Computation of the sample size and coverage for guaranteed-coverage nonnormal tolerance intervals
We propose Monte Carlo algorithms to estimate the sample size and coverage of guaranteed-coverage tolerance intervals for nonnormal distributions. The current literature focuses on computation of the tolerance factor, but addresses less on the sample size, coverage, and confidence, which need to be set prior to the tolerance factor. The coverage estimation algorithm, which always converges, is based on our proof that the coverage is a quantile of an observable random variable. The sample-size estimation algorithm, which seems to converge in empirical results if the root is unique, is based on the general stochastic root-finding algorithm, retrospective approximation. Following previous sensitivity analysis for the tolerance factor, we analyze relationships among the sample size, coverage, and confidence.
quantile retrospective approximation reliability stochastic root finding