Tolerance intervals method

[#1]

Dear sir/Madam,
As we know that is only have two available methods are Assume Normal Distribution and Nonparametric from tolerance intervals module, If I have 30 samples data that using Fitted Weibull/lognormal distribution and the P-value is >0.05. How do we using Tolerance interval for Weibull and lognormal distribution?

[#2]

Hi @SengYew : If your data are Lognormal, then the natural log of the data will be normally distributed.

1. If X is your data, calculate Y=ln(X): Y has a normal distribution.

2. Get the desired Normal Tolerance Interval for Y.

3. Back transform the interval ( exp[lower TI], exp[upper TI] ) to get the Tolerance interval back on the original X scale.

Weibull? Not so straightforward I'm afraid:  

See the following: Lawless, J. F. (1975). Construction of tolerance bounds for the extreme-value and the Weibull distribution. Technometrics, 17, 255—261.