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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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    Cited by:

    1. 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.
    2. 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.

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