The disclosed embodiments relate to a system that determines whether an inferential model is susceptible to spillover false alarms. During operation, the system receives a set of time-series signals from sensors in a monitored system. The system then trains the inferential model using the set of time-series signals. Next, the system tests the inferential model for susceptibility to spillover false alarms by performing the following operations for one signal at a time in the set of time-series signals. First, the system adds degradation to the signal to produce a degraded signal. The system then uses the inferential model to perform prognostic-surveillance operations on the time-series signals with the degraded signal. Finally, the system detects spillover false alarms based on results of the prognostic-surveillance operations.