IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v50y2003i5p462-480.html
   My bibliography  Save this article

Analysis of a machine repair problem with an unreliable server and phase type repairs and services

Author

Listed:
  • Srinivas R. Chakravarthy
  • Atul Agarwal

Abstract

In this paper we study a machine repair problem in which a single unreliable server maintains N identical machines. The breakdown times of the machines are assumed to follow an exponential distribution. The server is subject to failure and the failure times are exponentially distributed. The repair times of the machine and the service times of the repairman are assumed to be of phase type. Using matrix‐analytic methods, we perform steady state analysis of this model. The time spent by a failed machine in service and the total time in the repair facility are shown to be of phase type. Several performance measures are evaluated. An optimization problem to determine the number of machines to be assigned to the server that will maximize the expected total profit per unit time is discussed. An illustrative numerical example is presented. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 462–480, 2003

Suggested Citation

  • Srinivas R. Chakravarthy & Atul Agarwal, 2003. "Analysis of a machine repair problem with an unreliable server and phase type repairs and services," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 462-480, August.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:5:p:462-480
    DOI: 10.1002/nav.10069
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10069
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10069?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
    ---><---

    References listed on IDEAS

    as
    1. Tapani Lehtonen, 1984. "On the optimal policies of an exponential machine repair problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 173-181, June.
    2. F. A. Van Der Duyn Schouten & P. Wartenhorst, 1993. "A two‐machine repair model with variable repair rate," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 495-523, June.
    3. B. D. Sivazlian & K. H. Wang, 1990. "Diffusion approximation to the G/G/R machine repair problem with warm standby spares," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 753-772, October.
    4. Wartenhorst, Pieter, 1995. "N parallel queueing systems with server breakdown and repair," European Journal of Operational Research, Elsevier, vol. 82(2), pages 302-322, April.
    5. Frostig, Esther, 1999. "Jointly optimal allocation of a repairman and optimal control of service rate for machine repairman problem," European Journal of Operational Research, Elsevier, vol. 116(2), pages 274-280, July.
    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. Pedram Sahba & Barış Balcıog̃lu & Dragan Banjevic, 2022. "The impact of disruption characteristics on the performance of a server," Annals of Operations Research, Springer, vol. 317(1), pages 239-252, October.
    2. Pedram Sahba & Bariş Balciog̃lu & Dragan Banjevic, 2013. "Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 331-342, June.

    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. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    2. K. H. Adjallah & K. P. Adzakpa, 2007. "Minimizing maintenance cost involving flow-time and tardiness penalty with unequal release dates," Journal of Risk and Reliability, , vol. 221(1), pages 57-65, March.
    3. Doroudi, Sherwin & Avgerinos, Thanassis & Harchol-Balter, Mor, 2021. "To clean or not to clean: Malware removal strategies for servers under load," European Journal of Operational Research, Elsevier, vol. 292(2), pages 596-609.
    4. Delasay, Mohammad & Kolfal, Bora & Ingolfsson, Armann, 2012. "Maximizing throughput in finite-source parallel queue systems," European Journal of Operational Research, Elsevier, vol. 217(3), pages 554-559.
    5. Shengli Lv, 2021. "Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate," Mathematics, MDPI, vol. 9(11), pages 1-16, June.
    6. Tan, Baris, 1998. "Effects of variability on the due-time performance of a continuous materials flow production system in series," International Journal of Production Economics, Elsevier, vol. 54(1), pages 87-100, January.
    7. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    8. Zhou, Wenhui & Zheng, Zhibin & Xie, Wei, 2017. "A control-chart-based queueing approach for service facility maintenance with energy-delay tradeoff," European Journal of Operational Research, Elsevier, vol. 261(2), pages 613-625.

    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:wly:navres:v:50:y:2003:i:5:p:462-480. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.