Statistical Intervals, 2nd Edition

Chapter 9 Sample Size Requirements for Tolerance Intervals, Tolerance Bounds, and Related Demonstration Tests

Objectives and Overview

This chapter shows how to determine sample size requirements for tolerance intervals and for related demonstration tests concerning the proportion of product that exceeds (or is exceeded by) a specified value. This chapter explains sample size determination methods for:

• Normal distribution tolerance intervals and bounds (Section 9.1).
• A one-sided demonstration test based on normally distributed measurements to give a desired probability of successful demonstration (Section 9.2).
• Minimum sample size for distribution-free two-sided tolerance intervals and one-sided tolerance bounds (Section 9.3).
• Distribution-free two-sided tolerance intervals and one-sided distribution-free tolerance bounds with a specified amount of precision (Section 9.4).
• A one-sided demonstration test based on binomial data to give a desired probability of successful demonstration (Section 9.5).

9.1 Sample Size for Normal Distribution Tolerance Intervals and One-Sided Tolerance Bounds

This section provides simple methods for finding the sample size needed to achieve a specified level of precision when the data are to be used to compute a two-sided tolerance interval or a one-sided tolerance bound to contain at least a specified proportion of a sampled normal distribution. As the sample size increases, the computed tolerance interval will approach the probability interval ...