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The log-normal modified Weibull distribution and its reliability implications

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  • Shakhatreh, Mohammed K.
  • Lemonte, Artur J.
  • Moreno–Arenas, Germán

Abstract

This paper introduces a new lifetime distribution to describe and analyze monotone, upside-down bathtub, bathtub-shaped and modified bathtub-shaped failure rates. An important property of the new distribution is that it can have a bathtub-shaped failure rate function with a long flat region, which may be very useful in reliability contexts. Some structural properties of the new model are obtained, and a detailed study of its mean residual life function is provided. In particular, we focus on the fundamental associations between the failure rate and mean residual life regarding their change points. The maximum likelihood method is used to estimate the model parameters. The usefulness of the new distribution is illustrated by means of empirical applications to three real datasets from engineering reliability in order to prove its versatility in practice.

Suggested Citation

  • Shakhatreh, Mohammed K. & Lemonte, Artur J. & Moreno–Arenas, Germán, 2019. "The log-normal modified Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 6-22.
    • Handle: RePEc:eee:reensy:v:188:y:2019:i:c:p:6-22
    DOI: 10.1016/j.ress.2019.03.014
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    1. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    2. He, Bo & Cui, Weimin & Du, Xiaofeng, 2016. "An additive modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 28-37.
    3. Zeng, Hongtao & Lan, Tian & Chen, Qiming, 2016. "Five and four-parameter lifetime distributions for bathtub-shaped failure rate using Perks mortality equation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 307-315.
    4. Xu, Meng & Droguett, Enrique López & Lins, Isis Didier & das Chagas Moura, Márcio, 2017. "On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 93-105.
    5. Almalki, Saad J. & Yuan, Jingsong, 2013. "A new modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 164-170.
    6. Zhang, Tieling & Xie, Min, 2011. "On the upper truncated Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 194-200.
    7. Baker, Rose, 2019. "New survival distributions that quantify the gain from eliminating flawed components," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 493-501.
    8. Jiang, R., 2013. "A new bathtub curve model with a finite support," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 44-51.
    9. Domma, Filippo & Condino, Francesca, 2014. "A new class of distribution functions for lifetime data," Reliability Engineering and System Safety, Elsevier, vol. 129(C), pages 36-45.
    10. Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.
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    Cited by:

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    2. Tien Thanh Thach & Radim Bris, 2020. "Improved new modified Weibull distribution: A Bayes study using Hamiltonian Monte Carlo simulation," Journal of Risk and Reliability, , vol. 234(3), pages 496-511, June.
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    8. Gupta, Sanjib Kumar & Chattopadhyay, Gaurangadeb, 2022. "Early detection of reliability related problems from two-dimensional warranty data considering labour code priority index," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    9. Luis Carlos Méndez-González & Luis Alberto Rodríguez-Picón & Manuel Iván Rodríguez Borbón & Hansuk Sohn, 2023. "The Chen–Perks Distribution: Properties and Reliability Applications," Mathematics, MDPI, vol. 11(13), pages 1-19, July.
    10. Christian Acal & Juan E. Ruiz-Castro & David Maldonado & Juan B. Roldán, 2021. "One Cut-Point Phase-Type Distributions in Reliability. An Application to Resistive Random Access Memories," Mathematics, MDPI, vol. 9(21), pages 1-13, October.

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