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This paper presents a simple method for deriving a symbolic reliability expression of some practical systems such as a communication system having fixed channel capacities of its links, a power distribution system having limited power ratings of its power lines, a transport system which might not allow traffic more than a particular value, or a chemical system in which oil or gas flow through pipes is permissible only up to some safe limits. A system is good if and only if it is possible to transmit successfully the required capacity from source node to the sink node. This paper defines a group as a set of branches such that success of these branches ensures system success, as defined above. All such groups are obtained from a knowledge of the minimal paths of the system graph. The method is computerized and implemented on DEC-20 computer. Two examples are considered and their solutions presented to illustrate the technique.