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The DFR Property for Counting Processes Stopped at an Independent Random Time

Published online by Cambridge University Press:  30 January 2018

F. G. Badía*
Affiliation:
University of Zaragoza
C. Sangüesa*
Affiliation:
University of Zaragoza
*
Postal address: Maria de Luna 3, Zaragoza, 50018, Spain. Email address: [email protected]
∗∗ Postal address: Pedro Cerbuna 11, Zaragoza, 50009, Spain. Email address: [email protected]
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Abstract

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In this 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 present 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 queueing models.

Type
Research Article
Copyright
© Applied Probability Trust 

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