We propose a new modeling approach for inspection data that provides a more useful interpretation of the patterns of detections of invasive pests, using cargo inspection as a motivating example. Methods that are currently in use generally classify shipments according to their likelihood of carrying biosecurity risk material, given available historical and contextual data. Ideally, decisions regarding which cargo containers to inspect should be made in real time, and the models used should be able to focus efforts when the risk is higher. In this study, we propose a dynamic approach that treats the data as a time series in order to detect periods of high risk. A regulatory organization will respond differently to evidence of systematic problems than evidence of random problems, so testing for serial correlation is of major interest. We compare three models that account for various degrees of serial dependence within the data. First is the independence model where the prediction of the arrival of a risky shipment is made solely on the basis of contextual information. We also consider a Markov chain that allows dependence between successive observations, and a hidden Markov model that allows further dependence on past data. The predictive performance of the models is then evaluated using ROC and leakage curves. We illustrate this methodology on two sets of real inspection data.