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Performance analysis and control F-policy for fault-tolerant system with working vacation

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Abstract

This investigation presents a Markov model for the performance analysis of the fault tolerant machining system with failure-prone server and supported by warm standbys. To utilize the server’s idle time, provision of server’s working vacation has been done which make the system cost effective. The online and warm standby machines may fail and can be repaired by a single skilled repairman. Due to capacity constraint, when the system reaches its full capacity, no more jobs for repairing of failed machines are allowed until the workload of repair jobs reduces to a threshold level ‘F’. Before initiating the repair of the failed machines in case of coming back from the vacation state, the server requires the setup time. To make system fault tolerable, apart from standby provisioning and repairing of failed machines, the concepts of reboot and recovery are included for the formulation of Markov model. The various performance measures including the reliability indices are derived by using the transient probabilities which are computed using Runge–Kutta method. By taking a suitable numerical illustration, various system indices are examined with respect to different parameters. The computational tractability and sensitivity analysis carried out for the established metrics will provides valuable insights for the maintainability and up-gradation of the existing machining systems.

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Acknowledgements

The authors would like to thank the editorial board and anonymous referees for the valuable constructive comments and suggestions on an earlier version of this paper. The author (CS) extends his sincere thanks to funding agency DST FIST for a financial grant to the department having number SR/FST/MSI-090/2013(C).

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Authors and Affiliations

  1. Department of Mathematics, IIT Roorkee, Roorkee, 247 667, India

    Madhu Jain

  2. Department of Mathematics, Birla Institute of Technology and Science, Pilani Campus, Pilani, 333 031, Rajasthan, India

    Chandra Shekhar

  3. Department of Mathematics, Hansraj College University of Delhi, Delhi, 110 007, India

    Rakesh Kumar Meena

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  1. Madhu Jain
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  2. Chandra Shekhar
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  3. Rakesh Kumar Meena
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Correspondence to Rakesh Kumar Meena.

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Jain, M., Shekhar, C. & Meena, R.K. Performance analysis and control F-policy for fault-tolerant system with working vacation. OPSEARCH 56, 409–431 (2019). https://doi.org/10.1007/s12597-019-00369-0

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