Copula-based representations for the reliability of the residual lifetimes of coherent systems with dependent components

In the context of coherent systems, we obtain representations for the reliability function of the residual lifetime at time t under different assumptions. Specifically, four cases are considered based on system information at time t: the system is working (case 1); all the components of the system are working (case 2); some components have failed at given times t1,…,tr