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Processes with new better than used first-passage times

Published online by Cambridge University Press:  01 July 2016

J. G. Shanthikumar
J. G. Shanthikumar*
Affiliation:
University of Arizona
*
∗Postal address: Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, U.S.A.
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Abstract

Let with Z(0) = 0 be a random process under investigation and N be a point process associated with Z. Both Z and N are defined on the same probability space. Let with R0 = 0 denote the consecutive positions of points of N on the half-line . In this paper we present sufficient conditions under which (Z, R) is a new better than used (NBU) process and give several examples of NBU processes satisfying these conditions. In particular we consider the processes in which N is a renewal and a general point process. The NBU property of some semi-Markov processes is also presented.

Keywords

QUEUESDAMSINVENTORY MODELSSHOCK MODELSSEMI-MARKOV PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 3 , September 1984 , pp. 667 - 686
Copyright
Copyright © Applied Probability Trust 1984 

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