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On the HNBUE property in a class of correlated cumulative shock models

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  01 July 2016

Rafael Pérez-Ocón  and
M. Luz Gámiz-Pérez
Rafael Pérez-Ocón*
Affiliation:
University of Granada
M. Luz Gámiz-Pérez*
Affiliation:
University of Granada
*
* Postal address: Department of Statistics and OR, University of Granada, 18071 Granada, Spain.
* Postal address: Department of Statistics and OR, University of Granada, 18071 Granada, Spain.
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Abstract

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Conditions for a correlated cumulative shock model under which the system failure time is HNBUE are given. It is shown that the proof of a theorem given by Sumita and Shanthikumar (1985) relative to this property is not correct and a correct proof of the theorem is given.

Keywords

HARMONIC NEW BETTER THAN USED IN EXPECTATIONPOISSON PROCESSRENEWAL PROCESS

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing
Type
Letter to the Editor
Information
Advances in Applied Probability , Volume 27 , Issue 4 , December 1995 , pp. 1186 - 1188
Copyright
Copyright © Applied Probability Trust 1995 

References

[1] ÇInlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
[2] Klefsjö, B. (1981) HNBUE survival under some shock models. Scand. J. Statist. 8, 39–47.Google Scholar
[3] Sumita, U. and Shanthikumar, J. G. (1985) A class of correlated cumulative shock models. Adv. Appl. Prob. 17, 347–366.CrossRefGoogle Scholar