# One sided dist-free tolerance intervals and testing

I am involved in writing a standard where test labs are trying to decide sample sizes for a new device.

The suggestion has been that using ISO 16269-6: Table F.1 ("sample size for a proportion p at confidence level $1-\alpha$") that selecting $1-\alpha=0.95$ and $p=0.95$, giving a sample size of 59. You can do the calculation with the 'tolerance' package:

distfree.est(alpha=0.05,P=0.95,side=1)


Am I correct in my interpretation of this - that if we test 59 devices and none of them fail, that gives us confidence (at a 0.05 level) that 95% of the production run is compliant?

• Note that, if you want to do the sums in your head instead of in R, for 95% confidence intervals only, the required sample size is well approximated as $\frac{3}{p}$. – Scortchi - Reinstate Monica Jul 3 '13 at 13:52