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Distributive lattices in the problems of structural analysis for complex systems

Grishkevich A.A.

Informatyka Teoretyczna i Stosowana

2005

R. 5, nr 8

19-27

The problem of estimating structural reliability of complex systems is considered, the model of these systems being represented as a graph of a network type. The structural reliability is understood as the reliability component conditioned by the structure of a system, i.e. by the composition of its elements and their interconnection, the quantitative calculation of the operation particularities of functioning of the elements being not taken into account. A breach connection between the two marked vertices (source and sink) is considered as the criterion of the system's failure. In mathematical terms the solution to this problem is formulated as the problem of finding cuts (minimum cuts) of a graph separating the twa marked vertices (source, sink). Lattice-theory properties of the minimum cuts allowing to achieve an effective method for their search and enumeration are considered.