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False Alarm Probability Function of Cusum Charts

Author

Listed:
  • Nishina Ken

    (Department of Systems Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan. nishina@system.nitech.ac.jp)

  • Nishiyuki Shintaro

    (Department of Systems Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan)

Abstract

In this paper, standard Cusum charts with head start value zero are compared with fast initial response (FIR) Cusum charts proposed by Lucas and Crosier (Technometrics 24: 199–205, 1982) from the viewpoint of the false alarm probability function. The focus in this comparison is conservativeness. The concept of conservativeness is based on the relationship between the in-control ARL and the false alarm probability function by regarding the Cusum statistic as a Markov process. The comparison shows that standard Cusum charts are conservative in contrast to FIR Cusum charts. Moreover, the concept of false alarm probability function provides an easy probabilistic interpretation of the in-control ARL.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:ecqcon:v:18:y:2003:i:1:p:101-112:n:1
    DOI: 10.1515/EQC.2003.101
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    References listed on IDEAS

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    1. 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.
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