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A new class of bivariate Lindley distributions based on stress and shock models and some of their reliability properties

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  • Oliveira, Ricardo P.
  • Achcar, Jorge A.
  • Mazucheli, Josmar
  • Bertoli, Wesley

Abstract

Shock and stress models are used in reliability analysis to describe different kinds of applications. For instance, shock may refer to damage caused to vital organs by illness or environmental causes. On the other hand, stress can relate, for example, to two components that were maintained working independently, and had joint maintenance scheduled at a fixed time. In this context, the presented paper is aimed to introduce a new class of bivariate Lindley distribution of the Marshall–Olkin type to evaluate a 2-component series system’s reliability function. The proposed methodology is based on introducing a latent variable following an Exponential or a Lindley distribution. The obtained results generalize those achieved by using a Marshall–Olkin bivariate Exponential distribution, suggesting a useful way to search for appropriate bivariate lifetime distributions, especially under engineering reliability studies or in other areas of quantitative research.

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  • Oliveira, Ricardo P. & Achcar, Jorge A. & Mazucheli, Josmar & Bertoli, Wesley, 2021. "A new class of bivariate Lindley distributions based on stress and shock models and some of their reliability properties," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:reensy:v:211:y:2021:i:c:s0951832021000880
    DOI: 10.1016/j.ress.2021.107528
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Yousefi, Nooshin & Coit, David W. & Song, Sanling, 2020. "Reliability analysis of systems considering clusters of dependent degrading components," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    3. Torres-Alves, Gina Alexandra & Morales-Nápoles, Oswaldo, 2020. "Reliability analysis of flood defenses: The case of the Nezahualcoyotl dike in the aztec city of Tenochtitlan," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    4. Chi, Zhexiang & Chen, Ruoran & Huang, Simin & Li, Yan-Fu & Zhou, Bin & Zhang, Wenjuan, 2020. "Multi-State System Modeling and Reliability Assessment for Groups of High-speed Train Wheels," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    5. Park, Jae-Hyun, 2017. "Time-dependent reliability of wireless networks with dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 47-61.
    6. Wu, Bei & Cui, Lirong, 2020. "Reliability evaluation of Markov renewal shock models with multiple failure mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    7. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    8. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    9. Jafary, Bentolhoda & Mele, Andrew & Fiondella, Lance, 2020. "Component-based system reliability subject to positive and negative correlation," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
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    Cited by:

    1. Abba, Badamasi & Wang, Hong & Bakouch, Hassan S., 2022. "A reliability and survival model for one and two failure modes system with applications to complete and censored datasets," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    2. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.

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