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

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  30 January 2018

F. G. Badía  and
C. Sangüesa
F. G. Badía*
Affiliation:
University of Zaragoza
C. Sangüesa*
Affiliation:
University of Zaragoza
*
∗ Postal address: Maria de Luna 3, Zaragoza, 50018, Spain. Email address: gbadia@unizar.es
∗∗ Postal address: Pedro Cerbuna 11, Zaragoza, 50009, Spain. Email address: csangues@unizar.es
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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.

Keywords

Decreasing failure ratecounting processrenewal processstochastic orderassociationLittle's law

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 574 - 585
Copyright
© Applied Probability Trust 

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