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2, do not have a simple series– parallel topology and cannot be handled by this method. The decomposition method described next, avoids this limitation. 2 DECOMPOSITION METHOD FOR RELIABILITY ANALYSIS OF SYSTEMS WITH COMPLEX TOPOLOGY AND ITS LIMITATIONS The decomposition method is based on conditioning a complex system on the state of a key component K1 . As can be verified from the Venn diagram in Fig. tex 28/9/2006 16: 24 Page 33 3. 2 The event S (system is working) is the union of two mutually exclusive events: K 1 ∩ S and K1 ∩ S.

The process of determining S[i] continues until i becomes equal to n − k + 1. Then F(n) is simply equal to S[n − k + 1]. 1 NETWORK REDUCTION METHOD FOR RELIABILITY ANALYSIS OF COMPLEX SYSTEMS AND ITS LIMITATIONS In the reliability literature, there exist a number of methods for system reliability analysis oriented mainly towards systems with simple topology. Such are for example the method of network reduction and the event-tree method (Billinton and Allan, 1992). The essence of the network reduction method for example is reducing the entire system to a single equivalent element, by systematically combining appropriate series and parallel branches of the reliability network.

Only edges can fail, not nodes. Let us postulate the node with the lowest index to be the start node and the node with the largest index to be the end node Fig. 13. Reliability is then defined as the probability of existence of a path through working edges, from the start to the end node, at the end of the specified time interval. 1 A network of Type ‘Full Square Lattice’ The elementary building blocks of the system of type full square lattice in Fig. 13 are the cells in Fig. 13(b). The smallest system similar to the one in Fig.