Elementary Methods for Reliability Evaluation

  • Ilya GertsbakhEmail author
  • Yoseph Shpungin
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


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).


CMC State enumeration DSS rel.err. Dynamic reliability 


  1. 1.
    Gertsbakh, I., & Shpungin, Y. (2009). Models of Network Reliability: Analysis Combinatorics and Monte Carlo. Boca Raton: CRC Press.zbMATHGoogle Scholar
  2. 2.
    Cormen, T., Leiserson, C., Rivest, R., & Stein, C. (2010) Introduction to Algorithms. (3rd ed.). Cambridge: The MIT Press.Google Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsBen Gurion UniversityBeer-ShevaIsrael
  2. 2.Software Engineering DepartmentShamoon College of EngineeringBeer-ShevaIsrael

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