Estimation of Two Parameter Birnbaum-Saunders Distribution Based on Type-II Right Censored Reliability Data Using Genetic Algorithm

Authors

  • Ali Assoumani Rassoul Department of Statistics, Çukurova University, Turkey
  • Güzin Yüksel Department of Statistics, Çukurova University, Turkey https://orcid.org/0000-0002-1644-3696

DOI:

https://doi.org/10.26713/cma.v16i1.2259

Keywords:

Birnbaum-Saunders distribution, Genetic Algorithm, Maximum Likelihood, Type-II right censored data

Abstract

The Birnbaum-Saunders (BS) distribution is a common reliability distribution used in scientific studies. There have been studies in the literature on parameter estimates for this distribution. Furthermore, in many studies, it is recommended to use Genetic Algorithm (GA) optimization methods for parameter estimation in modeling. This article focuses on estimating the model parameters of a twoparameter Birnbaum-Saunders distribution for Type II right censored reliability data. For parameter estimation of the Birnbaum-Saunders distribution, we propose the Genetic Algorithm (GA) method as an alternative to the Maximum Likelihood (ML) estimation method. Psi31 data is often used as an example to show the limitations of prediction methods when using inaccurate data. In addition, the performances of ML and GA methods were investigated through Monte Carlo simulation with different sample sizes and censorship rates.

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References

Ö. Akay, E. Tekeli and G. Yüksel, Genetic algorithm with new fitness function for clustering, Iranian Journal of Science and Technology, Transactions A: Science 44 (2020), 865 – 874, DOI: 10.1007/s40995-020-00890-8.

N. Balakrishnan and A. Cohen, Order Statistics and Inference: Estimation Methods, Academic Press, San Diego, (1990), DOI: 10.1016/C2009-0-22411-1.

Z. W. Birnbaum and S. C. Saunders, Estimation for a family of life distributions with applications to fatigue, Journal of Applied Probability 6(2) (1969), 328 – 347, DOI: 10.2307/3212004.

J. H. Holland, Adaptation in Natural and Artificial Systems, 2nd edition, University of Michigan Press, MIT Press, Ann Arbor, (1992).

N. L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, Volume 2, 2nd edition, John Wiley, New York, xix + 719 pages (1995).

D. Kundu, N. Kannan and N. Balakrishnan, On the hazard function of Birnbaum–Saunders distribution and associated inference, Computational Statistics & Data Analysis 52(5) (2008), 2692 – 2702, DOI: 10.1016/j.csda.2007.09.021.

Y. H. Lee, S. K. Park and D.-E. Chang, Parameter estimation using the genetic algorithm and its impact on quantitative precipitation forecast, Annales Geophysicae 24(12) (2006), 3185 – 3189, DOI: 10.5194/angeo-24-3185-2006.

M. Naderi, A. Arabpour, T.-I. Lin and A. Jamalizadeh, Nonlinear regression models based on the normal mean–variance mixture of Birnbaum–Saunders distribution, Journal of the Korean Statistical Society 46(3) (2017), 476 – 485, DOI: 10.1016/j.jkss.2017.02.002.

H. K. T. Ng, D. Kundu and N. Balakrishnan, Point and interval estimation for the two-parameter Birnbaum–Saunders distribution based on Type-II censored samples, Computational Statistics & Data Analysis 50(11) (2006), 3222 – 3242, DOI: 10.1016/j.csda.2005.06.002.

E. Tekeli and G. Yüksel, Estimating the parameters of twofold Weibull mixturemodel in rightcensored reliability data by using genetic algorithm, Communications in Statistics - Simulation and Computation 51(11) (2022), 6621 – 6634, DOI: 10.1080/03610918.2020.1808681.

E. Ursu and J.-C. Pereau, Estimation and identification of periodic autoregressive models with one exogenous variable, Journal of the Korean Statistical Society 46(4) (2017), 629 – 640, DOI: 10.1016/j.jkss.2017.07.001

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Published

01-07-2025
CITATION

How to Cite

Rassoul, A. A., & Yüksel, G. (2025). Estimation of Two Parameter Birnbaum-Saunders Distribution Based on Type-II Right Censored Reliability Data Using Genetic Algorithm. Communications in Mathematics and Applications, 16(1), 353–366. https://doi.org/10.26713/cma.v16i1.2259

Issue

Vol. 16 No. 1 (2025)

Section

Research Article

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