%0 Journal Article
%T On the Decreasing Failure Rate property for general counting process. Results based on conditional interarrival times
%A F. G. Bad¨ªa
%A C. Sang¨¹esa
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1209.1256v1