Reliability of a Network with Heterogeneous Components

  • Ilya B. GertsbakhEmail author
  • Yoseph Shpungin
  • Radislav Vaisman
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


We investigate reliability of network-type systems under the assumption that the network has \(K>1\) types of i.i.d. components. Our method is an extension the D-spectra method to K dimensions. It is based on Monte Carlo simulation for estimating the number of system failure sets having \(k_i\) components of i-th type, \(i=1,2,\ldots ,K\). We demonstrate our approach on a Barabasi-Albert network with 68 edges and 34 nodes and terminal connectivity as an operational criterion, for \(K=2\) types of nodes or edges as the components subject to failure.


Network terminal reliability Several types of components Two-dimensional spectrum Monte Carlo simulation Two-dimensional quantile 



The work of Radislav Vaisman was supported by the Australian Research Council Centre of Excellence for Mathematical & Statistical Frontiers, under grant number CE140100049.


  1. 1.
    Barabasi A, Albert R (1999) Emergence of scaling in random networks. Science 286:509–551MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Daqing L, Qiong Z, Zio E, Havlin S, Kang R (2015) Network reliability analysis based on percolation theory. Eng Reliab Syst Saf 142:1–15CrossRefGoogle Scholar
  3. 3.
    ElperinT Gertsbakh I, Lomonosov M (1991) Estimation of network reliability using graph evolution models. IEEE Trans Reliab 40:572–581CrossRefzbMATHGoogle Scholar
  4. 4.
    Gertsbakh I, Shpungin Y (2010) Models of network reliability: analysis, combinatorics and Monte Carlo. CRC Press, Boca RatonGoogle Scholar
  5. 5.
    Gertsbakh I, Shpungin Y (2011) Network reliability and resilience. Springer briefs in electrical and computer engineering. Springer, BerlinGoogle Scholar
  6. 6.
    Gertsbakh I, Shpungin Y (2012) Using D-spectra in Monte Carlo estimation of system reliability and component importance. In: FrenkelI LA (ed) Recent advances in system reliability. Springer, London, pp 49–61Google Scholar
  7. 7.
    Hudges J, Healy K (2014) Measuring the resilience of transport infrastructure. New Zealand Transport Agency, Report No. 546Google Scholar
  8. 8.
    Nagurney A, Qlang Q (2007) Robustness of transportation networks subject to degradable links. Lett J Explor Front PhysGoogle Scholar
  9. 9.
    Newman M (2010) Networks. Oxford University PressGoogle Scholar
  10. 10.
    Peeta S, Salman S, Gunnec D, Kannan V (2010) Predisaster investment decisions for strengthening a highway network. Comput Oper Res 37:1708–1719CrossRefzbMATHGoogle Scholar
  11. 11.
    Schneider C, Yazdani N, Araujo N, Havlin S, Herrmann H (2013) Toward designing robust coupled networks. Scientific reportsGoogle Scholar
  12. 12.
    Samaniego F (1985) On closure of the IFR under formation of coherent systems. IEEE Trans Reliab 34:69–72CrossRefzbMATHGoogle Scholar
  13. 13.
    Samaniego F (2007) System signatures and their applications in engineering reliability. SpringerGoogle Scholar
  14. 14.
    Samaniego F, Navarro J, Balakrishnan N (2011) Signature-based representation of the reliability of systems with heterogeneous components. J Appl Probab 48:856–867MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Sanchez-Silva M, Daniels M, Lieras G, Patino D (2005) A transport network reliability model for the efficient assignment of resources. Transp Res Part B: Methodol 39(1):47CrossRefGoogle Scholar
  16. 16.
    Sering R (2005) Quantile functions for multivariate approaches and applications. Stat Neerl 56(part B):214–232Google Scholar
  17. 17.
    Sterbenz J, Hutchinson D, Çetinkayaa E, Jabbara A, Rohrera J, Schöllerc M, Smith P (2010) Resilience and survivability in communication networks: strategies, principles and survey of discipline. Comput Netw 54(8):1245–1265CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Ilya B. Gertsbakh
    • 1
    Email author
  • Yoseph Shpungin
    • 2
  • Radislav Vaisman
    • 3
  1. 1.Department of MathematicsBen-Gurion UniversityBeer-ShevaIsrael
  2. 2.Software Engineering DepartmentSami Shamoon College of EngineeringBeer-ShevaIsrael
  3. 3.School of Mathematics and PhysicsThe University of QueenslandBrisbaneAustralia

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