@faustoG
You seem intent on complaining about the JMP Student Edition. I'm not sure why, but I don't think it is productive. No software claims to do everything you want. In any case, your points 2-4 all pertain to control limits. I agree with point 4 - the usual control limits are set on the basis of a normal distribution - but there is the opportunity to override these based on some other distribution or other considerations. I still think it is important to distinguish between control limits (a property of the data) and specification limits (a property of the problem). In the case of medical issues (such as you have here), I would put more emphasis on the specification limits. A process could well be in control yet hazardous to your health.
By the way, if it JMP's difficulty dealing with your specific data that you have problems with, you can always try to find a Python or R program that suits your purpose and run that within JMP. Specialized methods are generally more available in R, given the relatively larger user base among statisticians. And, if you can specify the exact problem you are trying to solve that JMP does not have the built in capability for, you can often get someone willing to write a script to accomplish what you need - I have used the Community this way in the past.
I did find this recent article that you might be interested in: https://www.tandfonline.com/doi/full/10.1080/08839514.2024.2322362#d1e4814. I haven't examined it in detail, but it appears to be a kind of hybrid of control and specification limits - at least that is my high level attempt to interpret this. Inclusion of economic parameters seems like a way to introduce meaning into the control limits rather than just relying on a statistical calculation based on the data. If anybody can digest this paper, please confirm (or refute) this, and expand the interpretation if possible.