Abstract
Fault trees constitute one of the essential formalisms for static safety analysis of various industrial systems. Dynamic fault trees (DFT) enrich the formalism by support for time-dependent behaviour, e.g., repairs or dynamic dependencies. This enables more realistic and more precise modelling, and can thereby avoid overly pessimistic analysis results. But analysis of DFT is so far limited to substantially smaller models than those required for instance in the domain of nuclear power safety. This paper considers so called SD fault trees, where the user is free to express each equipment failure either statically, without modelling temporal information, or dynamically, allowing repairs and other timed interdependencies. We introduce an analysis algorithm for an important subclass of SD fault trees. The algorithm employs automatic abstraction techniques effectively, and thereby scales similarly to static analysis algorithms, albeit allowing for a more realistic modelling and analysis. We demonstrate the applicability of the method by an experimental evaluation on fault trees of nuclear power plants.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
This is to compensate for the cutoff error bound \(\varepsilon _{g}\).
- 2.
Whenever the event \(b_i\) belongs to a cutset of a gate \(g \not \in G_i\), we create a copy of \(b_i\) and direct all the transitions from gates g to \(b_i\) to the new basic event. Thus whenever \(b_i\) is abstracted in gates \(g \in G_i\), it is not abstracted away in gates \(g \not \in G_i\).
- 3.
Reduction of a triggered basic event is possible due to reduction of its triggering gate.
References
Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans. Softw. Eng. 29(6), 524–541 (2003)
Dugan, B.J., Bavuso, S.J., Boyd, M.: Dynamic fault-tree models for fault-tolerant computer systems. IEEE Trans. Reliab. 41(3), 363–377 (1992)
Boudali, H., Crouzen, P., Stoelinga, M.: A rigorous, compositional, and extensible framework for dynamic fault tree analysis. IEEE Trans. Depandable Sec. Compt. 7(2), 128–143 (2010)
Bouissou, M., Bon, J.L.: A new formalism that combines advantages of fault-trees and Markov models: Boolean logic driven Markov processes. Reliab. Eng. Syst. Saf. 82(2), 149–163 (2003)
Brázdil, T., Hermanns, H., Krčál, J., Křetínský, J., Řehák, V.: Verification of open interactive Markov chains. In: FSTTCS. LIPIcs, vol. 18, pp. 474–485 (2012)
Butkova, Y., Hatefi, H., Hermanns, H., Krcál, J.: Optimal continuous time Markov decisions. In: Finkbeiner, B., et al. (eds.) ATVA 2015. LNCS, vol. 9364, pp. 166–182. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24953-7_12
Center for Chemical Process Safety: Guidelines for Hazard Evaluation Procedures, 3rd edn. Wiley, Hoboken (2008)
Fussell, J.B., Vesely, W.E.: A new methodology for obtaining cut sets for fault trees. Trans. Am. Nucl. Soc. 15, 262–263 (1972)
IAEA: Development and Application of Level 1 Probabilistic Safety Assessment for Nuclear Power Plants, IAEA Safety Standards Series No. SSG-3 (2010)
IAEA: Development and Application of Level 2 Probabilistic Safety Assessment for Nuclear Power Plants, IAEA Safety Standards Series No. SSG-4 (2010)
Krčál, J., Krčál, P.: Scalable analysis of fault trees with dynamic features. In: DSN 2015, pp. 89–100 (2015)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)
Lloyd’s Register Consulting: RiskSpectrum, Theory Manual (2013)
NASA: Fault Tree Handbook with Aerospace Applications (2002)
Ruijters, E.J.J., Stoelinga, M.I.A.: Fault tree analysis: a survey of the state of the art in modeling, analysis and tools. Comput. Sci. Rev. 15, 29–62 (2015)
Vesely, W., Davis, T., Denning, R., Saltos, N.: Measures of risk importance and their application (NUREG/CR-3385). US Nuclear Regulatory Commission (1983)
Vesely, W., Goldberg, F., Roberts, N., Haasl, D.: Fault Tree Handbook(NUREG/CR-0492). US Nuclear Regulatory Commission (1981)
Wood, S., Smith, C.L., Kvarfordt, K.J., Beck, S.: Systems Analysis Programs for Hands-on Integrated Reliability Evaluations (SAPHIRE): Summary Manual (NUREG/CR-6952, vol. 1). US Nuclear Regulatory Commission (2008)
Acknowledgments
This work is partly supported by the ERC Advanced Investigators Grant 695614 (POWVER), by the EU 7th Framework Programme under grant agreement no. 318490 (SENSATION) and 288175 (CERTAINTY), by the DFG Transregional Collaborative Research Centre SFB/TR 14 AVACS, by the CDZ project 1023 (CAP), and by the Czech Science Foundation, grant No. P202/12/G061.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Bäckström, O., Butkova, Y., Hermanns, H., Krčál, J., Krčál, P. (2016). Effective Static and Dynamic Fault Tree Analysis. In: Skavhaug, A., Guiochet, J., Bitsch, F. (eds) Computer Safety, Reliability, and Security. SAFECOMP 2016. Lecture Notes in Computer Science(), vol 9922. Springer, Cham. https://doi.org/10.1007/978-3-319-45477-1_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-45477-1_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45476-4
Online ISBN: 978-3-319-45477-1
eBook Packages: Computer ScienceComputer Science (R0)