Scan statistics are concerned with clusters of events over time. In the realm of critical care medicine, such clusters might include the occurrence of ventilator-associated pneumonia (VAP). Given N patients over time, the number of observations in a “moving window” of fixed length can be counted and the maximum cluster value becomes a scan statistic for which both parametric and exact methods exist to calculate its rarity. A statistically unusual cluster may indicate a breakdown in quality. Another approach to monitoring rare events is a g-type statistical process control chart where prospectively observing unusually long periods of time between events can indicate a significant improvement in quality. Both methods are presented in detail and applied to a 24-bed medical/surgical ICU's experience with VAP during a 27-month period.