| Description |
ToleranceFactor computes the exact tolerance factor k for the two-sided (optionally also for the one-sided) p-content and gamma-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 from the distribution N(mu,sig2) with unknown mean mu and variance sig2.
The value of the tolerance factor k is determined such that the tolerance intervals with the confidence gamma 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 ]= gamma,
for X ~ N(mu,sig2) which is independent with Xmean and S. For more details see e.g. Krishnamoorthy and Mathew (2009).
Syntax:
k = ToleranceFactor(n,coverage,confidence)
[k,options] = ToleranceFactor(n,coverage,confidence)
or
k = ToleranceFactor(n,coverage,confidence,options)
References:
Krishnamoorthy K., Mathew T.: Statistical Tolerance Regions: Theory, Applications, and Computation. Wiley, ISBN: 978-0-470-38026-0, 512 pages, May 2009.
ISO 16269-6:2005: Statistical interpretation of data - Part 6: Determination of statistical tolerance intervals.
Janiga I., Garaj I.: Two-sided tolerance limits of normal distributions with unknown means and unknown common variability. MEASUREMENT SCIENCE REVIEW, Volume 3, Section 1, 2003, 75-78.
Viktor Witkovsky
Institute of Mesaurement Science
Slovak Academy of Sciences
Dubravska cesta 9
84104 Bratislava
Slovak Republic
E-mail: witkovsky@savba.sk
http://www.um.sav.sk/en/department-03/viktor-witkovsky.html |
