Alternate Shewhart-type statistical control charts, called "g" and "h" charts, are developed and evaluated for monitoring the number of cases between hospital-acquired infections and other adverse events, such as heart surgery complications, catheter-related infections, surgical site infections, contaminated needle sticks, and other iatrically induced outcomes. These new charts, based on inverse sampling from geometric and negative binomial distributions, are simple to use and can exhibit significantly greater detection power over conventional binomial-based approaches, particularly for infrequent events and low "defect" rates. A companion article illustrates several interesting properties of these charts and design modifications that significantly can improve their statistical properties, operating characteristics, and sensitivity.