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Alarm rates for quality control charts

Author

Listed:
  • Margavio, Thomas M.
  • Conerly, Michael D.
  • Woodall, William H.
  • Drake, Laurel G.

Abstract

There is a direct relationship between a single alarm probability and the average run length only for basic Shewhart charts such as the . Alarm rates are defined in this paper that can be applied with charts such as the cumulative sum (CUSUM) chart and the exponentially weighted moving average (EWMA) chart that base decisions on several observations, not just the most recent one. Methods for determining EWMA chart limits are compared on the basis of their false alarm rates. It is shown how control charts can be more flexibly and carefully defined by considering a desired pattern of in-control false alarm rates in conjunction with a desired in-control average run length.

Suggested Citation

  • Margavio, Thomas M. & Conerly, Michael D. & Woodall, William H. & Drake, Laurel G., 1995. "Alarm rates for quality control charts," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 219-224, August.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:3:p:219-224
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    References listed on IDEAS

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    1. K.‐H. Waldmann, 1986. "Bounds for the Distribution of the Run Length of Geometric Moving Average Charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 35(2), pages 151-158, June.
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    Cited by:

    1. Nishina Ken & Nishiyuki Shintaro, 2003. "False Alarm Probability Function of Cusum Charts," Stochastics and Quality Control, De Gruyter, vol. 18(1), pages 101-112, January.
    2. Marianne Frisén, 2003. "Statistical Surveillance. Optimality and Methods," International Statistical Review, International Statistical Institute, vol. 71(2), pages 403-434, August.
    3. Taras Lazariv & Wolfgang Schmid, 2019. "Surveillance of non-stationary processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 305-331, September.
    4. Tingting Huang & Shanggang Wang & Shunkun Yang & Wei Dai, 2021. "Statistical process monitoring in a specified period for the image data of fused deposition modeling parts with consistent layers," Journal of Intelligent Manufacturing, Springer, vol. 32(8), pages 2181-2196, December.
    5. Xiaobei Shen & Changliang Zou & Wei Jiang & Fugee Tsung, 2013. "Monitoring poisson count data with probability control limits when sample sizes are time varying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 625-636, December.
    6. Seven Knoth, 2005. "Fast initial response features for EWMA control charts," Statistical Papers, Springer, vol. 46(1), pages 47-64, January.
    7. William H. Woodall & J Brooke Marshall & Michael D. Joner Jr & Shannon E Fraker & Abdel‐Salam G Abdel‐Salam, 2008. "On the use and evaluation of prospective scan methods for health‐related surveillance," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 223-237, January.
    8. Rafajlowicz, Ewaryst & Pawlak, Mirosław & Steland, Ansgar, 2004. "Non-parametric vertical box control chart for monitoring the mean," Technical Reports 2004,52, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Wenjuan Liang & Xiaolong Pu & Dongdong Xiang, 2017. "A distribution-free multivariate CUSUM control chart using dynamic control limits," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2075-2093, August.

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