Abstract
In this paper we consider general counting processes stopped at a random timeT, independent of the process. Provided thatThas the decreasing failure rate (DFR) property, we present sufficient conditions on the arrival times so that the number of events occurring beforeTpreserves the DFR property ofT. In particular, when the interarrival times are independent, we consider applications concerning the DFR property of the stationary number of customers waiting in queue for specific queueing models.
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