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A system is considered, which is subject to external and possibly fatalshocks, with dependence between the fatality of a shock and the system age.Apart from these shocks, the system suffers from competing soft and suddenfailures, where soft failures refer to the reaching of a given thresh-old forthe degradation level, and sudden failures to accidental failures,characterized by a failure rate. A non-fatal shock increases both degradationlevel and failure rate of a random amount, with possible dependence between thetwo increments. The system reliability is calculated by four different methods.Conditions under which the system lifetime is New Better than Used areproposed. The in uence of various parameters of the shocks environment on thesystem lifetime is studied.

A random shock model with mixed effect, including competing soft and sudden failures, and dependence