Exact algorithm for computing two-sided statistical tolerance intervals under a normal distribution assumption using Python.
NOTE: This repository exists for historical purposes only. The code has been integrated into the tolerance_interval_py project, and all future maintenance to the code will happen under that project.
The function tolerance_factor computes (by Gauss-Kronod quadrature)
the exact tolerance factor k for the
two-sided coverage-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 algorithm is a Python port of the MATLAB algorithm ToleranceFactor, contributed to the MATLAB Central File Exchange by Viktor Witkovsky. The port attempts to preserve the basic function structure of the algorithm so comparisons back against the MATLAB code are easier to conduct.
For more details on statistical tolerance intervals the technical background on how to compute them, see the following 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.
- Meeker, William Q.; Hahn, Gerald J.; Escobar, Luis A.. Statistical Intervals: A Guide for Practitioners and Researchers (Wiley Series in Probability and Statistics). Wiley.
- 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 16269-6:2014: 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.
The notebook example.ipynb provides a very brief application example.
The file environment.yml can be used to produce a conda environment suitable
for running the example notebook and the unit tests.
The algorithm accurately reproduces tables of two-sided normal tolerance interval factors from standard sources, including the complete set of tables in ISO 16269-6:2014 Annex F. The unit tests included here represent a sampling of that reproduction for brevity.
To run all the unit tests, invoke the following:
python -m unittest discover -v
MIT License