Elementary Methods for Reliability Evaluation
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This chapter describes elementary approaches to network reliability evaluation. The first method is based on making a list of all \(2^n\) binary network states. This method is very good but is applicable only to rather small networks with \(n=4-6\) elements. For \(n>6\) we need a computer to make the list of all states. Next in line is so-called Crude Monte Carlo (CMC). It consists of performing a series of M lottery-type random experiments of modelling element states and analysing the network state (UP/DOWN) as the result of this experiment. If we observe \(M_1\) times the network in DOWN state, \(M_1/M\) is the CMC estimate of network DOWN probability. CMC has, however, an algorithmic complication in identifying the random lottery result as the network DOWN or UP state. We describe in Sect. 4.5 a technique called DSS (disjoint set structures) for simple and fast identification of network state. During the first reading of this chapter, Sect. 4.5 can be omitted and studied only when the reader starts writing computer codes. This chapter contains also estimation of rel.err. of the CMC, and demonstrates how to analyse network reliability in time (dynamic reliability).