Weibull distribution: solving for a "pooled" Weibull beta?

[#1]

Previously there was a thread on fixing the Weibull beta as well as the p-factor in a Defective Subpopulation analysis.

https://community.jmp.com/t5/Discussions/Life-Distribution-Fixing-p-and-fixing-Weibull-beta-in-DS-We...

I have 3 "flavors" of the same population but with different stress conditions. Theoretically if we have the same failure mechanism then the Weibull beta should be the same for all 3 datasets with only the failure rate and the Weibull alpha differing.  Based on interval spacing and other factors, the Weibull beta on the JMP regression can change +/- 20%.

With the link above, I read how I can constrain the Weibull beta and then resolve for the Weibull alpha.  That's great but what to set the beta to?

Does JMP give the capability with the Life Distribution analysis and the "by" filter to solve 2 different datasets but to converge on 1 Weibull beta slope?

[#2]

There aren't 3 "flavors". It's 3 random groups from the same population. Poorly worded...

[#3]

You fix the shape parameter based on historical evidence and the belief that the current population has the same shape parameter. You use a historical estimate for the shape parameter.

You might want to test the assumption with the three samples ('flavors,' 'groups') using the Life Distribution platform. Select the Compare Groups tab before casting your data columns into analysis roles.