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A model-free statistical method for detecting failures in dynamic systems controlled via output feedback is described. In such systems, the impact of the failure on the output is minimized but the failure causes a change in the control signal, which can be detected. Assuming that historical data of the process with and without failure is available, optimization theory can be used to determine detection thresholds that ensure any desired level of false alarms or detection rate. The proposed method is illustrated on a hypothetical bio-reactor and the results show that the proposed method allows for both rapid detection of the failure and continued operation despite the failure.