Heuristic rationalization to not worry about normality assumption if data is far from spec?

[amcoope3]

Are there any academic references I can use that rationalize or justify doing normal tolerance interval testing on data that is non-normal but where the mean is say 8-10 standard deviations away from spec? I understand by tolerance interval bounds may be over or under-inflated but it doesnt really matter if my data is so far from spec.

It makes practical sense to me that I don't really care about normality assumptions if I am so far from specifications but I need academic reference as armor in my statistical procedures to justify this shortcut. Any journal articles or academic references are okay (NIST is good example). But references to forums, wikipedia, etc would not be solid enough. Let me know if you have anything.

 

[Miner]

Why not use non-normal or nonparametric tolerance intervals?

 

[amcoope3]

I’m looking for a path when there is no good fit for any distribution and getting high sample size to do non parametric tolerance intervals to achieve a certain confidence is too high of a burden. Most of the time we can do what you suggest but I wanted to provide another option if normality, best fit of alternative distributions, and non-parametric don’t meet our needs