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Element Importance

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

Abstract

Birnbaum Importance Measure (BIM) of element j is defined as \(\partial R/\partial p_j\), where R is system reliability. \(BIM_j\) measures the influence of element j reliability \(p_j\) on system reliability R. Element importance analysis plays important role in system reliability design. We consider in this chapter several methods of calculating \(BIM_j\) based on Monte Carlo, direct enumeration and structure analysis for some simple structures like series and parallel systems. We demonstrate also the impact of most important element improvement on system reliability.

Keywords

BIM Series/parallel systems Enumeration Monte Carlo Optimal design 

References

  1. 1.
    Birnbaum, Z. W. (1969). On the importance of different components in multicomponent system. In P. R. Krishnaiah (Ed.), Multivariate Analysis (pp. 581–592). New York: Academic.Google Scholar
  2. 2.
    Gertsbakh, I., & Shpungin, Y. (2009). Models of network reliability: Analysis, combinatorics and Monte Carlo. Boca Raton: CRC Press.zbMATHGoogle Scholar
  3. 3.
    Gertsbakh, I., & Shpungin, Y. (2011). Network reliability and resilience. Berlin: Springer.Google Scholar
  4. 4.
    Gertsbakh, I., & Shpungin, Y. (2012). Combinatorial approach to computing importance indices of coherent systems. Probability in Engineering and Information Sciences, 26, 117–128.CrossRefGoogle 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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