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The paper describes an efficient algorithm for evaluating the minimal cut sets of any general network. The algorithm is based on Boolean algebra and set theory, and contains many important improvements. The four most important features are 1. only one set of topological input data is required to evaluate the minimal cuts and reliability indices of every output node; 2. a mix of undirectional, bidirectional and multi ended components can be included very simply; 3. any number of input nodes may be specified; 4. a new concept of overall system reliability permits different, large, and complex systems to be compared. The computational efficiency of the algorithm is clearly indicated by the fact that the time required to analyse Example 1 on a CDC7600 was 0.7 sec. The storage required with the appropriate arrays dimensioned for a system having 100 components and up to 125 minimal cut sets per output node is 15 k-words. These times and storage include the overall system reliability analysis.