Analytical target cascading (ATC) is a methodology for translating system design targets to design specifications for the elements comprising a decomposed engineering system. In previous work we extended the ATC formulation to reliability-based design optimization (RBDO) problems, where the bounds of the probabilistic design constraints for each subproblem were assigned arbitrarily and held fixed during the ATC process. In this work, we extend the probabilistic ATC formulation to include reliability targets in the cascaded quantities. We employ a series-system formulation to solve the RBDO problem associated with each element of the ATC hierarchy and to compute its reliability. Thus, we quantify the optimality-reliability tradeoffs for each element of the decomposed system, which allows us to determine the probabilistic constraint bounds required to satisfy the overall system reliability target. In this manner we cascade the latter to element reliability specifications