topic Re: 2-sided equal tailed tolerance intervals for normal distribution in Statistical Procedures

2-sided equal tailed tolerance intervals for normal distribution

ScottNLong — Thu, 01 Jun 2023 15:22:18 GMT

Can someone tell me if SAS has a procedure to calculate two-sided tolerance intervals, based on sampling, for a normal distribution that contains the central p-content of that distribution for some given confidence?

These are different than the two-sided tolerance intervals that merely contain p-content of the distribution.

D. B. Owen (1964) "Control of Percentages in Both Tails of the Normal Distribution," Technometrics is a good reference, as is the Krishnamoorthy and Mathew (2009) text book Statistical Tolerance Regions (see Chapter 2, and Table B3 in appendix.)

Appreciate any help!

Re: 2-sided equal tailed tolerance intervals for normal distribution

sbxkoenk — Thu, 01 Jun 2023 17:21:01 GMT

Hello,

It's easiest with the CAPABILITY procedure in SAS/QC (QC = Quality Control).

SAS/QC User's Guide
The CAPABILITY Procedure
Methods for Computing Statistical Intervals

Search on that page with key-word "tolerance"!

https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/qcug/qcug_capability_sect210.htm

For a thorough discussion of tolerance intervals and tolerance limits, see Krishnamoorthy and Mathew (2009).

Koen

Re: 2-sided equal tailed tolerance intervals for normal distribution

ScottNLong — Thu, 01 Jun 2023 17:43:52 GMT

Thanks! However, your link and its particular Krishnmoorthy reference (sec. 2.3.1) identify the procedure for calculating the 2-sided tolerance interval that contains p-content without requiring it to be centered on the underlying normal distribution. I would like to find a procedure for the one in sec. 2.3.2 which requires the p-content to be centered on the underlying distribution.

Re: 2-sided equal tailed tolerance intervals for normal distribution

sbxkoenk — Thu, 01 Jun 2023 19:46:42 GMT

Is this post helping you out?

Question Related to Tolerance Intervals
Posted 04-30-2016 01:44 PM (2787 views)
https://communities.sas.com/t5/Statistical-Procedures/Question-Related-to-Tolerance-Intervals/m-p/267433

Koen

Re: 2-sided equal tailed tolerance intervals for normal distribution

ScottNLong — Thu, 01 Jun 2023 19:58:41 GMT

That post doesn't help me, but I did leave a suggestion for tackling the problem posted. I'm guessing SAS doesn't perform the calculation I'm looking for. I hope I'm wrong!