A statistical model of terrain was developed to estimate the probability of a controlled ight into terrain accident following a ground proximity warning system (GPWS) alert. The terrain model was derived from an actual terrain database and used to create a Markov chain simulation. With this simulation the probability of terrain impact was computed as a function of terrain type and aircraft trajectory pro le. Contours of collision probability were then generated and plotted against current alerting thresholds, illustrating how threshold placement maps into safety. Example results for the GPWS excessive descent rate alerting mode are provided. Following a warning and the subsequent pilot reaction delay and pull-up maneuver, the probability of collision with relatively at terrain is less than 1 £ 10 ¡ 8 for high descent rates. In steep, rapidly changing terrain, the probability of collision following an alert increases to more than 0.01. A simple modi cation of alerting thresholds would not resolve this problem because of a resulting higher rate of nuisance alarms, as shown quantitatively by a performance tradeoff curve. Potential performance improvements through decreased response time or increased maneuvering load factor are also quanti ed.