On sequential detection of a shift in the probability of a rare event

Suppose one is monitoring a sequence of observations for a possible increase in the probability of a rare event, and that it is not possible to immediately stop the process under observation or influence it to return to its normal state. One would then desire a scheme which takes advantage of observations occurring after a detection of a change is proclaimed. A modification of Page’s CUSUM Procedure is developed, taking account of these additional observations. A table is given enabling one to select a modified Page procedure with a specified rate of false alarms. A comparison is made between the modified Page procedure and a procedure proposed by Chen (1978).