The International Monitoring System (IMS) infrasound network has been designed to acquire the necessary data to detect and locate explosions in the atmosphere with a yield equivalent to 1 kiloton of TNT anywhere on Earth. A major associated challenge is the task of automatically processing data from all IMS infrasound stations to identify possible nuclear tests for subsequent review by analysts. This paper is the first attempt to quantify the false alarm rate (FAR) of the IMS network, and in particular to assess how the FAR is affected by the numbers and distributions of detections at each infrasound station. To ensure that the results are sufficiently general, and not dependent entirely on one detection algorithm, the assessment is based on two detection algorithms that can be thought of as end members in their approach to the trade-off between missed detections and false alarms. The results show that the FAR for events formed at only two arrays is extremely high (ranging from 10s to 100s of false events per day across the IMS network, depending on the detector tuning). It is further shown that the FAR for events formed at three or more IMS arrays is driven by ocean-generated waves (microbaroms), despite efforts within both detection algorithms for avoiding these signals, indicating that further research into this issue is merited. Overall, the results highlight the challenge of processing data from a globally sparse network of stations to detect and form events. The results suggest that more work is required to reduce false alarms caused by the detection of microbarom signals.