Reliability properties of k-out-of-n system based on a new mixed δ-shock model

We consider the k-out-of-n system which is subject to a new version of mixed δ-shock models as a combination of δ-shock and extreme shock which occur randomly. In this mixed shock model, the system fails: first, when ℓ interarrival times between two successive shocks with magnitude larger than the critical threshold γ are in [δ₁,δ₂] , δ₁ < δ₂; second, the first interarrival time between two successive shocks is less than δ₁. We derive various mathematical properties of the new model, including hazard rate functions, moment properties, mean deviations, mean residual life, expected inactive time, Lorenz, Bonferroni and Zenga curves, stress strength probability and geometric mean. We also discuss maximum likelihood estimation of the parameters of the model.