create multi-factor DOE for nonlinear response

Question

Hello, I wonder if anyone has advice for how to create a multi-factor DOE for a nonlinear response. The chemist I'm working with says he wants to model an exponential growth curve with an upper asymptote, as pictured below.  It looks to me like a 3-paramter exponential could be appropriate.

How can I use JMP to create such a design?  Details below.  Thanks, Paul

He wants to compare two experimental factors, and there is one blocking factor.

Factor 1: Water - Customer vs. Synthetic

Factor 2: Additives:

HEDPPAAHPMA

Blocking: 2 sets of test equipment

Mark_Bailey · Answer

I would use the example above to create a JMP data table. Then select Analyze > Specialized Modeling > Fit Curve. Enter the data columns for the Y and X analysis roles and click OK. Click the red triangle and select the exponential model that they want to use. Use these estimates as guesses in the Nonlinear Design.

paulp · Answer

Thanks, Mark, that was helpful.  I think I came across a the key text "have a guess for the unknown parameters".  The researcher claims to not be able to predict anything more than the rough shape of the response.  There's also a language barrier, so trying to clarify almost anything has been tough.

I was hoping to get lucky and find something applicable to a 'generic' 3P exponential. I had seen in an earlier post that there needed to be as many experimental points as there were parameters.  For example, a 3 parameter exponential growth would need 3 settings along the X-axis.

A further complication is the growth curve's X-axis factor (chemistry concentration, which I neglected to list initially).  The concentrations are expected to be different for each chemistry, because one of the chemistries is expected to be 2x as active as the other.   And the 3rd chemistry is stronger still, therefore the asymptotes will begin in greatly different regions of  concentration.

Thanks for making things clearer.  regards, Paul

Mark_Bailey · Answer

Please read this explanation first and then return with questions.