Journal of Statistical Theory and Practice

, Volume 9, Issue 1, pp 88–121 | Cite as

An Extension of the Birnbaum-Saunders Distribution as a Model for Fatigue Failure Due to Multiple Cracks

  • Ricardo Leiva
  • Anuradha RoyEmail author
  • Rubén Bageta
  • Juan Carlos Pina


In this article, we propose an extension of the Birnbaum-Saunders distribution to model the more realistic situations where the fatigue failure time of a material is due to the growth of multiple cracks. Properties of the proposed extended Birnbaum-Saunders (EBS) distribution are discussed; hazard function and the change point of the hazard function of this EBS distribution are derived. Maximum likelihood estimates of the unknown parameters as well as the hazard functions for two special cases of the new EBS distribution are also obtained. Finally, Monte Carlo simulations are carried out to assess the performance of the EBS distribution parameters.


Birnbaum-Saunders distribution Hazard function Maximum likelihood estimates Monte Carlo simulations Multiple cracks 

AMS Subject Classification

Primary 62E15 Secondary 62H12 


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Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  • Ricardo Leiva
    • 1
  • Anuradha Roy
    • 2
    Email author
  • Rubén Bageta
    • 3
  • Juan Carlos Pina
    • 4
    • 5
  1. 1.F.C.E.Universidad Nacional de CuyoMendozaArgentina
  2. 2.Department of Management Science and StatisticsThe University of Texas at San AntonioSan AntonioUSA
  3. 3.F.C.A. and I.C.B.Universidad Nacional de CuyoMendozaArgentina
  4. 4.Materials Innovation Institute M2iDelftThe Netherlands
  5. 5.Eindhoven University of TechnologyEindhovenThe Netherlands

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