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

Abstract

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 $T$. 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.

Some changes made in the general results with respect to the previous version. Main result is now Theorem 3.1

Cited by in corpus (1)

• On the Decreasing Failure Rate property for general counting process. Results based on conditional interarrival times