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Survival under the pure birth shock model

Published online by Cambridge University Press:  14 July 2016

Bengt Klefsjö
Bengt Klefsjö*
Affiliation:
University of Luleå
*
∗Postal address: Department of Mathematics, University of Luleå, S-951 87 Luleå, Sweden.
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Abstract

Suppose that a device is subjected to shocks and that denotes the probability of surviving k shocks. Then is the probability that the device will survive beyond t, where is the counting process which governs the arrival of shocks. A-Hameed and Proschan (1975) considered the survival function H(t) under what they called the pure birth shock model. In this paper we shall prove that is IFRA and DMRL under conditions which differ from those used by A-Hameed and Proschan (1975).

Keywords

SHOCK MODELBIRTH PROCESSSURVIVAL FUNCTIONVARIATION DIMINISHING PROPERTYTOTAL POSITIVITYIFRADFRADMRLIMRL

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981, pp. 554 - 560
Copyright
Copyright © Applied Probability Trust 

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References

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