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Alerting systems used by current physiological monitors are designed to detect changes in the levels of vital signs, but they tend to be very sensitive to artifacts. This paper proposes a method to detect changes in the direction of trend and generate multilevel alerts according to the statistical significance of the detection. One-point-ahead signal predictions are calculated by averaging the historical data with the weights decreasing in the past. The two-sided cumulative sums (Cusum) of the prediction errors are tested against multiple thresholds to detect change points with two levels of certainty. The temporal shapes of the detected changes are analyzed using heuristics to determine whether to trigger an alert. The method was tested offline using 20 cases collected during surgery at a local hospital. The detection results were evaluated by two experienced anesthesiologists. The direction of trend was correctly detected in 90.2% of the annotated changes for end-tidal carbon dioxide, 89.4% for expiratory minute volume, 91.8% for peak airway pressure, and 95.4% for noninvasive blood pressure. The certainty levels of the true-positive alerts estimated by the algorithm have a high ratio of agreement with the anesthesiologists' evaluations.