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Age replacement models: A summary with new perspectives and methods

Author

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  • Zhao, Xufeng
  • Al-Khalifa, Khalifa N.
  • Magid Hamouda, Abdel
  • Nakagawa, Toshio

Abstract

Age replacement models are fundamental to maintenance theory. This paper summarizes our new perspectives and hods in age replacement models: First, we optimize the expected cost rate for a required availability level and vice versa. Second, an asymptotic model with simple calculation is proposed by using the cumulative hazard function skillfully. Third, we challenge the established theory such that preventive replacement should be non-random and only corrective replacement should be made for the unit with exponential failure. Fourth, three replacement policies with random working cycles are discussed, which are called overtime replacement, replacement first, and replacement last, respectively. Fifth, the policies of replacement first and last are formulated with general models. Sixth, age replacement is modified for the situation when the economical life cycle of the unit is a random variable with probability distribution. Finally, models of a parallel system with constant and random number of units are taken into considerations. The models of expected cost rates are obtained and optimal replacement times to minimize them are discussed analytically and computed numerically. Further studies and potential applications are also indicated at the end of discussions of the above models.

Suggested Citation

  • Zhao, Xufeng & Al-Khalifa, Khalifa N. & Magid Hamouda, Abdel & Nakagawa, Toshio, 2017. "Age replacement models: A summary with new perspectives and methods," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 95-105.
    • Handle: RePEc:eee:reensy:v:161:y:2017:i:c:p:95-105
    DOI: 10.1016/j.ress.2017.01.011
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    References listed on IDEAS

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    1. Toshio Nakagawa, 2014. "Random Maintenance Policies," Springer Series in Reliability Engineering, Springer, edition 127, number 978-1-4471-6575-0, September.
    2. Zhao, Xufeng & Al-Khalifa, Khalifa N. & Nakagawa, Toshio, 2015. "Approximate methods for optimal replacement, maintenance, and inspection policies," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 68-73.
    3. Xufeng Zhao & Toshio Nakagawa, 2015. "Optimal periodic and random inspections with first, last and overtime policies," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1648-1660, July.
    4. Coolen-Schrijner, P. & Coolen, F.P.A., 2007. "Nonparametric adaptive age replacement with a one-cycle criterion," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 74-84.
    5. Jiang, R., 2009. "An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1245-1250.
    6. Lim, J.H. & Qu, Jian & Zuo, Ming J., 2016. "Age replacement policy based on imperfect repair with random probability," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 24-33.
    7. Zhao, Xufeng & Nakagawa, Toshio, 2012. "Optimization problems of replacement first or last in reliability theory," European Journal of Operational Research, Elsevier, vol. 223(1), pages 141-149.
    8. Hamidi, Maryam & Szidarovszky, Ferenc & Szidarovszky, Miklos, 2016. "New one cycle criteria for optimizing preventive replacement policies," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 42-48.
    9. Sheu, Shey-Huei & Chang, Chin-Chih & Zhang, Zhe George & Chien, Yu-Hung, 2012. "A note on replacement policy for a system subject to non-homogeneous pure birth shocks," European Journal of Operational Research, Elsevier, vol. 216(2), pages 503-508.
    10. Zhao, Xufeng & Chen, Mingchih & Nakagawa, Toshio, 2016. "Replacement policies for a parallel system with shortage and excess costs," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 89-95.
    11. Nakagawa, T. & Mizutani, S., 2009. "A summary of maintenance policies for a finite interval," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 89-96.
    12. Lapa, Celso Marcelo F. & Pereira, Cláudio Márcio N.A. & de Barros, Márcio Paes, 2006. "A model for preventive maintenance planning by genetic algorithms based in cost and reliability," Reliability Engineering and System Safety, Elsevier, vol. 91(2), pages 233-240.
    13. Toshio Nakagawa, 2008. "Advanced Reliability Models and Maintenance Policies," Springer Series in Reliability Engineering, Springer, number 978-1-84800-294-4, September.
    14. Shafiee, Mahmood & Finkelstein, Maxim, 2015. "An optimal age-based group maintenance policy for multi-unit degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 230-238.
    15. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, September.
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