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Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model

Author

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  • Lina Bian

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

  • Bo Peng

    (School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China)

  • Yong Ye

    (School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China)

Abstract

A fresh censored δ shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored δ shock model. The generalized Pólya process is used for modeling because the generalized Pólya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Pólya process. Thus far, the lifetime properties of the censored δ shock model under the generalized Pólya process have not been studied. Therefore, for the established generalized Pólya censored δ shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy N , based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy N * by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model.

Suggested Citation

  • Lina Bian & Bo Peng & Yong Ye, 2023. "Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model," Mathematics, MDPI, vol. 11(21), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4560-:d:1274774
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    References listed on IDEAS

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    1. Hidetoshi Konno, 2010. "On the Exact Solution of a Generalized Polya Process," Advances in Mathematical Physics, Hindawi, vol. 2010, pages 1-12, November.
    2. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.
    3. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1627-1650, September.
    4. Chen, Jinyuan & Li, Zehui, 2008. "An extended extreme shock maintenance model for a deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1123-1129.
    5. Jozef L. Teugels & Petra Vynckier, 1996. "The structure distribution in a mixed Poisson process," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-8, January.
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