Preservation of reliability classes associated with the mean residual life by a renewal process stopped at a random time

Authors:
F.G. Badía;E.T. Salehi
Affiliations:
Department of Statistical Methods, University of Zaragoza, Zaragoza, 50018, Spain;Department of Industrial, Birjand University of Technology, Birjand, Iran
Venue:
Applied Stochastic Models in Business and Industry
Year:
2012

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Abstract

In this paper, we show that some ageing classes of a random time T related to the mean residual life are preserved by the discrete random count variable N(T), where {N(t) : t ⩾0}is a renewal process independent from T under suitable conditions. In the particular case of the Poisson process, we extend the results to more reliability classes. We also consider real examples of N(T) and apply the results to queuing systems. Copyright © 2011 John Wiley & Sons, Ltd.