On history-dependent mixed shock models

In this paper, we consider a history-dependent mixed shock model which is combination of the extreme and $\delta$ -shock model. We assume that shocks occur according to generalized Pólya process contains homogeneous Poisson process, non-homogeneous as particular cases. For defined survival model, derive corresponding function, mean lifetime failure rate. Further, study asymptotic monotonicity properties Finally, some applications proposed have also been included with relevant numerical examples.