The life distribution H(t) of a device subject to shocks governed by a Poisson process and pure birth process is considered as a function of probabilities Pk of not surviving the first k shocks. It is shown that some properties of a discrete distribution {P'k} are reflected on properties of the continuous life distribution H(t). In particular, if Pk has the discrete NBUFR properties, then H(t) has the continuous NBUFR and NBAFR properties. The NBUFR and NBAFR life distributions are obtained under suitable assumptions on birth rate and the probability of surviving a given number of shocks in a pure birth shock model. Some other general forms of shock models are also considered.
@article{urn:eudml:doc:40514,
title = {Shock models with NBUFR and NBAFR survivals.},
journal = {Trabajos de Estad\'\i stica},
volume = {3},
year = {1988},
pages = {97-113},
zbl = {0734.60086},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40514}
}
Abouammoh, A. M.; Hindi, M. I.; Ahmed, A. N. Shock models with NBUFR and NBAFR survivals.. Trabajos de Estadística, Tome 3 (1988) pp. 97-113. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40514/