The DFR property for counting processes stopped at an independent random time

Details The DFR property for counting processes stopped at an independent random time The DFR property for counting processes stopped at an independent random time

2012-01-12

arxiv.org/abs/1201.2545v1

Mathematics

Probability

Submitted to Applied Probability Trust

Scientific paper

In the present paper we consider general counting processes stopped at a random time T, independent of the process. Provided that T has the decreasing failure rate (DFR) property, we give sufficient conditions on the arrival times so that the number of events occurring before T preserves the DFR property of T. These conditions are: decreasing behaviour and association of the interarrival times. 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 queuing models.

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