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A trivariate optimal replacement policy for a deteriorating system based on cumulative damage and inspections

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  • Tsai, Hsin-Nan
  • Sheu, Shey-Huei
  • Zhang, Zhe George

Abstract

In this article, we study a trivariate replacement model for a deteriorating system consisting of two units. Failures of unit 1 can be classified into two types. Type I failure (minor failure) is fixed by a minimal repair and type II failure (catastrophic failure) is removed by a replacement. Both types of failures can only be detected through inspection. Each type I failure of unit 1 will result in a random amount of damage to unit 2 and the damages are cumulative. The probability of type I failure or type II failure is assumed to depend on the number of failures since the last replacement. We formulate a replacement policy based on the number of type I failure, the occurrence of the first type II failure, and the amount of accumulative damages. Hence the system is replaced either preventively or correctively at any of the following four conditions depend on whichever occurs first; preventively (a) at the Nth type I failure; or (b) when the total damage of unit 2 exceeds a pre-specified level Z (but less than the failure level l); and, correctively (c) at the first type II failure; or (d) when the total damage of unit 2 exceeds a failure level l, where Z and l represent the thresholds of total damage level for unit 2 to preventive and corrective replacements, respectively. Although a type I failure can be fixed by a minimal repair, but the operating period is stochastically decreasing and repair time is stochastically increasing as time goes on. The minimal total expected long-run net cost per unit time of the system is derived and a computational algorithm for determining the optimal policy is developed. A real-world application from electric power industry is provided. Several past studied are shown to be special cases of our model. Finally, a numerical example is presented.

Suggested Citation

  • Tsai, Hsin-Nan & Sheu, Shey-Huei & Zhang, Zhe George, 2017. "A trivariate optimal replacement policy for a deteriorating system based on cumulative damage and inspections," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 74-88.
    • Handle: RePEc:eee:reensy:v:160:y:2017:i:c:p:74-88
    DOI: 10.1016/j.ress.2016.10.031
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    1. Khac Tuan Huynh & Inma T. Castro & Anne Barros & Christophe Bérenguer, 2012. "Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks," Post-Print hal-00790729, HAL.
    2. Shey-Huei Sheu & Hsin-Nan Tsai & Tsung-Shin Hsu & Fu-Kwun Wang, 2015. "Optimal number of minimal repairs before replacement of a deteriorating system with inspections," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(8), pages 1367-1379, June.
    3. Sheu, Shey-Huei & Chang, Chin-Chih & Chen, Yen-Luan & George Zhang, Zhe, 2015. "Optimal preventive maintenance and repair policies for multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 78-87.
    4. Huynh, K.T. & Castro, I.T. & Barros, A. & Bérenguer, C., 2012. "Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks," European Journal of Operational Research, Elsevier, vol. 218(1), pages 140-151.
    5. Zhao, Xufeng & Qian, Cunhua & Nakagawa, Toshio, 2013. "Optimal policies for cumulative damage models with maintenance last and first," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 50-59.
    6. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George, 2012. "Optimal maintenance policy for a system subject to damage in a discrete time process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 1-10.
    7. Nakagawa, Toshio & Kowada, Masashi, 1983. "Analysis of a system with minimal repair and its application to replacement policy," European Journal of Operational Research, Elsevier, vol. 12(2), pages 176-182, February.
    8. Zhou, Xiaojun & Wu, Changjie & Li, Yanting & Xi, Lifeng, 2016. "A preventive maintenance model for leased equipment subject to internal degradation and external shock damage," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 1-7.
    9. 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.
    10. Toshio Nakagawa, 2014. "Random Inspection Policies," Springer Series in Reliability Engineering, in: Random Maintenance Policies, edition 127, chapter 0, pages 87-114, Springer.
    11. G.Q. Cheng & L. Li, 2012. "A geometric process repair model with inspections and its optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(9), pages 1650-1655.
    12. 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.
    13. Yen-Luan Chen, 2014. "Optimal Age Policy for a Used System with Imperfect Preventive Maintenance and Cumulative Damage Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(19), pages 4062-4073, October.
    14. Sheu, Shey-Huei, 1999. "Extended optimal replacement model for deteriorating systems," European Journal of Operational Research, Elsevier, vol. 112(3), pages 503-516, February.
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    4. Sheu, Shey-Huei & Liu, Tzu-Hsin & Sheu, Wei-Teng & Zhang, Zhe-George & Ke, Jau-Chuan, 2021. "Optimal replacement policy with replacement last under cumulative damage models," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    5. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    6. Qinglai Dong & Lirong Cui & Hongda Gao, 2019. "A bivariate replacement policy for an imperfect repair system based on geometric processes," Journal of Risk and Reliability, , vol. 233(4), pages 670-681, August.
    7. Song, Cen & Zhuang, Jun, 2017. "N-stage security screening strategies in the face of strategic applicants," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 292-301.
    8. Sheu, Shey-Huei & Tsai, Hsin-Nan & Sheu, Uan-Yu & Zhang, Zhe George, 2019. "Optimal replacement policies for a system based on a one-cycle criterion," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

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