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Detecting When a Monotonically Increasing Mean Has Crossed a Threshold

Summary: [This abstract is based on the authors' abstract.] For monitoring a sequence of random variables, the cumulative sum (CUSUM) sequential change-point detection scheme has optimality properties if the mean experiences a single, one-time jump increase. However, many monitoring situations are not described realistically by this model. Another model is introduced in which it is assumed only that the mean is nondecreasing over time. It is shown how to apply the CUSUM and the exponentially weighted moving average (EWMA) and how to compare these procedures to a repeated generalized likelihood ratio (GLR) test designed for the monotone setting. A simulation study demonstrates that the CUSUM and EWMA perform surprisingly well compared to the GLR test, usually outperforming it. The CUSUM is argued to be the best overall choice.

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  • Topics: Change Management, Statistical Process Control (SPC)
  • Keywords: Cumulative sum control chart (CUSUM),Simulations,Regression analysis,Likelihood methods,Change management,Statistical process control (SPC),Exponentially weighted moving average control charts (EWMA)
  • Author: Chang, Joseph T.; Fricker, Ronald D., Jr.
  • Journal: Journal of Quality Technology