Asymptotic optimized CUSUM and EWMA multi-charts for jointly detecting and diagnosing unknown change

ABSTRACT

This article not only shows that the CUSUM multi-chart which consists of several CUSUM charts, has the asymptotic optimal performance in jointly detecting and diagnosing the unknown change in a sequence of $i.i.d.$ observations but also provides a design method of optimizing the CUSUM and EWMA multi-charts. The numerical comparisons illustrate that the optimized CUSUM multi-chart has better performance in jointly detecting and diagnosing the mean and variance shifts in $i.i.d.$ normal observations than that of the optimized EWMA multi-chart. A real example for engineering surveillance using the electric power generation data was used to demonstrate the practicality of the schemes.

KEYWORDS:

• Change-point monitoring
• detection-diagnosis
• mean-variance
• optimized CUSUM and EWMA multi-charts

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Social Science Foundation of China (NSSFC) [11531001] and National Basic Research Program of China [2015CB856004].