Improving coverage probabilities for parametric tolerance intervals via bootstrap calibration

Statistical tolerance intervals are commonly employed in biomedical and pharmaceutical research, such as in lifetime analysis, the assessment of biosimilarity of branded and generic versions of biopharmaceutical drugs, and in quality control of drug products to ensure that a specified proportion of the products are covered within established acceptance limits. Exact two-sided parametric tolerance intervals are only available for the normal distribution, while exact one-sided parametric tolerance limits are available for a limited number of distributions. Approximations to two-sided parametric tolerance intervals often use the Bonferroni correction on the one-sided tolerance interval calculation; however, this often incurs a higher coverage probability than the nominal level. Recently, the usage of a bootstrap calibration has been demonstrated as a way to improve coverage probabilities of tolerance intervals for very specific and complex distributional settings. We present a focused treatment on using a single-layer bootstrap calibration to improve the coverage probabilities of two-sided parametric tolerance intervals. Simulation results clearly demonstrate the improved coverage probabilities towards the nominal level over the uncalibrated setting. Applications to medical data for various parametric distributions also highlight the utility of constructing these calibrated tolerance intervals.