arXiv subjects

F. G. Badía

Publications and source records attributed to F. G. Badía.

2 recordsLinked to original sources

arXiv2012

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

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.

math.PR↗

arXiv2012

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

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 involve the study of the conditional interarrival times. As a main application, we prove the DFR property in a context of maintenance models in reliability, by the consideration of Kijima type I virtual age models under quite general assumptions.

math.PR↗