In order to ensure the safe service of aero structure， it is of great significance to evaluate the reliability lifetime under the constraint of extremely small target failure probability. However， the computational efficiency of the existing reliability lifetime analysis methods is difficult to meet the requirements of reliability lifetime analysis under high reliability requirements in engineering effectively. For this issue， a sequential stratified importance sampling method based on the first failure instant is proposed to solve reliability lifetime. Firstly， a sequential stratified exploration strategy for the rare failure domain with the extremely small target failure probability is established， which transforms the exploration problem of the rare failure domain into a gradual exploration problem of a series of failure domains with large probabilities， and it can effectively reduce the difficulty of obtaining the rare failure domain information. Secondly， the method for hierarchically constructing the explicit rule importance sampling density function is proposed to reduce the difficulty and computational complexity of obtaining the importance sample in the rare failure domain， which improves the computational efficiency for solving the reliability lifetime. Finally， in order to reduce the number of model evaluations， the Kriging surrogate model is embedded into the proposed sequential stratified importance sampling method， and an adaptive update strategy guided by misjudgment of the first failure instant is designed， which improve the efficiency of the sequential stratified importance sampling method to solve the reliability lifetime under the constraint of the extremely small target failure probability. The results show that， for the test function， the proposed method reduces the number of model evaluations and computational time by up to 45.4% and 99.6%， respectively， compared with the state-of-the-art methods. For a certain type of aero-engine turbine shaft structure， the proposed method reduces the number of model evaluations and computational time by up to 40.2% and 90.7%， respectively， compared with the state-of-the-art methods.