Detecting Changes in a Poisson Process Monitored at Unequal Discrete Time Intervals

Marlo Brown

Communications in Statistics - Theory and Methods, 2009, vol. 38, issue 16-17, 2721-2732

Abstract: We look at a Poisson process where the arrival rate changes at some unknown time point. We monitor this process only at certain time points. At each time point, we count the number of arrivals that happened in that time interval. In previous work, it was assumed that the time intervals were equal. Since work schedules may prevent employees to monitor the process in the evenings or on weekends, we relax this assumption to allow for monitoring at unequal time intervals. For a loss function consisting of the cost of late detection and a penalty for early stopping, we develop, using dynamic programming, the one and two steps look ahead Bayesian stopping rules. We then compare various observation schemes to determine the best model. We provide some numerical results to illustrate the effectiveness of the detection procedures.

Date: 2009
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DOI: 10.1080/03610910902936257

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