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NBUE and NWUE properties of increasing Markov processes

Published online by Cambridge University Press:  14 July 2016

Izi Karasu  and
Süleyman Özekici
Izi Karasu
Affiliation:
Boǧazici University
Süleyman Özekici*
Affiliation:
Boǧazici University
*
∗ Boǧazici University, Department of Industrial Engineering, Bebek, Istanbul, Turkey.
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Abstract

Consider a device that deteriorates in time according to an increasing Markov process so that it fails as soon as a critical threshold is exceeded. NBUE and NWUE properties of the lifetime of the device are identified to extend the existing literature on the PFr, IFR, IFRA, and NBU cases. In particular, it is shown that NBUE and NWUE characterizations can be made through a monotonicity property on the potential operator of the Markov process.

Keywords

FIRST-PASSAGE TIMESLIFE DISTRIBUTIONSNBUE AND NWUE PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 827 - 834
Copyright
Copyright © Applied Probability Trust 1989 

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References

Abdel-Hameed, M. (1984a) Life distribution properties of a device subject to a pure jump damage process. J. Appl. Prob. 21, 816–825.CrossRefGoogle Scholar
Abdel-Hameed, M. (1984b) Life distribution properties of a device subject to a Lévy wear process. Math. Operat. Res. 9, 606–614.CrossRefGoogle Scholar
Assaf, D., Shaked, M. and Shanthikumar, J. G. (1985) First passage times with PFr densities. J. Appl. Prob. 22, 185–196.CrossRefGoogle Scholar
Brown, M. and Chaganty, N. R. (1983) On the first passage time distribution for a class of Markov chains. Ann. Prob. 11, 1000–1008.CrossRefGoogle Scholar
Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, N.J. Google Scholar
Derman, C, Ross, S. M. and Scheckner, Z. (1983) A note on first passage times in birth and death and non-negative diffusion processes. Naval Res. Logist. Qaurt. 30, 283–285.CrossRefGoogle Scholar
Keilson, J. (1979) Markov Chain Models — Rarity and Exponentially. Springer-Verlag, New York.Google Scholar
Keilson, J. and Kester, A. (1977) Monotone matrices and monotone Markov processes. Stoch. Proc. Appl. 5, 231–241.CrossRefGoogle Scholar
Marshall, A. M. and Shared, M. (1983) New better than used processes. Adv. Appl. Prob. 15, 601–615.CrossRefGoogle Scholar
Marshall, A. M. and Shared, M. (1986) NBU processes with general state space. Math. Operat. Res. 11, 95–109.CrossRefGoogle Scholar
Shared, M. and Shanthirumar, J. G. (1987) IFRA properties of some Markov jump processes with general state space. Math. Operat. Res. 12, 562–568.Google Scholar
Shanthirumar, J. G. (1984) Processes with new better than used first passage times. Adv. Appl. Prob. 16, 667–686.CrossRefGoogle Scholar