ToleranceFactor

Institute of Measurement Science SAS - ToleranceFactor computes the exact tolerance factor for the two-sided tolerance interval

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.

SYNTAX:

k = ToleranceFactor(n,coverage,confidence)

k = ToleranceFactor(n,coverage,confidence,m,nu,d2,options)

k = ToleranceFactor(n,coverage,confidence,[],[],[],options)

REFERENCES:

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:// ajs.data-analysis.at/index.php/ajs/article/viewFile/vol43-4-6/35

ISO 16269-6:2013: Statistical interpretation of data - Part 6: Determination of statistical tolerance intervals. https://www.iso.org/standard/57191.html