Cluster shock models
Keyword(s):
The survival distribution of a device subject to a sequence of shocks occurring randomly over time is studied by Esary, Marshall and Proschan (1973) and by A-Hameed and Proschan (1973), (1975). The present note treats the case in which shocks occur according to a homogeneous Poisson cluster process. It is shown that if [the device survives k shocks] = zk, 0 < z < 1, then the device exhibits a decreasing failure rate. A DFR preservation theorem is proved for completely monotonic . A counterexample to the IFR preservation theorem is given in which is strictly IFR while the failure rate is initially decreasing and then increasing.
1981 ◽
Vol 18
(01)
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pp. 104-111
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1979 ◽
Vol 16
(02)
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pp. 261-273
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2015 ◽
Vol 14
(2)
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pp. 1035-1047
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2010 ◽
Vol 33
(5)
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pp. 612-618
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2018 ◽
Vol 22
(5)
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pp. 1098-1101
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2018 ◽
Vol 66
(5)
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pp. 2219-2234
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1977 ◽
Vol 14
(02)
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pp. 396-398
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