Annals of Operations Research

, Volume 263, Issue 1–2, pp 163–189 | Cite as

Multi-sensor slope change detection

  • Yang Cao
  • Yao Xie
  • Nagi Gebraeel
Data Mining and Analytics


We develop a mixture procedure for multi-sensor systems to monitor data streams for a change-point that causes a gradual degradation to a subset of the streams. Observations are assumed to be initially normal random variables with known constant means and variances. After the change-point, observations in the subset will have increasing or decreasing means. The subset and the rate-of-changes are unknown. Our procedure uses a mixture statistics, which assumes that each sensor is affected by the change-point with probability \(p_0\). Analytic expressions are obtained for the average run length and the expected detection delay of the mixture procedure, which are demonstrated to be quite accurate numerically. We establish the asymptotic optimality of the mixture procedure. Numerical examples demonstrate the good performance of the proposed procedure. We also discuss an adaptive mixture procedure using empirical Bayes. This paper extends our earlier work on detecting an abrupt change-point that causes a mean-shift, by tackling the challenges posed by the non-stationarity of the slope-change problem.


Statistical quality control Change-point detection  Intelligent systems 



Authors would like to thank Professor Shi-Jie Deng at Georgia Tech for providing the financial time series data. This work is partially supported by NSF Grants CCF-1442635 and CMMI-1538746.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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