Predicting the time of failure is a topic of major concern in the field of geological risk management. Several approaches, based on the analysis of displacement monitoring data, have been proposed in recent years to deal with the issue. Among these, the inverse velocity method surely demonstrated its effectiveness in anticipating the time of collapse of rock slopes displaying accelerating trends of deformation rate. However, inferring suitable linear trend lines and deducing reliable failure predictions from inverse velocity plots are processes that may be hampered by the noise present in the measurements; data smoothing is therefore a very important phase of inverse velocity analyses. In this study, different filters are tested on velocity time series from four case studies of geomechanical failure in order to improve, in retrospect, the reliability of failure predictions: Specifically, three major landslides and the collapse of an historical city wall in Italy have been examined. The effects of noise on the interpretation of inverse velocity graphs are also assessed. General guidelines to conveniently perform data smoothing, in relation to the specific characteristics of the acceleration phase, are deduced. Finally, with the aim of improving the practical use of the method and supporting the definition of emergency response plans, some standard procedures to automatically setup failure alarm levels are proposed. The thresholds which separate the alarm levels would be established without needing a long period of neither reference historical data nor calibration on past failure events.