# Variation Tolerance

I came across a statement in my course book that 3$\sigma$ is considered as a means of tolerance. Can anyone explain it to me. I understand that +3$\sigma$ to -3$\sigma$ constitutes 99% of the samples. But how is tolerance related to this. Is it like a threshold we are putting on the sample's values.

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I assume that you are referring to statistical tolerance intervals. Tolerance intervals are like ocnfidence intervals on distributions. A 100(1-α)% tolerance interval is an interval at the 100(1-α)% confidence level includes a specified percentage of a probability distribution for a random variable. So for example a 95% coverage interval with 95% confidence is an interval that in repeated sampling would cover at least 95% of the distribution in 95% of the cases. The book Statistical Intervals by Hahn and Meeker provides excellent descriptions of the various type of statistical intervals and from it you can learn the difference between confidence intervals, tolerance intervals and prediction intervals.

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