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Assessing the reliability of complex systems (e.g. structures) is essential for a reliability-based optimal design that balances safety and costs of such systems. This paper proposes the Progressive Reliability Method (PRM) for the quantification of the reliability of complex systems. The proposed method is a closed-form solution for calculating the probability of failure. The new method is flexible to the definition of “failure” (i.e., can consider serviceability and ultimate-strength failures) and uses the rules of probability theory to estimate the failure probability of the system or its components. The method is first discussed in general and then illustrated in two examples, including a case study to find the safest configuration and orientation of a 12-line offshore mooring system. The PRM results are compared with results of a similar assessment based on the Monte Carlo simulations. It is shown in the example of two-component that using PRM, the importance of system components to system safety can be quantified and compared as input information for maintenance planning.