The system receives original time-series signals from sensors in a monitored system. Next, the system detects and removes spikes from the original time-series signals to produce despiked original time-series signals, which involves using the original time-series data to optimize a damping factor, which is applied to a threshold for a spike-detection technique, and using the spike-detection technique with the optimized damping factor to detect the spikes. The system then generates despiked synthetic time-series signals, which are statistically indistinguishable from the despiked original time-series signals. The system also includes synthetic spikes, which have the same temporal, amplitude and width distributions as the spikes in the original time-series signals, in the despiked synthetic time-series signals to produce synthetic time-series signals with spikes. The system uses the synthetic time-series signals with spikes to train an inferential model, and uses the inferential model to perform prognostic-surveillance operations on subsequently-received signals from the monitored system.