49 factor dsd design

[#1]

When designing dsd with 49 factors and 4 additional runs. Why do I get 109 runs and not 105 runs?

[#2 · Accepted solution]

Hi @ConditionalRam9,

Are you designing your DSD only with numerical factors, or does it contain also categorical factors ?

If you're thinking about obtaining 105 runs, I guess you remember the rule of thumb : "If you have a k even number of continuous factors, you need 2k+1 runs, and if you have a k odd number of continuous factors, you need 2k+3 runs" ? In your case 2x49 + 3 + 4 extra runs = 105 runs ?

I see at least two reasons that may explain why you don't obtain this number :

• Presence of categorical factors : Having categorical factors in the design may augment the required number of runs. For example, if you have a categorical factor, instead of having a single centre point you may need two centre points, with all the continuous factors set to 0, and each of the two "centre" points set to one of the two levels of the categorical factors.
• Non-existence of a conference matrix of order 49 : DSD are built on conference matrices, which have to respect some conditions to be generated. In your case, there are no conference matrix of order 49, so JMP choose the next largest conference matrix (in this case, 52 is possible, and you'll find the rule of thumb seen before : 52x2 + 1 (even number of "factors" 52) + 4 (extra runs) = 109).

The combination of these two parts may explain your situation. You can find more info here : Structure of Definitive Screening Designs

I hope this answer will help you,

[#3]

I have a different question...how confident are you that you'll actually get the required treatment combinations during experimental execution? 49 factors, varying randomly between -1, 0, or 1 levels are alot to manage during experimental execution. In my day in industry we were lucky to get even 5 or 6 factor experiments to execute flawlessly. The housekeeping associated with managing 49 factors simultaneously during experimental conduct is going to be substantial.

[#4]

To add to Mr. Bartell's astute comments, and what will you do with noise?  Replication? Repeats?  I would suggest directed sampling as a filter prior to experimentation.  Or (my guess) this will be run in a simulation....which means the model already exists.