Nuclear safeguards aim to confirm that nuclear materials and activities are used for peaceful purposes. To ensure that States are honoring their safeguards obligations, quantitative conclusions regarding nuclear material inventories and transfers are needed. Statistical analyses used to support these conclusions require uncertainty quantification (UQ), usually by estimating the relative standard deviation (RSD) in random and systematic errors associated with each measurement method. This paper has two main components. First, it reviews why UQ is needed in nuclear safeguards and examines recent efforts to improve both top-down (empirical) UQ and bottom-up (first-principles) UQ for calibration data. Second, simulation is used to evaluate the impact of uncertainty in measurement error RSDs on estimated nuclear material loss detection probabilities in sequences of measured material balances.

For statistical evaluations that involve within-group and between-group variance components (denoted σ W 2 and σ B 2 , respectively), there is sometimes a need to monitor for a shift in the mean of time-ordered data. Uncertainty in the estimates σ ^ W 2 and σ ^ B 2 should be accounted for when setting alarm thresholds to check for a mean shift as both σ W 2 and σ B 2 must be estimated. One-way random effects analysis of variance (ANOVA) is the main tool for analysing such grouped data. Nearly all of the ANOVA applications assume that both the within-group and between-group components are normally distributed. However, depending on the application, the within-group and/or between-group probability distributions might not be well approximated by a normal distribution. This review paper uses the same example throughout to illustrate the possible approaches to setting alarm limits in grouped data, depending on what is assumed about the within-group and between-group probability distributions. The example involves measurement data, for which systematic errors are assumed to remain constant within a group, and to change between groups. The false alarm probability depends on the assumed measurement error model and its within-group and between-group error variances, which are estimated while using historical data, usually with ample within-group data, but with a small number of groups (three to 10 typically). This paper illustrates the parametric, semi-parametric, and non-parametric options to setting alarm thresholds in such grouped data.

The nuclear industry must account for nuclear material (NM), such as items that contain plutonium‐239, uranium‐233, or uranium enriched in the 235 or 233 isotopes. Such materials are expensive, plus play a role in weapons production, so there are national and international security considerations. There are two fields of NM safeguards. First, the field of NM domestic safeguards protects NM and monitors for possible NM loss, and does not include the possibility that a facility might alter the accounting data to mask NM diversion. Second, the field of NM international safeguards does not control NM, but monitors for possible NM loss or diversion where inspectors take measurements to determine whether a facility diverted NM and could have altered the accounting records to try to mask the diversion. Domestic safeguards has two main components: physical security to monitor and control access to NM and accounting procedures to monitor the flow and location of NM quantities. Analogously, the banking industry also uses physical security (guards, cameras, locked vaults, etc.) together with accounting procedures to monitor money flow. However, the nuclear industry is more complicated owing to the multitude of physical forms and chemical compositions of NM in bulk quantities, resulting in measurement errors and statistical methods to monitor NM flow.