A Simple Approximate Procedure for Constructing Binomial and Poisson Tolerance Intervals

• Activity Number: 88
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
• Sponsor: Section on Quality and Productivity
• Author(s): Yanping Xia*+ and Kalimuthu Krishnamoorthy
• Companies: Southeast Missouri State University and University of Louisiana at Lafayette
• Keywords: Coverage probability ; Clopper-Pearson Confidence Interval ; Score Interval ; Equal-tailed tolerance interval ; Expected widths

Abstract

The problems of constructing tolerance intervals for the binomial and Poisson distributions are considered. Closed form approximate equal-tailed tolerance intervals for both distributions are proposed. Exact coverage probabilities and expected widths of the proposed equal-tailed tolerance intervals and the existing ones are evaluated. An adjustment to the nominal confidence levels is suggested so that an equal-tailed tolerance interval can be used as a tolerance interval. Comparison of such coverage adjusted tolerance intervals with respect to coverage probabilities and expected widths indicates that the closed form approximate tolerance intervals are comparable with others, and less conservative with minimum coverage probabilities close to the nominal level in most cases. The approximate tolerance intervals are easy to compute, and they can be recommended for practical applications.