1/how we can get this formula
This is based on Gaussian assumption
In particular, K below is usually called the reference value (or the slack value), and it is often chosen about halfway between the target mu_0 and the value of regression of the mean mu_1 that we are interested in detecting quickly.
In other words, K = (\mu_1 — \mu_0)/2
- C_i+ = max (0, x_i — (mu_0 + K) + C_(i-1)+)
- C_i- = max (0, (mu_0 — K) — x_i + C(i-1)-)
2/ variations of cusum
28 CHAPTER 2 CHANGE DETECTION ALGORITHMS is the signal-to-noise ratio. Therefore, the decision function (2.1.2) is S N 1 = b N X i =1 y i 0 2 (2.1.10) The stopping rule for the change detection algorithm is as in (2.1.4), with the decision rule deﬁned by
pay attention to following:
2.1 why ()_+, i.e. the test keeps taking the positive of accumulative value?
2.2 weighted cusum details on gaussian cases.
it directly talks about weighted cusum.