1/how we can get this formula

CUSUM算法_daimaxiaoxin的博客-CSDN博客_cusum

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

In

- 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

https://www.fs.isy.liu.se/Edu/Courses/TSFS06/PDFs/Basseville.pdf

Change Detection Algorithms — Linköping University

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.

3/

CUSUM

https://en.wikipedia.org/wiki/CUSUM

it directly talks about weighted cusum.

Weighted cusum