Sample size determination strategies for normal tolerance intervals using historical data

Statistical tolerance intervals are often used during design verification or process validation in diverse applications, such as the manufacturing of medical devices, the construction of nuclear reactors, and the development of protective armor for the military. Like other statistical problems, the determination of a minimum required sample size when using tolerance intervals commonly arises. Under the Faulkenberry-Weeks approach for sample size determination of parametric tolerance intervals, the user must specify two quantities—typically set to rule-of-thumb values—that characterize the desired precision of the tolerance interval. Practical applications of sample size determination for tolerance intervals often have historical data that one expects to closely follow the distribution of the future data to be collected. Moreover, such data are typically required to meet specification limits. We provide a strategy for specifying the precision quantities in the Faulkenberry-Weeks approach that utilizes both historical data and the required specification limits. Our strategy is motivated by a sampling plan problem for the manufacturing of a certain medical device that requires calculation of normal tolerance intervals. Both classical and Bayesian normal tolerance intervals are considered. Additional numerical studies are provided to demonstrate the general applicability of our strategy for setting the precision quantities.