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Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks

Author

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  • Chien-Kuo Sung
  • Shey-Huei Sheu
  • Tsung-Shin Hsu
  • Yan-Chun Chen

Abstract

This study presents an extended replacement policy for a two-unit system which is subjected to shocks and exhibits failure rate from interaction. The external shocks that affect the system are of two types. A type I shock causes a minor failure of unit-A and the damage that is caused by such a failure affects unit-B, whereas a type II shock causes a total failure of the system (catastrophic failure). All unit-A failures can be recovered by making minimal repairs. The system also exhibits the interaction between the failure rates of units: a failure of any unit-A causes an internal shock that increases the failure rate of unit-B, whereas a failure of a unit-B causes instantaneous failure of unit-A. The goal of this study is to derive the long-run cost per unit time of replacement by introducing relative costs as a factor in determining optimality; then, the optimal replacement period, T*, and the optimal number of unit-A failures, n*, which minimise that cost can be determined. A numerical example illustrates the method.

Suggested Citation

  • Chien-Kuo Sung & Shey-Huei Sheu & Tsung-Shin Hsu & Yan-Chun Chen, 2013. "Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 877-888.
    • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:5:p:877-888
    DOI: 10.1080/00207721.2011.626905
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    Citations

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    Cited by:

    1. Juan Eloy Ruiz-Castro, 2015. "A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1600-1613, July.
    2. Yousefi, Nooshin & Coit, David W. & Song, Sanling & Feng, Qianmei, 2019. "Optimization of on-condition thresholds for a system of degrading components with competing dependent failure processes," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    3. Meango, Toualith Jean-Marc & Ouali, Mohamed-Salah, 2020. "Failure interaction model based on extreme shock and Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    4. Zhuoqi Zhang & Su Wu & Binfeng Li & Seungchul Lee, 2015. "(, ) type maintenance policy for multi-component systems with failure interactions," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 1051-1064, April.
    5. Dao, Cuong D. & Zuo, Ming J., 2017. "Selective maintenance of multi-state systems with structural dependence," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 184-195.
    6. Min-Tsai Lai & Huey Yan, 2016. "Optimal number of minimal repairs with cumulative repair cost limit for a two-unit system with failure rate interactions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(2), pages 466-473, January.
    7. 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.
    8. Shey-Huei Sheu & Tzu-Hsin Liu & Zhe-George Zhang & Hsin-Nan Tsai & Jung-Chih Chen, 2016. "Optimal two-threshold replacement policy in a cumulative damage model," Annals of Operations Research, Springer, vol. 244(1), pages 23-47, September.

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