Dynamic Sampling Plan in Shiryayev-Roberts Procedure for Detecting a Change in the Drift of Brownian Motion

Abstract

In this paper, a dynamic sampling plan in the Shiryayev-Roberts procedure 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 Assaf and Ritov. The generalizations to the fast initial response and to the CUSUM procedure are also briefly discussed.