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New generalized-X family: Modeling the reliability engineering applications

Author

Listed:
  • Wanting Wang
  • Zubair Ahmad
  • Omid Kharazmi
  • Clement Boateng Ampadu
  • E H Hafez
  • Marwa M Mohie El-Din

Abstract

As is already known, statistical models are very important for modeling data in applied fields, particularly in engineering, medicine, and many other disciplines. In this paper, we propose a new family to introduce new distributions suitable for modeling reliability engineering data. We called our proposed family a new generalized-X family of distributions. For the practical illustration, we introduced a new special sub-model, called the new generalized-Weibull distribution, to describe the new family’s significance. For the proposed family, we introduced some mathematical reliability properties. The maximum likelihood estimators for the parameters of the new generalized-X distributions are derived. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. To assess the efficiency of the proposed model, the new generalized-Weibull model is applied to the coating machine failure time data. Finally, Bayesian analysis and performance of Gibbs sampling for the coating machine failure time data are also carried out. Furthermore, the measures such as Gelman-Rubin, Geweke and Raftery-Lewis are used to track algorithm convergence.

Suggested Citation

  • Wanting Wang & Zubair Ahmad & Omid Kharazmi & Clement Boateng Ampadu & E H Hafez & Marwa M Mohie El-Din, 2021. "New generalized-X family: Modeling the reliability engineering applications," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-26, March.
    • Handle: RePEc:plo:pone00:0248312
    DOI: 10.1371/journal.pone.0248312
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    References listed on IDEAS

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    1. Omid Kharazmi & Ali Saadatinik & Shahla Jahangard, 2019. "Odd Hyperbolic Cosine Exponential-Exponential (OHC-EE) Distribution," Annals of Data Science, Springer, vol. 6(4), pages 765-785, December.
    2. Faton Merovci & Morad Alizadeh & Haitham M. Yousof & G. G. Hamedani, 2017. "The exponentiated transmuted-G family of distributions: Theory and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10800-10822, November.
    3. Suleman Nasiru & Peter N. Mwita & Oscar Ngesa, 2017. "Exponentiated Generalized Transformed-Transformer Family of Distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(4), pages 1-1.
    4. Wei Zhao & Saima K Khosa & Zubair Ahmad & Muhammad Aslam & Ahmed Z Afify, 2020. "Type-I heavy tailed family with applications in medicine, engineering and insurance," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-24, August.
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