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A bivariate competing risks model is considered for a general class of survival models. The lifetime distribution of each component is indexed by a frailty parameter. Under the assumption of conditional independence of components the correlated frailty model is considered. The explicit asymptotic formula for the mixture failure rate of a system is derived. It is proved that asymptotically, as t→∞, the remaining lifetimes of components tend to be independent in the defined sense.
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