Dedicated surveys using different detection pipelines are being carried out at multiple observatories to find more Fast Radio Bursts (FRBs). Understanding the efficiency of detection algorithms and the survey completeness function is important to enable unbiased estimation of the underlying FRB population properties. One method to achieve end-to-end testing of the system is by injecting mock FRBs in the live data-stream and searching for them blindly. Mock FRB injection is particularly effective for machine-learning-based classifiers, for which analytic characterisation is impractical. We describe a first-of-its-kind implementation of a real-time mock FRB injection system at the upgraded Molonglo Observatory Synthesis Telescope (UTMOST) and present our results for a set of 20,000 mock FRB injections. The injections have yielded clear insight into the detection efficiencies and have provided a survey completeness function for pulse width, fluence and DM. Mock FRBs are recovered with uniform efficiency over the full range of injected DMs, however the recovery fraction is found to be a strong function of the width and Signal-to-Noise (SNR). For low widths ($lesssim 20$ ms) and high SNR ($gtrsim$ 9) the recovery is highly effective with recovery fractions exceeding 90%. We find that the presence of radio frequency interference causes the recovered SNR values to be systematically lower by up to 20% compared to the injected values. We find that wider FRBs become increasingly hard to recover for the machine-learning-based classifier employed at UTMOST. We encourage other observatories to implement live injection set-ups for similar testing of their surveys.
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