduce the amount of suppliers to test)

Considering each supplier as a block, I would run a fractional factorial design, including the concentration as a design factor, process factors and already mapped noise as factors following the same strategy mentioned above instead of a one factor experiment for each of the suppliers (blocks) and including replicates, however this is up to you given the cost of each run and the information you already have (at the end this strategy may also needs a lot of runs due to the replication)

Once you run the first fractional factorial design for the first block, you might be able to tell the important effects and they would make sense for the other blocks, you can use this knowledge to refine the experiment for the other blocks.

The block with the factorial designs including the process factors might not sound like the strategy with the minimum number of runs, however I believe it is going to help you build a solid knowledge foundation about your process factors and their interaction with the supplier material.

Please let me know if you would like to further discuss the topic,

Sincerely,

Yours truly,

Emmanuel

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Keep It Simple and Sequential