Estimation in Shewhart control charts: effects and corrections

Willem Albers, Wilbert C.M. Kallenberg

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The influence of the estimation of parameters in Shewhart control charts is investigated. It is shown by simulation and asymptotics that (very) large sample sizes are needed to accurately determine control charts if estimators are plugged in. Correction terms are developed to get accurate control limits for common sample sizes in the in-control situation. Simulation and theory show that the new corrections work very well. The performance of the corrected control charts in the out-of-control situation is studied as well. It turns out that the correction terms do not disturb the behavior of the control charts in the out-of-control situation. On the contrary, for moderate sample sizes the corrected control charts remain powerful and therefore, the recommendation to take at least 300 observations can be reduced to 40 observations when corrected control charts are applied.
Original languageEnglish
Pages (from-to)207-234
Number of pages28
Issue number3
Publication statusPublished - 2004


  • MSC-62F12
  • MSC-62P30
  • Out of control
  • Statistical process control
  • Phase II control limits
  • Second order unbiasedness


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  • Estimation in Shewhart control charts

    Albers, W. & Kallenberg, W. C. M., 2000, Enschede: University of Twente. 32 p. (Memorandum; no. 1559)

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