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Cumulative sum (CUSUM) procedures are among the most powerful tools for detecting a shift from a good quality distribution to a bad quality distribution. This article discusses the natural application of CUSUM procedures to the multivariate normal distribution. It discusses two cases, detecting a shift in the mean vector and detecting a shift in the covariance matrix. As an example, the procedure is applied to measurements taken on optical fibers.
John Healy (Sun,) studied this question.