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Critical States and Importance Factors

In: Reliability Assessment of Safety and Production Systems

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  • Jean-Pierre Signoret

    (Total Professeurs Associés)

  • Alain Leroy

Abstract

This chapter introduces the concepts of critical states and of importance factors and deals with coherent systems but non-coherent situations are also illustrated. The critical states are of utmost importance for calculating failure rates and frequencies from Boolean (Chap. 22 ) or Markovian (Chap. 31 ) models and also to understand the meaning of the importance factors. The importance factors are indicators measuring the impact of a component probability of failure/success with regards to the overall system probability of failure/success. This can be done for various purposes and the following importance factors (IF) are presented and analysed: Vesely-Fussell IF which is of utmost importance when minimal cut sets are involved, MIF (marginal or Birnbaum IF) which is the basis for failure frequency and failure rate calculations, CIF (critical or Lambert IF), DIF (diagnostic IF), RAW (risk achievement worth), RRW (risk reduction worth), DIM (differential importance measure) and BPIF (Barlow-Proschan IF). The difference between the meanings and interest of some of them is rather subtle and clarifications are provided. An example is provided at the end to illustrate how, for a given simple system, the component impacts are ranked according to each of them.

Suggested Citation

  • Jean-Pierre Signoret & Alain Leroy, 2021. "Critical States and Importance Factors," Springer Series in Reliability Engineering, in: Reliability Assessment of Safety and Production Systems, chapter 0, pages 333-371, Springer.
    • Handle: RePEc:spr:ssrchp:978-3-030-64708-7_24
    DOI: 10.1007/978-3-030-64708-7_24
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    Cited by:

    1. Ali Nouri Qarahasanlou & Ali Zamani & Abbas Barabadi & Mahdi Mokhberdoran, 2021. "Resilience Assessment: A Performance-Based Importance Measure," Energies, MDPI, vol. 14(22), pages 1-16, November.

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