Many real-world systems, particularly those with limited power resources, are designed with cold-standby redundancy for achieving fault tolerance and high reliability. Cold-standby units are unpowered and, thus, do not consume any power until needed to replace a faulty online component. Cold-standby redundancy creates sequential dependence between the online component and standby components; in particular, a standby component can start to work and then fail only after the online component has failed. Traditional approaches to handling the cold-standby redundancy are typically state-space-based or simulation-based or inclusion/exclusion-based methods. Those methods, however, have the state-space explosion problem and/or require long computation time particularly when results with a high degree of accuracy are desired. In this paper, we propose an analytical method based on sequential binary decision diagrams (SBDD) for combinatorial reliability analysis of nonrepairable cold-standby systems. Different from the simulation-based methods, the proposed approach can generate exact system reliability results. In addition, the system SBDD model and reliability evaluation expression, once generated, are reusable for the reliability analysis with different component failure parameters. The approach has no limitation on the type of time-to-failure distributions for the system components or on the system structure. Application and advantages of the proposed approach are illustrated through several case studies.