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PRESERVATION PROPERTIES OF A RENEWAL PROCESS STOPPED AT A RANDOM DEPENDENT TIME

Published online by Cambridge University Press:  28 March 2013

F. G. Badía  and
Ji Hwan Cha
F. G. Badía
Affiliation:
Department of Statistics, University of Zaragoza, Zaragoza, 50018, Spain E-mail: [email protected]
Ji Hwan Cha
Affiliation:
Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea E-mail: [email protected]
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Abstract

One of the interesting problems on the stochastic behavior of random recurrent events in a random time interval is to obtain the conditions under which the reliability properties of a random time T are inherited by N(T), where {N(t):t≥0} is a stochastic process. Most of the studies on the topic has been done under the assumption that the random time T and the stochastic process {N(t):t≥0} are stochastically independent. However, in practice, there can be different cases when appropriate dependence structure is more appropriate. In this paper, we study the preservation of a renewal process stopped at a random time when they are “stochastically dependent.” We discuss the stochastic ordering properties and the preservation of reliability classes for the random counting variables N(T) when the corresponding counting process is a renewal process. Furthermore, we study the preservation of NBUE (NWUE) reliability class when the counting process is a homogeneous Poisson process.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 2 , April 2013 , pp. 163 - 175
Copyright
Copyright © Cambridge University Press 2013

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