Content‐adjusted tolerance intervals via bootstrap calibration

Abstract

Tolerance intervals (TIs) are commonly employed in numerous industries, ranging from engineering to pharmaceuticals. However, closed‐form TIs are unavailable for most distributions. Although some approximate methods can be used to obtain TIs, coverage probabilities (CPs) of these TIs cannot achieve the nominal level, or can be even far different from the nominal level. In this study, we propose two content‐adjusted procedures for TIs based on bootstrap. The first one is based on the bootstrap sample quantile, while the second one is based on the asymptotic normality of empirical distribution. The simulation results show that the two calibration procedures can improve CPs of TIs for some non‐normal distributions according to extensive numerical simulations, and they are both proved to be effective through real data examples.

Tolerance limits for mixture‐of‐normal distributions with application to COVID‐19 data

“…Other bootstrap methods can be applied to improve the CPs of TIs. Two content‐adjusted procedures for TIs based on bootstrap were proposed to improve the CPs of TIs for some non‐normal distributions or the normal mixture distribution (Jiao et al, 2022). Furthermore, a researcher might be also interested in exploring TIs for specific subpopulations as well as the entire population when assuming that the population has a normal mixture distribution.…”