Practical Aspects of False Alarm Control for Change Point Detection: Beyond Average Run Length

  • J. Kuhn
  • M. Mandjes
  • T. Taimre
Open Access


A popular method for detecting changes in the probability distribution of a sequence of observations is CUSUM, which proceeds by sequentially evaluating a log-likelihood ratio test statistic and comparing it to a predefined threshold; a change point is detected as soon as the threshold is exceeded. It is desirable to choose the threshold such that the number of false alarms is kept to a specified level. Traditionally, the number of false alarms is measured by the average run length – the expected stopping time until the first false alarm. However, this is does not in general allow one to control the number of false alarms at every particular time instance. Thus, in this paper two stronger false alarm criteria are considered, for which approximation methods are investigated to facilitate the selection of a threshold.


Change point detection False alarm control Threshold selection 

Mathematics Subject Classification (2010)




Julia Kuhn is supported by Australian Research Council (ARC) grant DP130100156. Michel Mandjes’ research is partly funded by the NWO Gravitation Project NETWORKS grant 024002003.


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.School of Mathematics and PhysicsThe University of QueenslandQueenslandAustralia

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