Monitoring medical outcomes is desirable to help quickly detect performance changes. Previous applications have focused mostly on binary outcomes, such as 30-day mortality after surgery. However, in many applications the survival time data are routinely collected. In this paper, we propose an updating exponentially weighted moving average (EWMA) control chart to monitor risk-adjusted survival times. The updating EWMA (uEWMA) operates in a continuous time; hence, the scores for each patient always reflect the most up-to-date information. The uEWMA can be implemented based on a variety of survival-time models and can be set up to provide an ongoing estimate of a clinically interpretable average patient score. The efficiency of the uEWMA is shown to compare favorably with the competing methods.