I think you are referring to this dataset, with several samples (several Y for the same X values) ? : https://community.jmp.com/t5/Discussions/How-to-obtain-the-optimum-formulation/m-p/762444#M94169
If you have identified the samples in your datatable, you can use the Nonlinear platform and use your sample ID in the "By" variable to fit the piecewise equation to each sample independently. You can press CTRL + click on "Go" to launch the estimation of parameters for all samples independently and simultaneously.
Then you can aggregate the parameters values (right-click in the panel "Solution" on the table with the parameters estimates, and click on "Make Combined Data Table"), compare them, and link/analyze them vs. your factor variable (for example by updating the generated table with the V/B ratio, splitting the data table by parameters and analyzing the correlations between the parameters values and the V/B ratio) :
I attach the dataset so that you can test and see the steps used in my response,
Victor GUILLER
L'Oréal Data & Analytics
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)