False Alarm Probability Function of Cusum Charts

Ken Nishina 1  and Shintaro Nishiyuki 2
  • 1 Department of Systems Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan. nishina@system.nitech.ac.jp
  • 2 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.

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