Nonparametric Method for Estimating the Distribution of Time to Failure of Engineering Materials

  • Antonio Meneses
  • Salvador NayaEmail author
  • Ignacio López-de-Ullibarri
  • Javier Tarrío-Saavedra
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 175)


The aim of this work is to develop and assess a new method to estimate lifetime distribution in materials subjected to mechanical fatigue efforts. This problem is addressed from a statistical semiparametric and nonparametric perspective. Taking into account that fatigue failures in materials are due to crack formation and the subsequently induced crack growth, linear mixed effects regression models with smoothing splines (based on the linearized Paris-Erdogan model) are applied to estimate crack length as a function of the number of fatigue cycles. This model allows to simultaneously estimate the dependence between crack length and number of cycles in a sample of specimens. Knowing the crack length that induces material failure, the lifetime of each specimen is the crossing point of the crack length limit and the model crack length estimate. The authors propose to estimate the lifetime distribution function by applying nonparametric kernel techniques. In order to assess the influence of factors such as material type, material heterogeneity, and also that of the parameters of the estimation procedure, a simulation study consisting of different scenarios is performed. The results are compared with those of a procedure proposed by Meeker and Escobar (Statistical Methods for Reliability Data, Wiley, 1998, [16]) based on nonlinear mixed effects regression. Functional data analysis techniques are applied to perform this task. The proposed methodology estimates lifetime distribution of materials under fatigue more accurately in a wide range of scenarios.


Fatigue crack growth Paris-Erdogan model Nonparametric kernel distribution function estimation Linear mixed effects Statistical learning Nonlinear mixed effects 



This research has been supported by the Spanish Ministry of Economy and Competitiveness, grant MTM2014-52876-R (ERDF included), and by the Secretariat for Higher Education, Science, Technology and Innovation of Ecuador (SENESCYT).


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Antonio Meneses
    • 1
  • Salvador Naya
    • 3
    Email author
  • Ignacio López-de-Ullibarri
    • 2
  • Javier Tarrío-Saavedra
    • 3
  1. 1.Universidad Nacional de ChimborazoRiobambaEcuador
  2. 2.Universidade da Coruña. Escola Universitaria PolitécnicaFerrolSpain
  3. 3.Universidade da Coruña. Escola Politécnica SuperiorFerrolSpain

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