Custom DOE design with Blocking

[#1]

Dear JMP community,

I am planning my first custom DOE and ran into a point I cannot solve at the moment.

Lot 1 has 20 wafers of Type A

Lot 2 has 20 wafers of Type B

I cannot change the composition of those lots anymore.

Then I have 6 continuous factors (and three main responses). I could reduce to 5 if necessary.

If I add the starting material as a categorical variable with 2 levels, a RSM model suggests 35 minimum runs. I could increase to 40 runs in total, making use of all wafers. 

But while I was writing this it struck me:

I could add the catergorical variable as a block with 20 runs per block... actually this is the only solution, am I correct?

How does the blocking now work: will I lose information about the effect between type A and type B wafers? I am expecting a difference in the outcome.

Thanks!

[#2]

Why don't you run the 40 runs completely randomized? And if you need to run your design in blocks you can do that with your 40 runs split into "how many blocks you want".
But I don't see the need for any blocking at all. Why do you think you have to build blocks?
You're right, if you run the whole experiment in two blocks and block 1 contains all runs with wafers type A and the other block is wafer type B, you loose information because the difference in A- and B-wafers is confounded with the block effect.

Andrea

[#3 · Accepted solution]

Do you expect the two lots to be the same or different? If you expect them to be the same, then you can follow Andrea's recommendation to use the 40 wafers as randomized experimental units. If you expect them to be different, then add Lot as a blocking factor of size 20.

If the lots are expected to be different because of known differences in composition, you can set up a data table with the composition values and then enter these variables as Covariate factors instead of blocking.

When you ask about the effect of Type A versus B, were these lots intentionally varied in some way? That would produce a fixed effect. Otherwise, as a block, Lot would be a random effect.

[#4]

Thanks for the input Andrea and Mark.

I cannot change the lot composition anymore, because the wafers are in the factory and physically laser marked already. Mixing them up would cause numerous errors on various tools that try to read the inscription. That's why I am unfortunately forced to keep them as they are.

The material has a different resistivity and I expect a significant impact. I have enough space to add some comparison wafers that are processed exactly the same way on both lots. I will use those results as input for the covariate factors, thanks!