1/how we can get this formula

https://blog.csdn.net/daimaxiaoxin/article/details/83832759?ops_request_misc=%257B%2522request%255Fid%2522%253A%2522159574541919726869050493%2522%252C%2522scm%2522%253A%252220140713.130102334..%2522%257D&request_id=159574541919726869050493&biz_id=0&utm_medium=distribute.pc_search_result.none-task-blog-2~all~first_rank_ecpm_v3~pc_rank_v2-3-83832759.first_rank_ecpm_v3_pc_rank_v2&utm_term=cusum&spm=1018.2118.3001.4187

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

www.fs.isy.liu.se

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