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

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Abstract

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.

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Authors and Affiliations

  1. F.C.E., Universidad Nacional de Cuyo, Mendoza, Argentina

    Ricardo Leiva

  2. Department of Management Science and Statistics, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA

    Anuradha Roy

  3. F.C.A. and I.C.B., Universidad Nacional de Cuyo, Mendoza, Argentina

    Rubén Bageta

  4. Materials Innovation Institute M2i, Delft, The Netherlands

    Juan Carlos Pina

  5. Eindhoven University of Technology, Eindhoven, The Netherlands

    Juan Carlos Pina

Authors
  1. Ricardo Leiva
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  2. Anuradha Roy
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  3. Rubén Bageta
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  4. Juan Carlos Pina
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Correspondence to Anuradha Roy.

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Leiva, R., Roy, A., Bageta, R. et al. An Extension of the Birnbaum-Saunders Distribution as a Model for Fatigue Failure Due to Multiple Cracks. J Stat Theory Pract 9, 88–121 (2015). https://doi.org/10.1080/15598608.2014.910149

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  • DOI: https://doi.org/10.1080/15598608.2014.910149

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