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Profit analysis of a 2-out-of-2 redundant system with single standby and degradation of the units after repair

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Abstract

The purpose of this paper is to carry out the profit analysis of a three unit redundant system in which two units work in parallel and one unit is kept as spare in cold standby. Each unit has direct complete failure from normal mode. There is a single repairman (called server) who visits the system immediately to do repair, inspection and replacement of the units. The unit does not work as new after repair and so called a degraded unit. The degraded unit at its further failure undergoes for inspection to see the feasibility of its repair. If the repair is not feasible, it is replaced immediately by new unit. The system is considered in up-state if any two of original and/or degraded units are operative. The time to failure, repair and inspection of the units are taken as arbitrary with different probability density functions. By adopting semi-Markov process and regenerative point technique, the results for some measures of system effectiveness are obtained in steady state.

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References

  • Chander S (2005) Reliability models with priority for operation and repair with arrival time of the server. J Pure Appl Math Sci LXI (1–2):9–22

    MathSciNet  Google Scholar 

  • Chander S, Mukender S (2009) Probabilistic analysis of a 2-out-of-3 redundant system subject to degradation. J Appl Probab Stat 4(1):33–44

    MathSciNet  MATH  Google Scholar 

  • Cox DR (1962) Renewal theory. Chapman & Hall

  • Gopalan MN, Naidu RS (1982) Cost benefit analysis of a one server system subject to inspection. Microelectron Reliab 22(4):699–705

    Article  Google Scholar 

  • Medhi J (1982) Stochastic processes. Wiley Eastern Limited, India

    MATH  Google Scholar 

  • Nakagawa T (1980) Optimum inspection policies for a standby unit. J Oper Res Soc Jpn 23(1):13–26

    MathSciNet  MATH  Google Scholar 

  • Singh SK (1989) Profit evaluation of a two unit cold standby system with random appearance and disappearance time of the service facility. Microelectron Reliab 29(1):21–24

    Article  Google Scholar 

  • Smith WL (1955) Regenerative stochastic processes. Proceedings of the royal society A 232 (1188):6–13

Download references

Acknowledgments

The authors are thankful to the reviewers for their valuable comments that led to an improved presentation of the paper.

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Authors and Affiliations

  1. Department of Statistics & O.R., Kurukshetra University, Kurukshetra, India

    Jitender Kumar & M. S. Kadyan

  2. Department of Statistics, M. D. University, Rohtak, India

    S. C. Malik

Authors
  1. Jitender Kumar
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  2. M. S. Kadyan
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  3. S. C. Malik
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Correspondence to Jitender Kumar.

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Kumar, J., Kadyan, M.S. & Malik, S.C. Profit analysis of a 2-out-of-2 redundant system with single standby and degradation of the units after repair. Int J Syst Assur Eng Manag 4, 424–434 (2013). https://doi.org/10.1007/s13198-012-0127-4

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  • DOI: https://doi.org/10.1007/s13198-012-0127-4

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