On asymptotic failure rates in bivariate frailty competing risks models

A bivariate competing risks problem is considered for a rather 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 the remaining lifetimes of components tend to be independent in the defined sense. Some simple examples are discussed.