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Change detection in the mean of a white Gaussian process by the backward standardized sum
Authors:Sungwhan Cho
Institution:Department of Electrical and Computer Engineering, The University of Western Ontario, London, ON, Canada
Abstract:A statistical method for detection of a change in the mean of a white Gaussian noise process is developed in this paper. The decision function of the method searches for the maximum of the backward standardized sum in a moving window to detect the change. Statistical properties of the decision function are derived to set the detection threshold. The derivation of the mean delay function and the optimal size of the moving window is also presented. The performance of the proposed method is compared, in terms of the mean delay for the detection, with that of the exponentially weighted moving average (EWMA). The mean delays of the cumulative sum control charts are also compared for benchmarking. The performance comparison is carried out by evaluating the average run length functions and by simulations. The results conclude that the mean detection delay of the proposed method is shorter than that of the standard EWMA for the same Type I error probability.
Keywords:Average run length  change detection  CUSUM  EWMA  SPRT  SSIT  
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