Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
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