Process monitoring (PM) for nuclear safeguards sometimes requires estimation of thresholds corresponding to small false alarm rates. Threshold estimation dates to the 1920s with the Shewhart control chart; however, because possible new roles for PM are being evaluated in nuclear safeguards, it is timely to consider modern model selection options in the context of threshold estimation. One of the possible new PM roles involves PM residuals, where a residual is defined as residual = data ？ prediction. This paper reviews alarm threshold estimation, introduces model selection options, and considers a range of assumptions regarding the data-generating mechanism for PM residuals. Two PM examples from nuclear safeguards are included to motivate the need for alarm threshold estimation. The first example involves mixtures of probability distributions that arise in solution monitoring, which is a common type of PM. The second example involves periodic partial cleanout of in-process inventory, leading to challenging structure in the time series of PM residuals. 1. Introduction Nuclear material accounting (NMA) is a component of nuclear safeguards, which are designed to deter or detect diversion of special nuclear material (SNM) from the fuel cycle to a weapons program. NMA consists of periodic, low frequency, comparisons of measured SNM inputs to measured SNM outputs, with adjustments for measured changes in inventory. Specifically, the residuals in NMA are the material balances defined as , where is a transfer and is an inventory. Process monitoring (PM) is a relatively recent safeguards component. Although usually collected very frequently, PM data are often only an indirect measurement of the SNM and are typically used as a qualitative measure to supplement NMA or to support indirect estimation of difficult-to-measure inventory for NMA [1–3]. However, possible new roles for PM are being evaluated in nuclear safeguards. One of the possible new PM roles involves PM residuals, where a residual is defined as residual = data ？ prediction. One challenge in combining NMA and PM data is that PM residuals often have a probability distribution that cannot be adequately modeled by a normal (Gaussian) distribution but instead have an unknown distribution that must be inferred from training data. We assume throughout that typical behavior of PM residuals, as defined by the probability distribution of the PM residuals, must be estimated using training data that is assumed to be free of loss (by diversion or innocent loss). Because of this assumption, it is helpful to
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