Alarm fatigue has been increasingly recognized as one of the most significant problems in the hospital environment. One of the major causes is the excessive number of false physiologic monitor alarms. An underlying problem is the inefficient traditional threshold alarm system for physiologic parameters such as low blood oxygen saturation (SpO2). In this paper, we propose a robust classification procedure based on the AdaBoost algorithm with reject option that can identify and silence false SpO2 alarms, while ensuring zero misclassified clinically significant alarms. Alarms and vital signs related to SpO2 such as heart rate and pulse rate, within monitoring interval are extracted into different numerical features for the classifier. We propose a variant of AdaBoost with reject option by allowing a third decision (i.e., reject) expressing doubt. Weighted outputs of each weak classifier are input to a softmax function optimizing to satisfy a desired false negative rate upper bound while minimizing false positive rate and indecision rate. We evaluate the proposed classifier using a dataset collected from 100 hospitalized children at Children's Hospital of Philadelphia and show that the classifier can silence 23.12% of false SpO2 alarms without missing any clinically significant alarms.