CUSUM multi-chart based on nonparametric likelihood approach for detecting unknown abrupt changes and its application for network data

Abstract

This article deals with the online monitoring of changes when the distributions (including the form of distributions) of pre-change and post-change are unknown. We not only construct a nonparametric CUSUM multi-chart based on the nonparametric likelihood function to deal with the online change detection problem, but also give a strategy for choosing the appropriate value if we choose only one truncated value of u. And under the measurement called nonparametric Control chart Performance Index (CPI), we show an asymptotic optimal design for the allocation of the reference post-change Cumulative Distribution Functions (C.D.F.s). Finally, we use simulated data to present the related results. Moreover, we apply the method in this paper to network data, which is very common at present.

Keywords:

• Nonparametric CUSUM multi-chart
• optimal design
• cumulative distribution function

MSC 2010 subject classifications:

• Primary 62L10
• Secondary 62L15

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [11531001].