IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v235y2015i1p757-76910.1007-s10479-015-1950-1.html
   My bibliography  Save this article

Bounds on uptime distribution based on aging for systems with finite lifetimes

Author

Listed:
  • Charles Wells

Abstract

Consider a system which is subject to occasional failures over its lifetime. Under general stochastic assumptions concerning the occurrence of these failures, the duration of the repair times, and the length of the system’s lifetime, the distribution of the total uptime the system accumulates over its lifetime may be determined. While the distribution is unfortunately complicated except in certain circumstances, it is possible to derive useful bounds based on the aging characteristics of the distributions of interfailure times, repair times, and system life. Bounds are developed for the cases where the system lifetime follows (1) a degenerate distribution (or constant mission duration), (2) an exponential distribution, and (3) a general distribution. These bounds may be interpreted as extensions of well-known bounds based on aging notions from renewal theory. Conditions are identified for when the bounds are sharp, and examples are used to show the computational tractability and usefulness of the results. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Charles Wells, 2015. "Bounds on uptime distribution based on aging for systems with finite lifetimes," Annals of Operations Research, Springer, vol. 235(1), pages 757-769, December.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:757-769:10.1007/s10479-015-1950-1
    DOI: 10.1007/s10479-015-1950-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-015-1950-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-015-1950-1?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. Charles E. Wells & John L. Bryant, 1985. "On the Replenishment of Repair Kit Inventories for Systems with Life Distributions of Phase Type," Management Science, INFORMS, vol. 31(11), pages 1440-1450, November.
    2. 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.
    3. Mark Brown, 2013. "Sharp bounds for NBUE distributions," Annals of Operations Research, Springer, vol. 208(1), pages 245-250, September.
    4. John L. Bryant & Richard A. Murphy, 1983. "Stocking Repair Kits for Systems with Limited Life," Management Science, INFORMS, vol. 29(5), pages 546-558, May.
    5. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2009. "Balancing burn-in and mission times in environments with catastrophic and repairable failures," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1314-1321.
    6. 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.
    7. Wells, Charles E., 2014. "Reliability analysis of a single warm-standby system subject to repairable and nonrepairable failures," European Journal of Operational Research, Elsevier, vol. 235(1), pages 180-186.
    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. M. S. Patel & A. A. Khalifa & M. S. Liew & Zahiraniza Mustaffa & Andrew Whyte, 2022. "Downtime cost analysis of offloading operations due to influence of partially standing waves in Malaysian waters and development of graphical user interface," Annals of Operations Research, Springer, vol. 315(2), pages 1263-1289, August.

    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. A Ponchet & M Fouladirad & A Grall, 2011. "Maintenance policy on a finite time span for a gradually deteriorating system with imperfect improvements," Journal of Risk and Reliability, , vol. 225(2), pages 105-116, June.
    2. 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.
    3. Kurtuluş Barış Öner & Alan Scheller-Wolf & Geert-Jan van Houtum, 2013. "Redundancy Optimization for Critical Components in High-Availability Technical Systems," Operations Research, INFORMS, vol. 61(1), pages 244-264, February.
    4. de Jonge, Bram & Dijkstra, Arjan S. & Romeijnders, Ward, 2015. "Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 15-21.
    5. Cheng, Tianjin & Pandey, Mahesh D. & van der Weide, J.A.M., 2012. "The probability distribution of maintenance cost of a system affected by the gamma process of degradation: Finite time solution," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 65-76.
    6. Dursun, İpek & Akçay, Alp & van Houtum, Geert-Jan, 2022. "Age-based maintenance under population heterogeneity: Optimal exploration and exploitation," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1007-1020.
    7. Amirhossain Chambari & Javad Sadeghi & Fakhri Bakhtiari & Reza Jahangard, 2016. "A note on a reliability redundancy allocation problem using a tuned parameter genetic algorithm," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 426-442, June.
    8. Chen, Wu-Lin & Wang, Kuo-Hsiung, 2018. "Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 476-486.
    9. Yonit Barron, 2018. "Group maintenance policies for an R-out-of-N system with phase-type distribution," Annals of Operations Research, Springer, vol. 261(1), pages 79-105, February.
    10. M D Pandey & T Cheng & J A M van der Weide, 2011. "Finite-time maintenance cost analysis of engineering systems affected by stochastic degradation," Journal of Risk and Reliability, , vol. 225(2), pages 241-250, June.
    11. Jiawen Hu & Zuhua Jiang & Hong Wang, 2016. "Preventive maintenance for a single-machine system under variable operational conditions," Journal of Risk and Reliability, , vol. 230(4), pages 391-404, August.
    12. Young Yun, Won & Nakagawa, Toshio, 2010. "Replacement and inspection policies for products with random life cycle," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 161-165.
    13. 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.
    14. R. K. Bhardwaj & Komaldeep Kaur & S. C. Malik, 2017. "Reliability indices of a redundant system with standby failure and arbitrary distribution for repair and replacement times," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 423-431, June.
    15. Ruiz-Castro, Juan Eloy & Dawabsha, Mohammed & Alonso, Francisco Javier, 2018. "Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 114-127.
    16. Sidibé, I.B. & Khatab, A. & Diallo, C. & Adjallah, K.H., 2016. "Kernel estimator of maintenance optimization model for a stochastically degrading system under different operating environments," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 109-116.
    17. Wen Liang Chang, 2015. "Optimal single-replacement for repairable products with different failure rate under a finite planning horizon," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 1003-1009, April.
    18. Anushri Maji & Asoke Kumar Bhunia & Shyamal Kumar Mondal, 2022. "A production-reliability-inventory model for a series-parallel system with mixed strategy considering shortage, warranty period, credit period in crisp and stochastic sense," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 862-907, September.
    19. Sou-Sen Leu & Tao-Ming Ying, 2020. "Replacement and Maintenance Decision Analysis for Hydraulic Machinery Facilities at Reservoirs under Imperfect Maintenance," Energies, MDPI, vol. 13(10), pages 1-10, May.
    20. 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.

    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:spr:annopr:v:235:y:2015:i:1:p:757-769:10.1007/s10479-015-1950-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.