Model selection and change detection for a time-varying mean in process monitoring

Process monitoring (PM) for nuclear safeguards sometimes requires estimation of thresholds corresponding to small false alarm rates. Threshold estimation is an old topic; 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 alarm threshold estimation. One of the possible new PM roles involves PM residuals, where a residual is defined as residual=data−prediction. This paper briefly reviews alarm threshold estimation, introduces model selection options, and considers several assumptions regarding the data-generating mechanism for PM residuals. Four PM examples from nuclear safeguards are included. One example involves frequent by-batch material balance closures where a dissolution vessel has time-varying efficiency, leading to time-varying material holdup. Another example involves periodic partial cleanout of in-process inventory, leading to challenging structure in the time series of PM residuals. Our main focus is model selection to select a defensible model for normal behavior with a time-varying mean in a PM residual stream. We use approximate Bayesian computation to perform the model selection and parameter estimation for normal behavior. We then describe a simple lag-one-differencing option similar to that used to monitor non-stationary times series to monitor for off-normal behavior.