Advertisement

Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2825–2836 | Cite as

Performance Modeling of Fault-Tolerant Machining System with Working Vacation and Working Breakdown

  • Madhu Jain
  • Richa Sharma
  • Rakesh Kumar MeenaEmail author
Research Article - Systems Engineering
  • 40 Downloads

Abstract

This study deals with the performance modeling of finite Markov M/M/1/L/WV model for the fault-tolerant machining system (FTMS). The concepts of redundancy along with the provision of dissimilar warm standbys are taken into account in order to maintain the pre-required high reliability of the system. The repairman is allowed to take a vacation in case of no workload of broken down machines. The failed machines are also repaired with slower rate by the repairman during working vacation period. The analytical method, namely matrix method, is implemented for evaluating the transient queue size distribution and closed form expressions of the performance metrics of multi-component FTMS. Moreover, cost function is constructed, which can be further used to control the system cost and other factors. Numerical simulation is also carried out to exhibit the effect of parameters on various system indices.

Keywords

Fault tolerant Machine repair Working vacation Working breakdown Unreliable server Reliability Matrix method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The author (Rakesh Kumar Meena, Enrollment Number 12922036) is thankful to Ministry of Human Resource Development (Grant No. MHR-02-23-200-429) for providing grant in the form of Senior Research Fellowship (SRF) to carry out the research work.

References

  1. 1.
    Sivazlian, B.D.; Wang, K.-H.: Economic analysis of the M/M/R machine repair problem with warm standbys. Mlcroelectron. Reliab. 29, 25–35 (1989)CrossRefGoogle Scholar
  2. 2.
    Wang, K.-H.; Sivazlian, B.D.: Cost analysis of the M/M/R machine repair problem with spare operating under variable service rate. Microelectron. Reliab. 32, 1171–1183 (1992)CrossRefGoogle Scholar
  3. 3.
    Wang, K.-H.: Cost analysis of the M/M/R machine-repair problem with mixed standby spares. Microelectron. Reliab. 33, 1293–1301 (1993)CrossRefGoogle Scholar
  4. 4.
    Wang, K.-H.; Kuo, C.-C.: Cost and probabilistic analysis of series systems with mixed standby components. Appl. Math. Model. 24, 957–967 (2000)CrossRefzbMATHGoogle Scholar
  5. 5.
    Jain, M.; Rakhee,; Singh, M.: Bilevel control of degraded machining system with warm standbys, setup and vacation. Appl. Math. Model. 28, 1015–1026 (2004)CrossRefzbMATHGoogle Scholar
  6. 6.
    Wang, K.-H.; Ke, J.-B.; Ke, J.-C.: Profit analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Comput. Oper. Res. 34, 835–847 (2007)CrossRefzbMATHGoogle Scholar
  7. 7.
    Jain, M.; Sharma, G.C.; Sharma, R.: Performance modeling of state dependent system with mixed standbys and two modes of failure. Appl. Math. Model. 32, 712–724 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ke, J.-C.; Lin, C.-H.: Sensitivity analysis of machine repair problems in manufacturing systems with service interruptions. Appl. Math. Model. 32, 2087–2105 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ke, J.-C.; Wu, C.-H.: Multi-server machine repair model with standbys and synchronous multiple vacation. Comput. Ind. Eng. 62, 296–305 (2012)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Jain, M.: Reliability prediction of repairable redundant system with imperfect switching and repair. Arab. J. Sci. Eng. 41, 3717–3725 (2016)CrossRefzbMATHGoogle Scholar
  12. 12.
    Jain, M.; Meena, R.K.: Fault tolerant system with imperfect coverage, reboot and server vacation. J. Ind. Eng. Int. 13, 171–180 (2016)CrossRefGoogle Scholar
  13. 13.
    Doshi, B.T.: Queueing systems with vacations-a survey. Queueing Syst. 1, 29–66 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gupta, S.M.: Machine interference problem with warm spares, server vacations and exhaustive service. Perform. Eval. 29, 195–211 (1997)CrossRefGoogle Scholar
  15. 15.
    Ke, J.-C.; Wang, K.-H.: Vacation policies for machine repair problem with two type spares. Appl. Math. Model. 31, 880–894 (2007)CrossRefzbMATHGoogle Scholar
  16. 16.
    Servi, L.D.; Finn, S.G.: M / M / 1 queues with working vacations (M / M / 1 / WV) *. Perform. Eval. 50, 41–52 (2002)CrossRefGoogle Scholar
  17. 17.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Yang, D.Y.; Wang, K.H.; Wu, C.H.: Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation. J. Comput. Appl. Math. 234, 545–556 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Liu, B.; Cui, L.; Wen, Y.; Shen, J.: A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process. Reliab. Eng. Syst. Saf. 142, 1–8 (2015)CrossRefGoogle Scholar
  20. 20.
    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)CrossRefzbMATHGoogle Scholar
  21. 21.
    Jain, M.; Jain, A.: Working vacations queueing model with multiple types of server breakdowns. Appl. Math. Model. 34, 1–13 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Ke, J.C.; Hsu, Y.L.; Liu, T.H.; George Zhang, Z.: Computational analysis of machine repair problem with unreliable multi-repairmen. Comput. Oper. Res. 40, 848–855 (2013)CrossRefzbMATHGoogle Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    Wang, K.-H.; Liou, C.-D.; Wang, Y.-L.: Profit optimisation of the multiple-vacation machine repair problem using particle swarm optimisation. Int. J. Syst. Sci. 45, 1769–1780 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Jain, M.; Shekhar, C.; Rani, V.: N-policy for a multi-component machining system with imperfect coverage, reboot and unreliable server. Prod. Manuf. Res. 2, 457–476 (2014)Google Scholar
  26. 26.
    Yen, T.-C.; Chen, W.-L.; Chen, J.-Y.: Reliability and sensitivity analysis of the controllable repair system with warm standbys and working breakdown. Comput. Ind. Eng. 97, 84–92 (2016)CrossRefGoogle Scholar
  27. 27.
    Jain, M.; Meena, R.K.: Markovian analysis of unreliable multi-components redundant fault tolerant system with working vacation and F-policy. Cogent Math. 4, 1–17 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of MathematicsIIT RoorkeeRoorkeeIndia
  2. 2.Department of MathematicsJK Lakshmipat UniversityJaipurIndia

Personalised recommendations