As part of its preparation to review a potential license application from the U.S. Department of Energy (DOE), the U.S. Nuclear Regulatory Commission (NRC) is examining the performance of the proposed Yucca Mountain nuclear waste repository. In this regard, we evaluated postclosure repository performance using Monte Carlo analyses with an NRC-developed system model that has 950 input parameters, of which 330 are sampled to represent system uncertainties. The quantitative compliance criterion for dose was established by NRC to protect inhabitants who might be exposed to any releases from the repository. The NRC criterion limits the peak-of-the-mean dose, which in our analysis is estimated by averaging the potential exposure at any instant in time for all Monte Carlo realizations, and then determining the maximum value of the mean curve within 10,000 years, the compliance period. This procedure contrasts in important ways with a more common measure of risk based on the mean of the ensemble of peaks from each Monte Carlo realization. The NRC chose the former (peak-of-the-mean) because it more correctly represents the risk to an exposed individual. Procedures for calculating risk in the expected case of slow repository degradation differ from those for low-probability cases of disruption by external forces such as volcanism. We also explored the possibility of risk dilution (i.e., lower calculated risk) that could result from arbitrarily defining wide probability distributions for certain parameters. Finally, our sensitivity analyses to identify influential parameters used two approaches: (1) the ensemble of doses from each Monte Carlo realization at the time of the peak risk (i.e., peak-of-the-mean) and (2) the ensemble of peak doses calculated from each realization within 10,000 years. The latter measure appears to have more discriminatory power than the former for many parameters (based on the greater magnitude of the sensitivity coefficient), but can yield different rankings, especially for parameters that influence the timing of releases.