IDEAS home Printed from https://ideas.repec.org/a/taf/tsysxx/v46y2015i8p1367-1379.html
   My bibliography  Save this article

Optimal number of minimal repairs before replacement of a deteriorating system with inspections

Author

Listed:
  • Shey-Huei Sheu
  • Hsin-Nan Tsai
  • Tsung-Shin Hsu
  • Fu-Kwun Wang

Abstract

In this study, we propose a generalised replacement model for a deteriorating system with failures that could only be detected through inspection work. The system is assumed to have two types of failures and is replaced at the Nth type I failure (minor failure) or first type II failure (catastrophic failure), depending on whichever occurs first. The probability of type I and II failures depends on the number of failures since the last replacement. Such systems can be repaired upon type I failure, but are stochastically deteriorating, that is, the lengths of the operating intervals are stochastically decreasing, whereas the durations of the repairs are stochastically increasing. Then, the expected net cost rate is obtained. Some special cases are considered. Finally, a numerical example is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:8:p:1367-1379
    DOI: 10.1080/00207721.2013.822125
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207721.2013.822125
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207721.2013.822125?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Laurence A. Baxter, 1982. "Reliability applications of the relevation transform," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(2), pages 323-330, June.
    2. Wang, Wenbin, 2009. "An inspection model for a process with two types of inspections and repairs," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 526-533.
    3. Shey‐Huei Sheu & William S. Griffith, 1996. "Optimal number of minimal repairs before replacement of a system subject to shocks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 319-333, April.
    4. 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.
    5. Nakagawa, T. & Mizutani, S. & Chen, M., 2010. "A summary of periodic and random inspection policies," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 906-911.
    6. Sheu, Shey-Huei, 1999. "Extended optimal replacement model for deteriorating systems," European Journal of Operational Research, Elsevier, vol. 112(3), pages 503-516, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Shey-Huei Sheu & Tzu-Hsin Liu & Wei-Teng Sheu & Yu-Hung Chien & Zhe-George Zhang, 2024. "Extended replacement policy for a system under shocks effect," Annals of Operations Research, Springer, vol. 340(1), pages 507-530, September.
    3. 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 122-135.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sheu, Shey-Huei & Tsai, Hsin-Nan & Wang, Fu-Kwun & Zhang, Zhe George, 2015. "An extended optimal replacement model for a deteriorating system with inspections," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 33-49.
    2. 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.
    3. Yang, Li & Ma, Xiaobing & Zhai, Qingqing & Zhao, Yu, 2016. "A delay time model for a mission-based system subject to periodic and random inspection and postponed replacement," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 96-104.
    4. 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 122-135.
    5. 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.
    6. Wang, Wenbin & Zhao, Fei & Peng, Rui, 2014. "A preventive maintenance model with a two-level inspection policy based on a three-stage failure process," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 207-220.
    7. 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.
    8. Antonio Di Crescenzo & Patrizia Di Gironimo, 2018. "Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model," Mathematics, MDPI, vol. 6(10), pages 1-13, October.
    9. Flage, Roger, 2014. "A delay time model with imperfect and failure-inducing inspections," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 1-12.
    10. Tang, Ya-yong & Lam, Yeh, 2006. "A [delta]-shock maintenance model for a deteriorating system," European Journal of Operational Research, Elsevier, vol. 168(2), pages 541-556, January.
    11. Wenke Gao, 2020. "An extended geometric process and its application in replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 88-103, February.
    12. Wang, Wenbin & Banjevic, Dragan, 2012. "Ergodicity of forward times of the renewal process in a block-based inspection model using the delay time concept," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 1-7.
    13. Levitin, Gregory & Finkelstein, Maxim & Huang, Hong-Zhong, 2019. "Scheduling of imperfect inspections for reliability critical systems with shock-driven defects and delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 89-98.
    14. Wang, Wenbin, 2011. "An inspection model based on a three-stage failure process," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 838-848.
    15. Zio, Enrico & Compare, Michele, 2013. "Evaluating maintenance policies by quantitative modeling and analysis," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 53-65.
    16. Wang, Wenbin, 2012. "An overview of the recent advances in delay-time-based maintenance modelling," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 165-178.
    17. Miaomiao Yu & Yinghui Tang, 2024. "Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method," Journal of Risk and Reliability, , vol. 238(2), pages 233-246, April.
    18. Shey-Huei Sheu & Chin-Chih Chang & Yu-Hung Chien, 2011. "Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks," Annals of Operations Research, Springer, vol. 186(1), pages 317-329, June.
    19. Zhao, Qian Qian & Yun, Won Young, 2018. "Determining the inspection intervals for one-shot systems with support equipment," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 63-75.
    20. Wang, Wen-Ying & Sheu, Shey-Huei & Chen, Yan-Chun & Horng, Der-Juinn, 2009. "Economic optimization of off-line inspection with rework consideration," European Journal of Operational Research, Elsevier, vol. 194(3), pages 807-813, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:tsysxx:v:46:y:2015:i:8:p:1367-1379. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TSYS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.