Skip to main content
SpringerLink
Log in

Dynamic Control of a Machine Repair Problem with Switching Failure and Unreliable Repairmen

  • Research Article - Systems Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

This study examines the dynamic control of an M/M/2 machine repair system with R operating machines, S standbys, and two unreliable repairmen, wherein standbys are subject to switching failures. We apply the matrix analytic method to derive explicit expressions of the stationary probability distributions as well as matrix expressions of the system performance measures. We construct a cost model and determine the optimal dynamic operating policy to minimize the expected cost function per unit time. Sensitivity analysis is conducted using numerical examples. The results of sensitivity analysis indicate that the optimal thresholds and corresponding minimum expected cost increase as the number of operating machines or standbys increases. Moreover, the minimum expected cost is sensitive to the mean arrival and repair rates. The results provide managers with decision reference for productivity improvement and cost reduction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Haque, L.; Armstrong, M.J.: A survey of the machine interference problem. Eur. J. Oper. Res. 179, 469–482 (2007)

    Article  Google Scholar 

  2. Shekhar, C.; Raina, A.A.; Kumar, A.; Iqbal, J.: A survey on queues in machining system: progress from 2010 to 2017. Yugoslav J. Oper. Res. 27, 391–413 (2017)

    Article  MathSciNet  Google Scholar 

  3. Chen, W.-L.; Wang, K.-H.: Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy. Reliab. Eng. Syst. Saf. 180, 476–486 (2018)

    Article  Google Scholar 

  4. Ching, W.K.: Machine repairing models for production systems. Int. J. Prod. Econ. 70, 257–266 (2001)

    Article  Google Scholar 

  5. Wang, K.-H.; Liou, C.-D.; Lin, Y.-H.: Comparative analysis of the machine repair problem with imperfect coverage and service pressure condition. Appl. Math. Model. 37, 2870–2880 (2013)

    Article  MathSciNet  Google Scholar 

  6. Yang, D.-Y.; Chang, Y.-D.: Sensitivity analysis of the machine repair problem with general repeated attempts. Int. J. Comput. Math. 95, 1761–1774 (2018)

    Article  MathSciNet  Google Scholar 

  7. Yue, D.; Yue, W.; Qi, H.: Performance analysis and optimization of a machine repair problem with warm spares and two heterogeneous repairmen. Optim. Eng. 13, 545–562 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Jain, M.; Bhargava, C.: N-policy machine repair system with mixed standbys and unreliable server. Qual. Technol. Quant. Manag. 6, 171–184 (2009)

    Article  MathSciNet  Google Scholar 

  9. Ke, J.-C.; Hsu, Y.-L.; Liu, T.-H.; Zhang, Z.-G.: Computational analysis of machine repair problem with unreliable multi-repairmen. Comput. Oper. Res. 40, 848–855 (2013)

    Article  Google Scholar 

  10. Yang, D.-Y.; Chiang, Y.-C.: An evolutionary algorithm for optimizing the machine repair problem under a threshold recovery policy. J. Chin. Inst. Eng. 37, 224–231 (2014)

    Article  Google Scholar 

  11. Chen, W.-L.: System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy. Syst. Eng. 21, 59–69 (2016)

    Article  Google Scholar 

  12. Wang, K.-H.; Yen, T.-C.; Chen, J.-Y.: Optimization analysis of retrial machine repair problem with server breakdown and threshold recovery policy. J. Test. Eval. 46, 2630–2640 (2018)

    Google Scholar 

  13. Huang, H.-I.; Lin, C.-H.; Ke, J.-C.: Parametric nonlinear programming approach for a repairable system with switching failure and fuzzy parameters. Appl. Math. Comput. 183, 508–517 (2006)

    MathSciNet  MATH  Google Scholar 

  14. Liu, T.-H.; Ke, J.-C.; Hsu, Y.-L.; Hsu, Y.L.: Bootstrapping computation of availability for a repairable system with standby subject to imperfect switching. Commun. Stat. Simul. Comput. 40, 469–483 (2011)

