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Comparison of EWMA, CUSUM and Shiryayev-Roberts procedures for detecting a shift in the mean. (English) Zbl 0816.62068

Summary: M. Pollak and D. Siegmund [Biometrika 72, 267-280 (1985; Zbl 0571.60084)] compared the Shiryayev-Roberts procedure [A. N. Shiryayev, Theor. Probab. Appl. 8, 22-46 (1963); translation from Teor. Veroyatn. Primen. 8, 26-51 (1963; Zbl 0213.438); S. W. Roberts, Technometrics 8, 411-430 (1966)] with the CUSUM procedure for detecting a change in the drift of a Brownian motion based on the conditional average delay time. In this paper, the exponentially weighted moving average (EWMA) procedure proposed by Roberts is compared with the Shiryayev- Roberts and CUSUM procedures. The comparison is based on the stationary average delay time as advocated by Shiryayev. The optimal design for the EWMA procedure and its asymptotic properties are studied when the average-in-control run length is large. The results show that the EWMA procedure is less efficient than the other two procedures.

MSC:

62L10 Sequential statistical analysis
62P30 Applications of statistics in engineering and industry; control charts
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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