Computing Tolerance Intervals and Regions Using R

Tolerance intervals provide bounds on a specified proportion of the sampled population (P) with a given confidence level (γ). While they are, perhaps, less known than confidence and prediction intervals, there are some applications where tolerance intervals are commonly used, such as in quality control, setting engineering tolerances, and environmental monitoring. We present a general introduction to the topic followed by overviews of how to calculate tolerance intervals for some continuous and discrete distributions, nonparametric tolerance limits, tolerance intervals for regression settings, and multivariate normal tolerance regions. Calculating tolerance intervals and regions under these as well as other settings can be accomplished using the R package tolerance (Young, 2010). For the settings in our discussion, we present real-data examples and demonstrate how to calculate tolerance intervals and regions using the tolerance package.