tolerance: Statistical Tolerance Intervals and Regions

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The tolerance package provides functions for estimating tolerance limits (intervals) for various univariate distributions, Bayesian normal tolerance limits, multivariate normal tolerance regions, nonparametric tolerance intervals, tolerance bands for regression settings, and analysis of variance tolerance intervals. Visualizations in the form of histograms, scatterplots, and control charts are also available for many of these settings. More details about the package are included in both the original JSS article as well as a subsequent Handbook of Statistics book chapter.

Other highlights:


The JSS article and the Handbook of Statistics book chapter both provide documentation about the tolerance package. The RJ article provides an extensive overview of most of the normal-based procedures available within the tolerance package. Moreover, the help file also documents the references used for each function.


Additional examples for the tolerance package are currently being developed for a Shiny app.


Released and tested versions of tolerance are available via the CRAN network, and can be installed from within R via



The issue tickets at the GitHub repo are the primary bug reporting interface. As with the other web resources, previous issues can be searched as well.


Derek S. Young


GPL (>= 2)

Funding Acknowledgment

This package is based upon work supported by the Chan Zuckerberg Initiative, Grant Number 2020-225193.

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