    Article  MathSciNet  Google Scholar 

  15. Hsu, Y.-L.; Ke, J.-C.; Liu, T.-H.; Wu, C.-H.: Modeling of multi-server repair problem with switching failure and reboot delay and related profit analysis. Comput. Ind. Eng. 69, 21–28 (2014)

    Article  Google Scholar 

  16. Ke, J.-C.; Liu, T.-H.; Yang, D.-Y.: Machine repairing systems with standby switching failure. Comput. Ind. Eng. 99, 223–228 (2016)

    Article  Google Scholar 

  17. Lee, Y.: Availability analysis of redundancy model with generally distributed repair time, imperfect switchover, and interrupted repair. Electron. Lett. 52, 1851–1853 (2016)

    Article  Google Scholar 

  18. Ke, J.-C.; Liu, T.-H.; Yang, D.-Y.: Modeling of machine interference problem with unreliable repairman and standbys imperfect switchover. Reliab. Eng. Syst. Saf. 174, 12–18 (2018)

    Article  Google Scholar 

  19. Levy, Y.; Yechiali, U.: Utilization of idle time in an M/G/1 queueing system. Manage. Sci. 22, 202–211 (1975)

    Article  Google Scholar 

  20. Doshi, B.T.: Queueing systems with vacations—a survey. Queueing Syst. 1, 29–66 (1986)

    Article  MathSciNet  Google Scholar 

  21. Tian, N.; Zhang, Z.G.: Vacation Queueing Models: Theory and Applications. Springer, New York (2006)

    Book  Google Scholar 

  22. Ke, J.-C.; Wu, C.-H.; Zhang, Z.-G.: Recent developments in vacation queueing models: a short survey. Int. J. Oper. Res. 7, 3–8 (2010)

    Google Scholar 

  23. Jain, M.; Singh, M.: Bilevel control of degraded machining system with warm standbys, setup and vacation. Appl. Math. Model. 28, 1015–1026 (2004)

    Article  Google Scholar 

  24. Ke, J.-C.; Wang, K.-H.: Vacation policies for machine repair problem with two type spares. Appl. Math. Model. 31, 880–894 (2007)

    Article  Google Scholar 

  25. Wang, K.-H.; Chen, W.-L.; Yang, D.-Y.: Optimal management of the machine repair problem with working vacation: Newton’s method. J. Comput. Appl. Math. 233, 449–458 (2009)

    Article  MathSciNet  Google Scholar 

  26. Jain, M.; Shekhar, C.; Meena, R.K.: Admission control policy of maintenance for unreliable server machining system with working vacation. Arab. J. Sci. Eng. 42, 2993–3005 (2017)

    Article  Google Scholar 

  27. Ke, J.-C.; Wu, C.-H.: Multi-server machine repair model with standbys and synchronous multiple vacation. Comput. Ind. Eng. 62, 296–305 (2012)

    Article  Google Scholar 

  28. Liou, C.D.: Optimization analysis of the machine repair problem with multiple vacations and working breakdowns. J. Ind. Manag. Optim. 11, 83–104 (2015)

    MathSciNet  MATH  Google Scholar 

  29. Jain, M.; Sharma, R.; Meena, R.K.: Performance modeling of fault-tolerant machining system with working vacation and working breakdown. Arab. J. Sci. Eng. 44, 2825–2836 (2019)

    Article  Google Scholar 

  30. Yang, D.-Y.; Tsao, C.-L.: Reliability and availability analysis of standby systems with working vacations and retrial of failed components. Reliab. Eng. Syst. Saf. 182, 46–55 (2019)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, Taiwan

    Chia-Huang Wu

  2. Institute of Information and Decision Sciences, National Taipei University of Business, Taipei, Taiwan

    Dong-Yuh Yang

Authors
  1. Chia-Huang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dong-Yuh Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong-Yuh Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, CH., Yang, DY. Dynamic Control of a Machine Repair Problem with Switching Failure and Unreliable Repairmen. Arab J Sci Eng 45, 2219–2234 (2020). https://doi.org/10.1007/s13369-019-04196-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-019-04196-9

Keywords

Search

Navigation