An efficient approach for series system reliability-based design optimization (RBDO) is presented. The key idea is to apportion optimally the system reliability among the failure modes by considering the target values of the failure probabilities of the modes as design variables. Critical failure modes that contribute the most to the overall system reliability are identified. This paper proposes a computationally efficient, system RBDO approach using a single-loop method where the searches for the optimum design and for the most probable failure points proceed simultaneously. Specifically, in each iteration, the optimizer uses approximated most probable failure points from the previous iteration to search for the optimum. A second-order Ditlevsen upper bound is used for estimating the system failure probability considering the joint failure probabilities of failure modes. Also, an easy to implement active strategy set is employed to improve algorithmic stability. The approach is demonstrated on two design examples involving a beam and an internal combustion engine.