image thumbnail


version (483 KB) by Viktor Witkovsky
Institute of Measurement Science SAS - ToleranceFactor computes the exact tolerance factor for the two-sided tolerance interval


Updated 20 Nov 2020

View License

ToleranceFactor computes the exact tolerance factor k for the two-sided (optionally for the one-sided) p-content and (1-alpha)-confidence tolerance interval TI = [Xmean - k * S, Xmean + k * S], where Xmean = mean(X), S = std(X), X = [X_1,...,X_n] is a random sample of size n from the distribution N(mu,sig2) with unknown mean mu and variance sig2.
The tolerance factor k is determined such that the tolerance intervals with the confidence (1-alpha) cover at least the fraction p ('coverage') of the distribution N(mu,sigma^2), i.e.
Prob[ Prob( Xmean - k * S < X < Xmean + k * S ) >= p ]= 1-alpha, for X ~ N(mu,sig2) which is independent with Xmean and S.
k = ToleranceFactor(n,coverage,confidence)
k = ToleranceFactor(n,coverage,confidence,m,nu,d2,options)
k = ToleranceFactor(n,coverage,confidence,[],[],[],options)


Krishnamoorthy K, Mathew T. (2009). Statistical Tolerance Regions: Theory, Applications, and Computation. John Wiley & Sons, Inc., Hoboken, New Jersey. ISBN: 978-0-470-38026-0, 512 pages.

Witkovsky V. On the exact two-sided tolerance intervals for univariate normal distribution and linear regression. Austrian Journal of Statistics 43(4), 2014, 279-92. http://

ISO 16269-6:2013: Statistical interpretation of data - Part 6: Determination of statistical tolerance intervals.

Cite As

Viktor Witkovsky (2021). ToleranceFactor (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2017b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: NCTCDFVW

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!