Alternate Shewhart-type statistical control charts, called "g" and "h" charts, have been developed 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, medication errors, and other care-induced concerns. This article investigates the statistical properties of these new charts and illustrates several design considerations that significantly can improve their operating characteristics and sensitivity, including the use of within-limit rules, a new in-control rule, redefined Bernoulli trials, and probability-based limits. These new charts are based on inverse sampling from geometric and negative binomial distributions, are simple for practitioners to use, and in some cases exhibit significantly greater detection power over conventional binomial-based approaches, particularly for infrequent events and low "defect" rates.