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Inference for Two-Parameter Birnbaum–Saunders Distribution Based on Type-II Censored Data with Application to the Fatigue Life of Aluminum Coupon Cuts

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  • Omar M. Bdair

    (Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan
    Faculty of Medicine, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada
    Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada)

Abstract

This study addresses the problem of parameter estimation and prediction for type-II censored data from the two-parameter Birnbaum–Saunders (BS) distribution. The BS distribution is commonly used in reliability analysis, particularly in modeling fatigue life. Accurate estimation and prediction are crucial in many fields where censored data frequently appear, such as material science, medical studies and industrial applications. This paper presents both frequentist and Bayesian approaches to estimate the shape and scale parameters of the BS distribution, along with the prediction of unobserved failure times. Random data are generated from the BS distribution under type-II censoring, where a pre-specified number of failures ( m ) is observed. The generated data are used to calculate the Maximum Likelihood Estimation (MLE) and Bayesian inference and evaluate their performances. The Bayesian method employs Markov Chain Monte Carlo (MCMC) sampling for point predictions and credible intervals. We apply the methods to both datasets generated under type-II censoring and real-world data on the fatigue life of 6061-T6 aluminum coupons. Although the results show that the two methods yield similar parameter estimates, the Bayesian approach offers more flexible and reliable prediction intervals. Extensive R codes are used to explain the practical application of these methods. Our findings confirm the advantages of Bayesian inference in handling censored data, especially when prior information is available for estimation. This work not only supports the theoretical understanding of the BS distribution under type-II censoring but also provides practical tools for analyzing real data in reliability and survival studies. Future research will discuss extensions of these methods to the multi-sample progressive censoring model with larger datasets and the integration of degradation models commonly encountered in industrial applications.

Suggested Citation

  • Omar M. Bdair, 2025. "Inference for Two-Parameter Birnbaum–Saunders Distribution Based on Type-II Censored Data with Application to the Fatigue Life of Aluminum Coupon Cuts," Mathematics, MDPI, vol. 13(4), pages 1-24, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:590-:d:1588556
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    References listed on IDEAS

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    1. Achcar, Jorge Alberto, 1993. "Inferences for the Birnbaum-- Saunders fatigue life model using bayesian methods," Computational Statistics & Data Analysis, Elsevier, vol. 15(4), pages 367-380, May.
    2. Min Wang & Xiaoqian Sun & Chanseok Park, 2016. "Bayesian analysis of Birnbaum–Saunders distribution via the generalized ratio-of-uniforms method," Computational Statistics, Springer, vol. 31(1), pages 207-225, March.
    3. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
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