A New Look at Warning and Action Lines of Surveillance Schemes

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Abstract
Some authors have suggested an efficient dynamic monitoring procedure for detection of a change in the drift of a Brownian motion. Their procedure can be described as a sequence of extremely short sequential probability ratio tests (SPRT's) done in zero time with infinitesimal time between consecutive SPRT's. The drawbacks of this procedure are that it can be described only as a limit of practical procedures and it does not take into account the cost of initiating a test. In this article, we suggest a procedure that takes both sampling and overhead costs into account and that can reasonably be carried out in practice. In this procedure the process is monitored continuously with a constant sampling rate. The accumulated data are analyzed by the standard cumulative sum (CUSUM) statistics. Whenever the CUSUM procedure raises an alarm, data are accumulated as fast as possible until either the alarm is relaxed or the process is stopped.

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