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Mathematics for Probabilistic Safety Assessments

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Selected Topics in Probabilistic Safety Assessment

Part of the book series: Topics in Safety, Risk, Reliability and Quality ((TSRQ,volume 38))

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Abstract

The tasks of interest for PSA practitioners are highly based on specialized mathematical tools, which are presented in this chapter. They are related (but not limited) to the following: Presentation of the general theoretical basis for the discrete probability spaces, i.e. formulas, description of the concepts and special aspects related to the random variables and distributions, variance, covariance, correlation and dependent failures, as well as confidence limits. The important aspects of logical structures and how the importance of various contributors to the plant challenges might be calculated are also detailed. The chapter presents also basic definitions and results from special researches on the mathematical background of PSA, as for instance coherent fault trees.

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References

  1. IEC (2010) IEC 61508-6:2010 - Functional safety of electrical/electronic/programmable electronic safety- related systems - Part 6: Guidelines on the application of IEC 61508-2 and IEC 61508-3

    Google Scholar 

  2. ISA (2015) ISA- TR84.00.02-2015 - Safety Integrity Level (SIL) Verification of Safety Instrumented Functions

    Google Scholar 

  3. SINTEF (2013) Reliability Prediction Method for Safety Instrumented Systems - PDS Method Handbook. A24442, Trondheim

    Google Scholar 

  4. Xu H, Dugan JB (2004) Combining dynamic fault trees and event trees for probabilistic risk assessment. In: Annual Symposium Reliability and Maintainability, 2004 - RAMS, pp 214–219. https://doi.org/10.1109/RAMS.2004.1285450

  5. Agency NE (2018) NEA / CSNI report. www.oecd-nea.org/nsd/docs/indexcsni.html

  6. Andrews JD, Dunnett SJ (2000) Event-tree analysis using binary decision diagrams. IEEE Trans Reliab 49(2):230–238. https://doi.org/10.1109/24.877343

    Article  Google Scholar 

  7. Fussell JB, Aber EF, Rahl RG (1976) On the quantitative analysis of priority-and failure logic. IEEE Trans Reliab R-25(5):324–326. https://doi.org/10.1109/TR.1976.5220025

    Article  Google Scholar 

  8. Tang Z, Dugan JB (2004) Minimal cut set/sequence generation for dynamic fault trees. In: Annual symposium reliability and maintainability, 2004 - RAMS, pp 207–213. https://doi.org/10.1109/RAMS.2004.1285449

  9. (2013) Zamojski W, Mazurkiewicz J, Sugier J, Walkowiak T, Kacprzyk J (eds) (2013) Quantification of simultaneous-AND gates in temporal fault trees. Advances in intelligent systems and computing, vol 224. Springer, New York. https://doi.org/10.1007/978-3-319-00945-2

    Google Scholar 

  10. (2012) .1007/978-3-642-33678 Quantification of priority-OR gates in temporal fault trees. Lecture notes in computer science, vol 7612. Springer, New York. https://doi.org/10.1007/978-3-642-33678-2

    Google Scholar 

  11. Xing L, Shrestha A, Dai Y (2011) Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures. Reliab Eng Syst Saf 96(10):1375–1385. https://doi.org/10.1016/j.ress.2011.05.007, http://www.sciencedirect.com/science/article/pii/S0951832011001050

    Article  Google Scholar 

  12. Krčál J, Krčál P (2015) Scalable analysis of fault trees with dynamic features. In: 2015 45th Annual IEEE/IFIP international conference on dependable systems and networks, pp 89–100. https://doi.org/10.1109/DSN.2015.29

  13. Rauzy A (2015) Towards a sound semantics for dynamic fault trees. Reliab Eng Syst Saf 142:184–191. https://doi.org/10.1016/j.ress.2015.04.017

    Article  Google Scholar 

  14. Fussell JB (1975) How to hand-calculate system reliability and safety characteristics. IEEE Trans Reliab R-24(3):169–174. https://doi.org/10.1109/TR.1975.5215142

    Article  Google Scholar 

  15. Kuo W, Zhu X (2012) Importance measures in reliability, risk and optimization - principles and applications. Wiley, Chichester

    Book  Google Scholar 

  16. Lambert H (1975) Measures of importance of events and cut sets in fault trees. In: Barlow RE, Fussel JB, Singpurwalla ND (eds) Reliability and fault tree analysis. SIAM Press, Philadelphia, pp 77–100

    Google Scholar 

  17. Bryant RE (1986) Graph-based algorithms for boolean function manipulation. IEEE Trans Comput C-35(8):677–691. https://doi.org/10.1109/TC.1986.1676819

    Article  Google Scholar 

  18. Ulmeanu AP (2012) Analytical method to determine uncertainty propagation in fault trees by means of binary decision diagrams. IEEE Trans Reliab 61(1):84–94. https://doi.org/10.1109/TR.2012.2182812

    Article  Google Scholar 

  19. Dutuit Y, Rauzy A (2014) Importance factors of coherent systems: a review. Proc Inst Mech Eng Part O: J Risk Reliab 228(3):313–323. https://doi.org/10.1177/1748006X13512296

    Article  Google Scholar 

  20. Birnbaum ZW (1969) On the importance of different components in a multicomponent system. pp 581–592

    Google Scholar 

  21. Armstrong MJ (1995) Joint reliability-importance of components. IEEE Trans Reliab 44(3):408–412. https://doi.org/10.1109/24.406574

    Article  Google Scholar 

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Authors and Affiliations

  1. Division of Logic and Models in Science, Romanian Academy, Bucharest, Romania

    Dan Serbanescu

  2. Department of Power Generation and Use, Polytechnic University of Bucharest, Bucharest, Romania

    Anatoli Paul Ulmeanu

Authors
  1. Dan Serbanescu
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  2. Anatoli Paul Ulmeanu
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Correspondence to Dan Serbanescu .

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Serbanescu, D., Ulmeanu, A. (2020). Mathematics for Probabilistic Safety Assessments. In: Selected Topics in Probabilistic Safety Assessment. Topics in Safety, Risk, Reliability and Quality, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-030-40548-9_4

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  • DOI: https://doi.org/10.1007/978-3-030-40548-9_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-40547-2

  • Online ISBN: 978-3-030-40548-9

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