We describe a system that performs prognostic-surveillance operations based on an inferential model that dynamically adapts to evolving operational characteristics of a monitored asset. During a surveillance mode, the system receives a set of time-series signals gathered from sensors in the monitored asset. Next, the system uses an inferential model to generate estimated values for the set of time-series signals, and then performs a pairwise differencing operation between actual values and the estimated values for the set of time-series signals to produce residuals. Next, the system performs a sequential probability ratio test (SPRT) on the residuals to produce SPRT alarms. When a tripping frequency of the SPRT alarms exceeds a threshold value, which is indicative of an incipient anomaly in the monitored asset, the system triggers an alert. While the prognostic-surveillance system is operating in the surveillance mode, the system incrementally updates the inferential model based on the time-series signals.