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

TL;DR

This paper investigates conditions under which the number of events in a general counting process before a random time T retains the decreasing failure rate property, with applications in reliability maintenance models.

Contribution

It provides sufficient conditions involving conditional interarrival times for the DFR property to be preserved in counting processes stopped at T.

Findings

Number of events before T maintains DFR if conditions on interarrival times are met.

Application of results to Kijima type I virtual age models in reliability.

Establishment of DFR property preservation under general assumptions.

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.