Skip to main content

Stochastic Models for Risk and Failure Under Ageing

  • Chapter
  • First Online:
The Ageing of Materials and Structures
  • 598 Accesses

Abstract

We discuss several stochastic models for the failure of a material or for a risk event. Typically, the failure of a material occurs if the load on the material is higher than its designed maximal load value. However, the material can become weaker by age or use or slow deformation by near-critical loads. Such stochastic models are motivated by realistic situations where the critical load level of a material is not fixed and can change over time. Also, a Bayesian approach will be mentioned with possible applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  1. Cirillo P, Hüsler J (2009) An urn-based approach to generalized extreme shock models. Stat Probab Lett 79:969–976

    Article  MATH  Google Scholar 

  2. Cirillo P, Hüsler J (2009) On the upper tail of Italian firms size distri-bution. Physica A Stat Mech Appl 388:1546–1554

    Article  Google Scholar 

  3. Cirillo P, Hüsler J (2010) Shock models and firms’ default: parametric and nonparametric models. In: Festschrift T. Hettmansperger, WSPC proceedings

    Google Scholar 

  4. Cirillo P, Hüsler J, Muliere P (2010) A nonparametric approach to interacting failing systems with an application to credit risk modeling. Intern J Theor Appl Finance 13:1223–1240

    Article  MathSciNet  MATH  Google Scholar 

  5. Cirillo P, Hüsler J (2011) Generalized extreme shock models with a possibly increasing threshold. Probab Engine Inform Sci 25:1–16

    Article  MathSciNet  MATH  Google Scholar 

  6. Cirillo P, Hüsler J (2012) An urn model for cascading failures on a lattice. Probab Engine Inform Sci 26:509–534

    Article  MathSciNet  MATH  Google Scholar 

  7. Cirillo P, Hüsler J, Muliere P (2013) Alarm systems and catastrophesfrom a diverse point of view. Method Comp Appl Probab 15:821–839

    Article  MATH  Google Scholar 

  8. Cirillo P, Gallegati M, Hüsler J (2012) A Polya lattice model to study leverage dynamics and contagious financial fragility. Adv Compl Syst 15 supp. 02, 1250069 (26 pages)

    Google Scholar 

  9. Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling extremal events for insurance and finance. Springer, Berlin

    Book  MATH  Google Scholar 

  10. Falk M, Hüsler J, Reiss RD (2010) Laws of small numbers: extremesand rare events. In: DMV Seminar Band 23, 3rd edn. Birkhäuser, Basel

    Google Scholar 

  11. Gut A (1988) Stopped random walks. Springer, New York

    Book  MATH  Google Scholar 

  12. Gut A (1990) Cumulative shock models. Adv Appl Prob 22:504–507

    Article  MathSciNet  MATH  Google Scholar 

  13. Gut A, Hüsler J (2005) Realistic variation of shock models. Stat Probab Lett 74:187–204

    Article  MathSciNet  MATH  Google Scholar 

  14. Gut A, Hüsler J (1999) Extreme shock models. Extremes 2:293–305

    MathSciNet  MATH  Google Scholar 

  15. Gut A, Hüsler J (2009) Shock models. In: Nikulin MS et al (eds) Advances in Degradation Modeling: Applications to Reliability, Survival Analysis, and Finance. Series Statistics for Industry and Technology, Birkhäuser, Basel, pp 59–76

    Google Scholar 

  16. Gut A, Janson S (1983) The limiting behaviour of certain stopped sums and some applications. Scand J Statist 10:281–292

    MathSciNet  MATH  Google Scholar 

  17. de Haan L, Ferreira A (2006) Extreme value theory. Springer Series in Operations Research and Financial Engineering. Springer, New York

    Google Scholar 

  18. Reiss RD, Thomas M (2007) Statistical analysis of extreme values, 3rd edn. Birkhäuser, Basel

    MATH  Google Scholar 

  19. Resnick S (2007) Heavy-tail phenomena. Springer, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jürg Hüsler .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hüsler, J. (2018). Stochastic Models for Risk and Failure Under Ageing. In: van Breugel, K., Koleva, D., Beek, T. (eds) The Ageing of Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-70194-3_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70194-3_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70192-9

  • Online ISBN: 978-3-319-70194-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics