I found Chapter 2 of Dean Bodenham's PhD Thesis to be a good introduction to the subject.
One of the measures defined therein is the CUSUM process, which gives a sequence $S_0, S_1, \dots$ that becomes very large when the sequence $x_1, x_{2}, \dots$ is consistently exceeding the mean $\mu$ (taking into account the variance of the sequence $\sigma^2$). There is a different definition for the CUSUM that is more useful than the one given in Section 2.1.4 (Bodenham uses this definition in a different paper):
$$S_0 = 0,$$
$$S_j = \max(0, S_{j-1} + (x_j - \mu) / \sigma - k), \ \ \ \ j = \{1,2,\dots\}.$$
You would declare that a change has occurred once the process $S_t$ exceeds some threshold $h$. In the paper I mentioned, Bodenham sets $S_0 = \mu$, which I think is a mistake: if $\mu > h$ then we would trigger the end of the process immediately.
In addition to the CUSUM that checks for positive drift in the process $x_1, x_2, \dots$, you can also run a simultaneous CUSUM process $T_0, T_1, \dots$ given by
$$T_0 = 0,$$
$$T_j = \max(0, T_{j-1} - (x_j - \mu) / \sigma - k), \ \ \ \ j = \{1,2,\dots\},$$
which gets large when the process $x_1, x_2, \dots$ is consistently below the mean.
