论文信息 - Quasi-stationarity of CUSUM schemes for Erlang distributions

Quasi-stationarity of CUSUM schemes for Erlang distributions

Abstract. Given that no false alarm was made, the CUSUM process behaves like a stationary process. The corresponding transition density is derived for Erlang distributed random variables. Then a representation for the so-called average delay and a geometric approximation for the CUSUM run length distribution is obtained.

Sven Knoth

[1] William H. Woodall,et al. The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables , 1983 .

[2] M. Pollak. Optimal Detection of a Change in Distribution , 1985 .

[3] G. Lorden. PROCEDURES FOR REACTING TO A CHANGE IN DISTRIBUTION , 1971 .

[4] R. Madsen,et al. Ergodic Behavior for Nonnegative Kernels , 1973 .

[5] D. A. Evans,et al. An approach to the probability distribution of cusum run length , 1972 .

[6] D. Siegmund,et al. A diffusion process and its applications to detecting a change in the drift of Brownian motion , 1984 .

[7] Moshe Pollak,et al. A Small Sample Size Comparison of the Cusum and Shiryayev-Roberts Approaches: Changepoint Detection , 1991 .

[8] Morris S. Gold. The geometric approximation to the cusum run length distribution , 1989 .

[9] E. S. Page. CONTINUOUS INSPECTION SCHEMES , 1954 .

[10] S. W. Roberts. A Comparison of Some Control Chart Procedures , 1966 .

[11] Dietmar Kohlruss. Exact formulas for the oc and asn functions of the sprt for erlang distributions , 1994 .

[12] K. Waldmann,et al. Bounds for the Distribution of the Run Length of One-Sided and Two-Sided CUSUM Quality Control Schemes , 1986 .

[13] Seven Knoth,et al. Exact average run lengths of cusum schemes for erlang distributions: Exact average run lengths of cusum schemes , 1998 .