Alarm fatigue, a condition in which clinical staff become desensitized to alarms due to the high frequency of unnecessary alarms, is a major patient safety concern. Alarm fatigue is particularly prevalent in the pediatric setting, due to the high level of variation in vital signs with patient age. Existing studies have shown that the current default pediatric vital sign alarm thresholds are inappropriate, and lead to a larger than necessary alarm load. This study leverages a large database containing over 190 patient-years of heart rate data to accurately identify the 1st and 99th percentiles of an individual's heart rate on their first day of vital sign monitoring. These percentiles are then used as personalized vital sign thresholds, which are evaluated by comparing to non-default alarm thresholds used in practice, and by using the presence of major clinical events to infer alarm labels. Using the proposed personalized thresholds would decrease low and high heart rate alarms by up to 50% and 44% respectively, while maintaining sensitivity of 62% and increasing specificity to 49%. The proposed personalized vital sign alarm thresholds will reduce alarm fatigue, thus contributing to improved patient outcomes, shorter hospital stays, and reduced hospital costs.