Need to calculate tolerance Intervals with a set of non-normal data and 3-Parameter Weibull distribution

@Bev: They are going to qualify some process using a (reliability, confidence)-pair.

@randwick: You are trying to demonstrate/proof that your process meets some predefined goal. Therefore, I would argue that your are not allowed to omit the uncertainty of the threshold parameter of the distribution. Have you checked the tolerance interval of the non-parametric method? How many samples do you analyse?

This reminds me on a statement -- I believe it was Michel Baudin who said that statistics is used in the semiconductor industry, because these methods provide the correct answers, and it is used by people in the medical device industry, because they are told to do so by FDA.

@Semoi - I didn’t see that the OP was doing the work for his Customer regarding validation in the OP’s responses…none the less this old answer what the OP is doing with the results of such a calculation. It is not an answer to what kind prompted the use of this calculation.

I would also be concerned that if they are in fact submitting this analysis to “the FDA” or other regulatory body that they are not:
1) a degreed statistician who would know how to do this
2) trying to do this in MINITAB and not SAS or R as required by the FDA or USDA for certain medical devices, vaccines, pharmaceuticals, diagnostic tests, etc. FDA and USDA only accept EXCEL, Minitab, JMP for low risk things…

A Customer asking their supplier who does an internet search? If they aren’t familiar with how to perform the calculation(s) properly, how do we know they are trying to perform the correct calculation in the fist place? Again no offense to the second OP - they should be asking if they don’t how to do this - but perhaps the best help we can give them is to verify that this calculation is the correct one and then we will also know if uncertainty calculations are needed or not…

@Bev D: I fully agree that now it's time for the OPs to provide their input. However, as a side remark, I currently work on a class III medical product and we qualify all our processes via Minitab. Of course the clinical studies are setup and analysed by professional statisticians. However, if the processes are not working as advertised/qualified the analysis of the professionals will surly suffer, because their basic assumptions are not satisfied.

Up till now everybody (including a trainer for validation) told me that every software is fine for process qualifications as long as we ensure that it is working as expected (method qualification). Thus, I am very interested in the source of your information that Minitab, Excel, and JPM is only for "low risk" processes while SAS and R are generally accepted. Note that I'm not talking about the evaluation of clinical trials, but about process qualifications. After all, I suspect that this question is about a process qualification.

Sorry to clarify: I was intending to speak about product validation or verification as USDA refers to it. Label claim and Clinical trials included…. I do know that certain diagnostic instruments that are not definitive in diagnoses are exempt Heck the FDA even accepts RPN values and Cpk values