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Machine repair problem with an unreliable server and controlled arrival of failed machines

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Abstract

This investigation deals with a machine repair problem having an unreliable server where the accumulation of failed machines is controlled under F-policy. The failed machines will continue to accumulate in the system for the repair till its full capacity K; then the server provides the repair but will not allow other failed machines for repair until the queue length is reduced to the threshold value F at which the server starts accepting failed machines again. The server takes some time to initiate the service of failed machines. The server is also prone to breakdown and its repair time is exponentially distributed. The successive-over-relaxation method has been used to obtain the steady-state probabilities. Various performance characteristics have also been derived to study the system effectively. Numerical results have been presented to facilitate the sensitivity analysis by taking illustrations.

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Acknowledgments

The authors would like to thank the referees for their comments and suggestions that led the paper into the current form.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247 667, India

    Madhu Jain

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

    Chandra Shekhar

  3. Department of Mathematics, D.A.V. (PG) College, Dehra Dun, Uttarakhand, 248 001, India

    Shalini Shukla

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  1. Madhu Jain
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  2. Chandra Shekhar
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  3. Shalini Shukla
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Correspondence to Chandra Shekhar.

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Jain, M., Shekhar, C. & Shukla, S. Machine repair problem with an unreliable server and controlled arrival of failed machines. OPSEARCH 51, 416–433 (2014). https://doi.org/10.1007/s12597-013-0152-3

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