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CUSUM charts with controlled conditional performance under estimated parameters

Summary: [This abstract is based on the authors' abstract.] We study the effect of the Phase I estimation error on the cumulative sum (CUSUM) chart. Impractically large amounts of Phase I data are needed to sufficiently reduce the variation in the in-control average run lengths (ARL) between practitioners. To reduce the effect of estimation error on the chart’s performance we design the CUSUM chart such that the in-control ARL exceeds a desired value with a specified probability. This is achieved by adjusting the control limits using a bootstrap-based design technique. Such approach does affect the out-of-control performance of the chart; however, we find that this effect is relatively small.

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  • Topics: Engineering, Statistics
  • Keywords: Cumulative sum control chart (CUSUM), Statistical process control (SPC), Estimation, Error, Average run length (ARL), Control limits, Bootstrap methods
  • Author: Saleh, Nesma A.; Swetsloot, Inez M.; Mahmoud, Mahmoud A.; Woodall, William H.;
  • Journal: Quality Engineering