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Diagnostics in Birnbaum–Saunders accelerated life models with an application to fatigue data

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  • Víctor Leiva
  • Edgardo Rojas
  • Manuel Galea
  • Antonio Sanhueza

Abstract

In industrial statistics, there is great interest in predicting with precision lifetimes of specimens that operate under stress. For example, a bad estimation of the lower percentiles of a life distribution can produce significant monetary losses to organizations due to an excessive amount of warranty claims. The Birnbaum–Saunders distribution is useful for modeling lifetime data. This is because such a distribution allows us to relate the total time until the failure occurs to some type of cumulative damage produced by stress. In this paper, we propose a methodology for detecting influence of atypical data in accelerated life models on the basis of the Birnbaum–Saunders distribution. The methodology developed in this study should be considered in the design of structures and in the prediction of warranty claims. We conclude this work with an application of the proposed methodology on the basis of real fatigue life data, which illustrates its importance in a warranty claim problem. Copyright © 2012 John Wiley & Sons, Ltd.

Suggested Citation

  • Víctor Leiva & Edgardo Rojas & Manuel Galea & Antonio Sanhueza, 2014. "Diagnostics in Birnbaum–Saunders accelerated life models with an application to fatigue data," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(2), pages 115-131, March.
    • Handle: RePEc:wly:apsmbi:v:30:y:2014:i:2:p:115-131
    DOI: 10.1002/asmb.1944
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    Cited by:

    1. Mário Fernando De Sousa & Helton Saulo & Víctor Leiva & Paulo Scalco, 2018. "On Some Properties Of A New Asymmetry-Based Tobit Model," Anais do XLIV Encontro Nacional de Economia [Proceedings of the 44th Brazilian Economics Meeting] 129, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    2. Robert G. Aykroyd & Víctor Leiva & Carolina Marchant, 2018. "Multivariate Birnbaum-Saunders Distributions: Modelling and Applications," Risks, MDPI, vol. 6(1), pages 1-25, March.
    3. Leiva, Víctor & Ruggeri, Fabrizio & Saulo, Helton & Vivanco, Juan F., 2017. "A methodology based on the Birnbaum–Saunders distribution for reliability analysis applied to nano-materials," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 192-201.

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