Risk Importance Measures

  • Enrico Zio
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


Quantitative information about the role that the components of a system play with respect to its risk, safety, reliability and availability is of great practical aid to system designers and operators. Indeed, the identification of which components mostly contribute to the system failure behavior allows one to trace system design bottlenecks and provides guidelines for effective operation and maintenance actions for system performance improvement.


Basic Event Importance Measure Exceedance Measure Common Mode Failure System Failure Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The Author would like to thank Dr. Luca Podofillini of the Paul Scherrer Institute, Switzerland, for the preparation of the material and in particular for contributing to the development of the work related to Examples 6 and 7 and Mr. Michele Compare for contributing to the development of  Chap. 14. Finally, many thanks go to Mrs. Lucia Golea for assisting in the preparation of the manuscript.


  1. 1.
    Apostolakis GE (1990) The concept of probability in safety assessments of technological systems. Science 250:1359–1364CrossRefGoogle Scholar
  2. 2.
    Armstrong MJ (1995) Joint reliability-importance of elements. IEEE Trans Reliab 44(3):408–412CrossRefGoogle Scholar
  3. 3.
    Armstrong MJ (1997) Reliability-importance and dual failure-mode elements. IEEE Trans Reliab 46(2):212–221CrossRefGoogle Scholar
  4. 4.
    Aven T (1993) On performance measures for multistate monotone systems. Reliab Eng Syst Saf 41:259–266CrossRefGoogle Scholar
  5. 5.
    Aven T, Østebø R (1986) Two new importance measures for a flow network system. Reliab Eng 14:75–80CrossRefGoogle Scholar
  6. 6.
    Baraldi P, Zio E, Compare M (2008) Importance measures in presence of uncertainties. In: Proceedings of SSARS 2008, Gdańsk/Sopot, PolandGoogle Scholar
  7. 7.
    Birnbaum LW (1969) On the importance of different elements in a multi-element system. Multivariate analysis, vol 2. Academic Press, New YorkGoogle Scholar
  8. 8.
    Borgonovo E (2006) Measuring uncertainty importance: investigation and comparison of alternative approaches. Risk Anal 26(5):1349–1361CrossRefGoogle Scholar
  9. 9.
    Borgonovo E, Apostolakis GE (2001) A new importance measure for risk-informed decision making. Reliab Eng Syst Saf 72:193–212CrossRefGoogle Scholar
  10. 10.
    Cheok MC, Parry GW, Sherry RR (1998) Use of importance measures in risk informed applications. Reliab Eng Syst Saf 60:213–226CrossRefGoogle Scholar
  11. 11.
    Elsayed EA (1996) Reliability engineering. Addison Wesley Longman, EnglandGoogle Scholar
  12. 12.
    Fussell JB (1975) How to calculate system reliability and safety characteristics. IEEE Trans Reliab R-24(3):169–174CrossRefGoogle Scholar
  13. 13.
    Griffith WS (1980) Multistate reliability models. J Appl Prob 17:735–744MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Hoare CA (1962) Quicksort. Comput J 5:10–15MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Hong JS, Lie CH (1993) Joint reliability-importance of two edges in an undirected network. IEEE Trans Reliab 42(1):17–23MATHCrossRefGoogle Scholar
  16. 16.
    Høyland A, Rausand M (1994) System reliability theory: models and statistical methods. Wiley, NJGoogle Scholar
  17. 17.
    Kim C, Baxter LA (1987) Reliability importance for continuum structure functions. J Appl Prob 24:779–785MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Levitin G, Lisnianski A (1999) Importance and sensitivity analysis of multi-state systems using the universal generating function method. Reliab Eng Syst Saf 65:271–282CrossRefGoogle Scholar
  19. 19.
    Marseguerra M, Zio E, Podofillini L (2005) First-order sensitivity analysis of a nuclear safety system by Monte Carlo simulation. Reliab Eng Syst Saf 90:162–168CrossRefGoogle Scholar
  20. 20.
    Meng FC (1993) Element-relevancy and characterization results in multi-state systems. IEEE Trans Reliab 42(3):478–483MATHCrossRefGoogle Scholar
  21. 21.
    Meng FC (1995) Some further results on ranking the importance of system elements. Reliab Eng Syst Saf 47:97–101CrossRefGoogle Scholar
  22. 22.
    Meng FC (1996) Comparing the importance of system elements by some structural characteristics. IEEE Trans Reliab 45(1):59–65CrossRefGoogle Scholar
  23. 23.
    Modarres M (2006) Risk analysis in engineering: probabilistic techniques, tools and trends. CRC Press, USAGoogle Scholar
  24. 24.
    van der Borst M, Shoonakker H (2001) An overview of PSA importance measures. Reliab Eng Syst Saf 72(3):241–245CrossRefGoogle Scholar
  25. 25.
    Vasseur D, Llory M (1999) International survey on PSA figures of merit. Reliab Eng Syst Saf 66:261–274CrossRefGoogle Scholar
  26. 26.
    Vesely WE (1998) Supplemental viewpoints on the use of importance measures in risk-informed regulatory applications. Reliab Eng Syst Saf 60:257–259CrossRefGoogle Scholar
  27. 27.
    Wash-1400 (NUREG 75/014) (1975) Reactor safety study: an assessment of accident risks in US. Commercial Nuclear Power Plants, Appendix 2, Fault TreesGoogle Scholar
  28. 28.
    Wu S, Chan L (2003) Performance utility-analysis of multi-state systems. IEEE Trans Reliab 52(1):14–20CrossRefGoogle Scholar
  29. 29.
    Youngblood RW (2001) Risk significance and safety significance. Reliab Eng Syst Saf 73:121–136CrossRefGoogle Scholar
  30. 30.
    Zio E (2007) An introduction to the basics of reliability and risk analysis, Series in quality, reliability and engineering statistics, vol. 13, World Scientific, SingaporeGoogle Scholar
  31. 31.
    Zio E, Podofillini L (2003) Importance measures of multi-state components in multi-state systems. Int J Reliab Qual Safety Eng 10(3):289–310CrossRefGoogle Scholar
  32. 32.
    Zio E, Podofillini L (2004) A second-order differential importance measure for reliability and risk applications, SAMO, Sensitivity Analysis of Model Output, March 8–11, 2004, Santa Fe. Available on CD-romGoogle Scholar
  33. 33.
    Zio E, Marella M, Podofillini L (2004) A comparison of different importance measures for multistate systems, MMR, mathematical methods in reliability, June 21–25, Santa Fe, New Mexico, USAGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Ecole Centrale Paris et SupelecParisFrance
  2. 2.Politecnico di MilanoMilanItaly

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