Battery energy storage (BES) systems can effectively meet the diversified needs of power system dispatching and assist in renewable energy integration. The reliability of energy storage is essential to ensure the operational safety of the power grid. However, BES systems are composed of battery cells. This suggests that BES performance depends not only on the configuration but also on the operating state over different lifetime durations. The lack of safety and reliability is the main bottleneck preventing widespread applications of BES systems. Therefore, a reliability assessment algorithm and a weak-link analytical method for BES systems are proposed while considering battery lifetime degradation. Firstly, a novel lithium-ion battery model is proposed to identify the degradation rate of solid electrolyte interphase film formation and capacity plummeting. The impacts of different operating conditions are considered in stress factor models. Then, a reliability assessment algorithm for a BES system is introduced based on a universal generating function. An innovative weak-link analytical method based on the reliability importance index is proposed that combines the evaluation results of state-oriented and state-change-oriented indexes through an entropy weight method. The model, algorithm, indexes, and the usefulness are demonstrated in case studies based on aging test data and actual bus operating data. The results demonstrate the effects of the battery status and working conditions on BES reliability. Weak-link analysis is also used to assist BES systems in avoiding short-board batteries to achieve long lifetimes and efficient operation.