The disclosed embodiments relate to a system for validating a prognostic-surveillance mechanism, which detects anomalies that arise during operation of a computer system. During operation, the system obtains telemetry data comprising a set of raw signals gathered from sensors in the computer system during operation of the computer system, wherein the telemetry signals are gathered over a monitored time period. Next, for each raw signal in the set of raw signals, the system decomposes the raw signal into deterministic and stochastic components. The system then generates a corresponding set of synthesized signals based on the deterministic and stochastic components of the raw signals, wherein the synthesized signals are generated for a simulated time period, which is longer than the monitored time period. Finally, the system uses the set of synthesized signals to validate one or more performance metrics of the prognostic-surveillance mechanism.