In quantitative performance assessment (PA) for nuclear waste repositories, probabilistic (e.g., Monte Carlo) calculations are frequently used to estimate dose and risk [1], Each Monte Carlo realization represents the uncertain estimate of the future effect of the repository. There are at least two ways to interpret the model output; (1) take the peak doses from the Monte Carlo realizations and draw conclusions from their ensemble, e.g., the mean of the peak doses; and (2) at each instant of time, look at the ensemble of all realizations, and synthesize a representative dose-versus-time curve, e.g., the mean. Method 1 is easy to understand and explain. However, the calculation of the mean of the peak doses allows an additional degree of freedom that may inadvertently overestimate risk, because the peaks occur at different times and therefore the mean may include contributions from peaks outside of a single person’s life span. This dilemma has been discussed previously in connection with the definition of the critical group, e.g., Corbett [2]. The U.S. Nuclear Regulatory Commission (NRC) has adapted Method 2, taking the peak value of the mean curve to represent the dose that the Reasonably Maximally Exposed Individual (RMEI) could receive during the regulatory time period for the purpose of defining risk. We call this the “peak-of-the-mean (POM)” approach, and believe that it is the clearest and fairest definition of risk. However, calculations and sensitivity analyses with the POM must proceed thoughtfully, since there are computational pitfalls and results are sometimes counterintuitive.