For two probability distributions A(x) and B(x) in Rykov et al. (2020b), modified Laplace–Stieltjes transforms have been introduced. In terms of these transforms, the analytical expressions of the main reliability characteristics of a double redundant system with arbitrarily distributed life- and repair times of system components under the partial repair scenario have been found. In this chapter, we extend the investigation of the same model under the full repair scenario. The analytical expressions for the time-dependent and steady-state system probabilities as well as the system reliability function are presented in this chapter. The proposed approach and obtained analytical results also allow us to investigate the sensitivity of system reliability characteristics to the shape of system component life- and repair time distributions