With an increasing complexity of engineering systems, ensuring high system reliability and system performance robustness throughout a product life-cycle is of vital importance in practical engineering design. Dynamic reliability analysis, which is generally encountered due to time-variant system random inputs, becomes a primary challenge in reliability based robust design optimization (RBRDO). This paper presents a new approach to efficiently carry out dynamic reliability analysis for RBRDO. The key idea of our proposed approach is to convert time-variant probabilistic constraints to time-invariant ones through efficiently constructing a nested extreme response surface (NERS) and then carry out dynamic reliability analysis using NERS in iterative RBRDO process. The NERS employs efficient global optimization technique to identify the extreme time responses that correspond to the worst scenario of system time-variant limit state functions. With these extreme time samples, a Kriging-based time prediction model is built and used to estimate extreme responses for any given arbitrary design in design space. An adaptive response prediction and model maturation mechanism is developed to guarantee the accuracy and efficiency of the proposed NERS approach. The NERS is integrated with RBRDO with time-variant probabilistic constraints to achieve optimum designs of engineered system with desired reliability and performance robustness. A case study is used to demonstrate the efficacy of the proposed approach.