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Multi-sensor slope change detection

Author

Listed:
  • Yang Cao

    (Georgia Institute of Technology)

  • Yao Xie

    (Georgia Institute of Technology)

  • Nagi Gebraeel

    (Georgia Institute of Technology)

Abstract

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 $$p_0$$ 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.

Suggested Citation

  • Yang Cao & Yao Xie & Nagi Gebraeel, 2018. "Multi-sensor slope change detection," Annals of Operations Research, Springer, vol. 263(1), pages 163-189, April.
    • Handle: RePEc:spr:annopr:v:263:y:2018:i:1:d:10.1007_s10479-016-2185-5
    DOI: 10.1007/s10479-016-2185-5
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    References listed on IDEAS

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    1. Fang, Xiaolei & Zhou, Rensheng & Gebraeel, Nagi, 2015. "An adaptive functional regression-based prognostic model for applications with missing data," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 266-274.
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