Chosing High and Low levels for DSD

Question

Hi,

I have carried out range finding to determine high and levles on a set of variables I want to test with a definitive screening design.

I have found for most of them, that that above a certian point there is a reduction in activity in the effect I am trying to measure. So lets say at '1' the variable produces a low response, at '10' a high response, and at '100' back down to a low response.

With a definitive screening design I have the ability to test 3 levels for each factor. I was wondering what the best strategy to find the true maxima of the complete system (12 variables).

So I was thinking my options are:

Set low to '1' and high to '10'  (with the axial point being 5) ensuring the variables are in the linear increasing range. However, I am worried that this may miss the true maxima which could arise from interactions with the other variables.

Or

Set low to '1' and high to '100' with the axial point being 10. Therfore, if there were positive interations that may necessetate the higher concentration beyond my original range finding, then would this way be more appropriate?

I would appreciate any thoughts on this!

Phil_Kay · Answer

Sorry, I am late to this discussion.

I have encountered this in the past from my time in the lab. We had catalyst concentration as a factor and wanted to experiment at levels of 1, 10, 100. We used a log scale to do this. log10(concentration) = 0, 1, 2. The good thing is that you can always back transform to get the factor back on the original scale.

Hope that helps.

Regards,
Phil

Peter_Bartell · Answer

I'll add my two cents to the good advice from my colleague @Bill_Worley.

If your real overarching discovery goal is to 'find the true maxima of the entire system'...then my thinking is to use what most call, sequential DOE, as your strategy. How this might look for you is to leverage the power of a DSD to help you find active main and 2 factor interactions following the stagewise analysis built into the Fit DSD platform. Once you've done that though, I'm thinking a second experiment to include only the active factors from the first DSD...and from there build this second design leveraging what you learn from the first. It sounds like you have a fair amount of curvature in the response, if that's discovered post DSD analysis...maybe take a look at JMP 14's new A - optimality capability? Lacking JMP 14, then I'm thinking an I - optimal design?

Bill_Worley · Answer

A rule of thumb I was taught many years ago is to "be as bold as possible within reason" when selecting your factor ranges for any DOE.  Based on what you describe in your post you will want to be bold enough to capture any potential curvature/quadratic effects in your process.

The DSD design is going to pick mid-points for your factors so unless I am missing something and you pick a range from 1 - 100 your mid-point will be 50 which may be too high to see what effect 10 would have.  If what happens at 10 is important to you and you still want to use DSD then you should pick a range that will capture 10 and in this case that would 1 - 20.

If you want to prescribe the factor levels at something like 1, 10 and 100 then I would suggest you use Custom Design and use Discrete Numeric 3-Level to set your levels.

HTH

Bill