Computing statistical tolerance intervals in JMP

[#1]

Hi,

I am looking into the calculation of one-sided tolerance intervals. Searching the documentation, I found the following paragraph:

 

Now, please correct me if I am wrong, but as I understand it:

• s is the standard deviation of the data samples
• is the sample mean
• n is the number of samples
• 1-α is the confidence
• t is the noncentral t inverse cumulative distribution function
• and finally  is the inverse cumulative normal distribution

The reason I am asking is that I am having difficulties recreating the tolerance interval calculated by this method in matlab. Please let me know if there is something here that I got wtong. Thank you.

[#2 · Accepted solution]

It looks like you have it correct; for the one-sided case, g' can be calculated exactly (as shown in the documentation). For the two sided case, however, a variety of approximations are available and some are better than others. But, be warned, it is not the case that two one-sided tolerance intervals (lower and upper, respectively, each at 1-alpha/2 confidence) gives the same interval as a two-sided tolerance interval at 1-alpha confidence.