Survival under the pure birth shock model
- 1 June 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 18 (02) , 554-560
- https://doi.org/10.1017/s0021900200098247
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
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