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Fitting of the parameters of non-linear regression<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />

I can fit the data with non-linear function, namely Mechanistic Growth curve from the JMP library. See the example of the fit in the next figure. The fit equation is BA = a(1 - b e^{-c *PA}).

BA represents a parameter within sheet metal forming domain. I also now that this fit depends on the three parameters: P₁ - tooling dimension, P₂ - tooling dimension, and P₃ - plate thickness. Is it possible to couple the parameters of the fit curve (a, b, and c) and (P₁, P₂, and P₃)? I want to have equation in a form of BA = a(P₁, P₂, P₃)(1 - b(P₁, P₂, P₃) exp^{-c(P₁, P₂, P₃)*PA}).

What I've done so far is, I obtained the a, b, and c for every possible combination of P₁, P₂, and P₃. P₁, P₂, and P₃ are not nominal parameters, however I've done full factorial analysis for all available tooling dimensions and thicknesses.

I don't see where I should go further. Is there a way to obtain this kind of equation or during the non-linear fit or after obtainment of parameters?

Thanks in advance for your help.

Re: Fitting of the parameters of non-linear regression

Just a follow up to my previous comment.  

 

Susan Walsh did a paper on this (link) that goes through the platform in deep detail. 

Re: Fitting of the parameters of non-linear regression

Hi!  Since you know the relationships you could do this by doing a custom model in the nonlinear platform.  Setting up a custom equation is covered in Chapter 7 of the "Specialized Models" book found under Help > Books > Specialized Models.

Best,

M