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Multidimensional Spectra of Multistate Systems with Binary Components

In: Recent Advances in System Reliability

Author

Listed:
  • Ilya Gertsbakh

    (Ben Gurion University of the Negev)

  • Yoseph Shpungin

    (Sami Shamoon College of Engineering)

Abstract

We consider coherent systems with K > 1 UP states and binary components. Introducing uniform measure on $$ n! $$ permutations of component numbers, we define a system’s combinatorial invariant, so-called multidimensional D-spectrum. By means of its marginal distributions we determine the probability that the system is in state $$ i \in [0,1,2, \ldots ,K] $$ , where 0 denotes system DOWN state. Formulas establishing the connection between the cumulative D-spectra and the number of system failure sets are derived. We present an example of a four-dimensional cubic network with 16 nodes, 32 edges and four terminals and the probabilistic description of its disintegration into four isolated clusters in the process of random edge failures.

Suggested Citation

  • Ilya Gertsbakh & Yoseph Shpungin, 2012. "Multidimensional Spectra of Multistate Systems with Binary Components," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel (ed.), Recent Advances in System Reliability, chapter 0, pages 49-61, Springer.
    • Handle: RePEc:spr:ssrchp:978-1-4471-2207-4_4
    DOI: 10.1007/978-1-4471-2207-4_4
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    Citations

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    Cited by:

    1. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "Computation of survival signatures for multi-state consecutive-k systems," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    2. He Yi & Narayanaswamy Balakrishnan & Lirong Cui, 2021. "Comparisons of Multi-State Systems with Binary Components of Different Sizes," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1309-1321, December.
    3. He Yi & Narayanaswamy Balakrishnan & Xiang Li, 2023. "Multi-State Joint Survival Signature for Multi-State Systems with Shared Multi-State Components," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.

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