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Pure Categorical Factor DOE

Hi,

 

a customer has the following situation. It's about removing cells from a cell culture with filters to gain the liwuid rest only. Every charge has 4 filter positions, and three filter types can be positioned on those four places. The responses are the yield of the product (max.), and to minimize two kinds of pollutions which should be hold back by the filters. The product itself also is partly held back by the filters.

 

The question is now: What filters or filter combinations will provide max yield and min pollution?

 

The DOE has to be run in a production scenario. The filter setting can be changed from charge to charge but not within. As they do not want to risk too much waste all positions with the same filter type need to be avoided.

 

DOE(
 Custom Design,
 {Add Response( Maximize, "Mean Product", ., ., . ),
 Add Response( Minimize, "Pollution 1", ., ., . ),
 Add Response( Minimize, "Pollution 2", ., ., . ),
 Add Factor( Categorical, {"A", "B", "C"}, "X1", 0 ),
 Add Factor( Categorical, {"A", "B", "C"}, "X2", 0 ),
 Add Factor( Categorical, {"A", "B", "C"}, "X3", 0 ),
 Add Factor( Categorical, {"A", "B", "C"}, "X4", 0 ), Set Random Seed( 23936913 ),
 Number of Starts( 27053 ), Add Term( {1, 0} ), Add Term( {1, 1} ),
 Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
 Set Sample Size( 12 ), Disallowed Combinations(
  X1 == 1 & X2 == 1 & X3 == 1 & X4 == 1 | X1 == 2 & X2 == 2 & X3 == 2 & X4 ==
  2 | X1 == 3 & X2 == 3 & X3 == 3 & X4 == 3
 ), Make Design}
);

This was my first attemp.

 

Q: As filter combinations are present, I'd like t add interaction terms, but fear the increasing number of runs (Mainly because of the fact that one run means one produced charge, and if we add all interactions we have >30 runs. This probably is too many for the customer). Any comments on decreasing the number of runs in such a situation (even below the recommended number of 12 runs) from your experiences (from a estimation quality  point of view it's clear to me)?

 

I also saw a paper presentation by Silvio talking about exchanging categorical factors by (continuous) chemical properties, which might be a solution for better results. Any other ideas?

Thanks,

Martin

Re: Pure Categorical Factor DOEHi Martin,
The design looks good to me. None of the main effects or 2-factor interactions are confounded. So you could estimate a subset of any of them. But you will be limited by the number of runs you have.
I don't think there are any shortcuts here. If interactions are likely to be important, they will have to design an experiment that tests that.
They might want to try adding interactions as "If possible" effects in the model.
A sequential approach might be a good idea. E.g. you might find from a screening experiment that the type of the first filter has no effect. Then you can augment just on the other 3 factors. Or you might find that nothing comes out as significant in your screening design, in which case you have avoided wasting a lot of time on a big experiment.
I think that the approach Silvio used was in a situation of having a categorical factor with a large number of levels (e.g. different discrete chemical entities) and replacing with a number of continuous descriptor factors (molecular weight, boiling point etc...). That is not really the case here.
You could tell the customer that if they wanted to test all of the possible combinations, that would be 3^4 = 81 runs. Compared to that, 30 runs doesn't sound so bad!
Cheers,
Phil