One-sided nonparametric tolerance limits

Abstract

It is well known that a single order statistic can sometimes be used as a one-sided nonparametric tolerance limit. Unfortunately, there are often minimum sample sizes below which these single-order-statistic limits do not exist. Also, the number of confidence levels for exact limits is equal to the sample size, and this can lead to further conservatism for small samples. This article presents one-sided nonparametric tolerance limits, based on two or more order statistics, which do not have these limitations. These limits are an extension of the work of Hanson and Koopmans (1964) on conservative one-sided tolerance limits for large classes of distribution functions. The extensions include greatly improved algorithms for determining the constants required by the tolerance limits, and a generalization to more than two order statistics.

Keywords:

• increasing failure rate
• log-convex
• Hanson-Koopmans

^*This Work Was Completed While The Author Was At The Army Research Laboratory, Materials Directorate, In Watertown, Massachusetts

^*This Work Was Completed While The Author Was At The Army Research Laboratory, Materials Directorate, In Watertown, Massachusetts

Notes

^*This Work Was Completed While The Author Was At The Army Research Laboratory, Materials Directorate, In Watertown, Massachusetts