# Risk prediction and design of disposal systems

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## Abstract

The metrics of peak-of-the-mean, mean-of-the-peaks, and cumulative release that predict risks are quantitatively evaluated. These metrics determine the performance of a disposal system (hazardous and radioactive wastes), which must be determined for a site to obtain an operating license. Monte Carlo sampling is used to investigate the impacts of uncertainty and model bias on risk predictions. The sampling accounts for uncertainty within the disposal system using both normal and lognormal distributions for the model parameters. The effects on risk predictions of modeled events with an estimated probability of occurrence and of a particular compliance period are also analyzed. Risk predictions are calculated based on a simplified model that takes into account waste container failure, the release rate from the waste, and transport of the release with retardation to a receptor. Results from the simplified model are used to evaluate the stability and accuracy of risk predictions for each metric over a range of uncertainties and biases. The peak-of-the-mean metric provides the least stable and least accurate risk predictions, whereas the cumulative release metric is the most stable and the most accurate. The peak-of-the-mean metric also exhibits risk dilution (i.e., a decrease in the predicted risk with increased uncertainty). The impact of an event on a risk prediction when the modeled time of the event is either under-estimated or over-estimated is assessed. The cumulative release is the most stable and accurate metric. The peak-of-the-mean metric is stable but under-estimates risk. ^ The mean-of-the-peaks metric provides an accurate risk prediction if the time of the event is approximately equal to the modeled event time. If the modeled event time is either under-estimated or over-estimated, this metric under-estimates risk with respect to the nominal risk. Risk predictions for each metric are stable and accurate when the compliance period is greater than the containment time for the disposal system. If the compliance period is less than the containment period, risk predictions using these metrics can be unstable and inaccurate. For events with probabilities, under-estimating or over-estimating the modeled event time can have a significant effect on the predicted risk depending on the risk metric. The cumulative release metric is the most stable and accurate risk predictor for event probabilities that are either under-estimated or over-estimated. The mean-of-the-peaks metric shows risk dilution and the peak-of-the-mean metric consistently under-estimates risk. ^ This paper presents the behavior of metrics for different uncertainties, biases, compliance periods, and events with probabilities. It also illustrates how risk predictions can be moved in a direction that may or may not be expected or intended. ^

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