2
$\begingroup$

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?

$\endgroup$
2
$\begingroup$

Close: 59 is the smallest sample size for which observing no defects would allow you to reject (at a significance level of 5%) the hypothesis that 95% or less of the production run is compliant. So if you test 59 devices and none of them fail, the one-sided 95% confidence interval for the proportion compliant over the run does not include values of 95% or lower. The assumption is that the number of defects has a binomial distribution - reasonable if defects occur independently at a constant probability over each run, & if the sample is a small fraction of the total run.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Yes - of course - that makes sense. Thanks for your rapid reply. $\endgroup$ – PJP Jul 3 '13 at 13:17
  • $\begingroup$ 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 $\frac{3}{p}$. $\endgroup$ – Scortchi - Reinstate Monica Jul 3 '13 at 13:52
  • $\begingroup$ Neat! But why use my head when I can use R ? ;-) $\endgroup$ – PJP Jul 5 '13 at 8:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.