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Dynamic sampling plan in Shiryayev-Roberts procedure for detecting a change in the drift of Brownian motion. (English) Zbl 0816.62067

Summary: A dynamic sampling plan in 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)] is considered. It is shown that a two- rate dynamic sampling plan is optimal in the sense that it minimizes the stationary average delay time (SADT). Analytical results as well as numerical comparisons show that it is significantly superior to the fixed sampling plan. The comparison also shows that it is as powerful as the dynamic sampling procedure of D. Assaf and Y. Ritov [Ann. Stat. 17, No. 2, 793-800 (1989; Zbl 0672.62083)]. The generalizations to the fast initial response and to the CUSUM procedure are also briefly discussed.

MSC:

62L10 Sequential statistical analysis
62P30 Applications of statistics in engineering and industry; control charts
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