 CUSUM

A CUSUM accumulates evidence for a change in a monitored probability distribution. With $W_t$ a log-likelihood ratio increment favoring a specified changed distribution, reset the accumulated score at zero and signal when it exceeds a chosen boundary $h$. For $C_0=0$, $C_t$ is the largest nonnegative sum of successive increments ending at $t$. This permits repeated detection of a change with an unknown onset, rather than a single fixed-start test.