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

F. G. Badía; C. Sangüesa

doi:10.1016/j.apm.2015.12.032

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arXiv · 1209.1256

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

F. G. Badía·C. Sangüesa

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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 $T$. 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.

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F. G. Badía, C. Sangüesa. 2012-09-06. On the Decreasing Failure Rate property for general counting process. Results based on conditional interarrival times. https://doi.org/10.1016/j.apm.2015.12.032

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