The disclosed embodiments relate to a technique for training a prognostic pattern-recognition system to detect incipient anomalies that arise during execution of a computer system. During operation, the system gathers and stores telemetry data obtained from n sensors in the computer system during operation of the computer system. Next, the system uses the telemetry data gathered from the n sensors to train a baseline model for the prognostic pattern-recognition system. The prognostic pattern-recognition system then uses the baseline model in a surveillance mode to detect incipient anomalies that arise during execution of the computer system. The system also uses the stored telemetry data to train a set of additional models, wherein each additional model is trained to operate with one or more missing sensors. Finally, the system stores the additional models to be used in place of the baseline model when one or more sensors fail in the computer system.