Three-State Networks Subject to Shocks

In this paper, we consider a three-state network that is subject to shocks. We assume that these shocks occur according to a counting process and in each shock, more than one link may fail. Under some assumptions, we introduce a new variant of two-dimensional signature that is called two-dimensional t-signature. A mixture representation is provided for the joint reliability function of the states lifetimes of the network. Also, some stochastic and dependent properties of the states lifetimes of the network are investigated