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Markov approach for reliability-availability-maintainability analysis of a three unit repairable system

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Abstract

In this article, the use of Markov approach has been made to analyze the reliability, availability and maintainability of a repairable system. The system has three non-identical units which work simultaneously and system will completely be failed at the failure of all units. The distribution for failure and repair times is taken as negative exponential as transition rates follow homogenous continuous Markov process. The reliability measures are derived using Chapman-Kolmogorov equations. The use of Laplace transform technique has been made to solve the system equations. For particular values of the parameters, the reliability measures including reliability, MTSF, availability, MTTR and maintainability have been obtained considering all units identical in nature. The effect of failure rate, repair rate and operating time has been observed on these measures through graphs. The application of the research work has been discussed in case of crypto mining process.

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Acknowledgements

The authors would like to thank the editors and the anonymous referees for their valuable comments and suggestions which have helped in improving the quality and presentation of the paper.

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  1. Department of Statistics, Maharshi Dayanand University, Rohtak, India

    A. D. Yadav, N. Nandal, S. Malik & S. C. Malik

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  1. A. D. Yadav
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  2. N. Nandal
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  3. S. Malik
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  4. S. C. Malik
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Correspondence to S. C. Malik.

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Yadav, A.D., Nandal, N., Malik, S. et al. Markov approach for reliability-availability-maintainability analysis of a three unit repairable system. OPSEARCH 60, 1731–1756 (2023). https://doi.org/10.1007/s12597-023-00684-7

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