Approximations of tolerance intervals for normally distributed data

Tolerance intervals are lesser known relatives of confidence and prediction intervals. They can be very useful in many situations to make product or process quality assessments. Even for normally distributed data, their calculation is less trivial than confidence and prediction intervals, which makes them underutilized in practice. In addition, they are not always readily available in statistical software packages. As a result, there have been several approximate methods proposed in the literature to calculate them. After a review of tolerance intervals and their variations, we investigate those approximations and compare them with the exact values for one‐sided and two‐sided intervals. We first propose a modification of an approximation for a one‐sided interval. Then we propose new approximations for two‐sided intervals based on Bonferroni's Inequality. We find that these approximations are extremely satisfactory for practical applications. Copyright © 2008 John Wiley & Sons, Ltd.