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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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References

Barlow, R. E. and Proschan, F. (1976) Theory of maintained systems: distribution of time to first system failure. Math. Operat. Res. 1, 32–42.Google Scholar
Brown, M. (1980) Bounds, inequalities and monotonicity properties for some specialized renewal processes. Ann. Prob. 8, 227–240.Google Scholar
Buzacott, J. A. (1974) The effect of queue discipline on the capacity of queues with service time depending on waiting times. INFOR 12, 174–185.Google Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973) Shock models and wear processes. Ann. Prob. 1, 627–650.Google Scholar
Marshall, A. W. and Shaked, M. (1983) New better than used processes. Adv. Appl. Prob. 15, 601–615.Google Scholar
Miller, D. R. (1979) Almost sure comparisons of renewal processes and Poisson processes with application to reliability theory. Math. Operat. Res. 5, 110–119.Google Scholar
Posner, M. J. M. (1974) Single server queues with service time depending on waiting time. Operat. Res. 21, 610–616.CrossRefGoogle Scholar
Shanthikumar, J. G. (1983) Use of uniformization in random variate generation and simulation of renewal and non-homogeneous processes. Working paper #83-005, Systems and Industrial Engineering, University of Arizona, Tucson.Google Scholar
Shanthikumar, J. G. and Sumita, U. (1983) General shock models associated with correlated renewal sequences. J. Appl. Prob. 20, 600–614.Google Scholar
Shanthikumar, J. G. and Sumita, U. (1984) Distribution properties of the system failure times in general shock models associated with correlated renewal sequences. Adv. Appl. Prob. 16, 363–377.CrossRefGoogle Scholar
Sonderman, D. (1980) Comparing semi-Markov processes. Math. Operat. Res. 5, 110–119.Google Scholar