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Reliability of a Series System with Redundancy and Threshold Recovery Strategies

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Abstract

We propose a method for studying the reliability of series systems with redundancy and recovery strategies, which provide for a change in the repair intensity depending on the number of failed units. The case of the exponential distribution of the time to failure of units, the non-exponential distribution of the recovery time, and one repair channel are considered. Formulas for determining Laplace transforms of the distribution of the number of failed units during the busy period of the repair channel and of the distribution functions of the busy period and to calculate the stationary indices are obtained.

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References

  1. I. Ushakov, Probabilistic Reliability Models, John Wiley & Sons, Hoboken (2012).

    Book  Google Scholar 

  2. Yu. V. Zhernovyi, Reliability Simulation Models: Workshop on the Use of GPSS World [in Ukrainian], Zhytomyr-Poligraf, Zhytomyr (2020).

    Google Scholar 

  3. L. A. Ovcharov, Applied Problems of Queueing Theory [in Russian], Mashinostroyeniye, Moscow (1969)

    Google Scholar 

  4. Yu. Zhernovyi and K. Zhernovyi, The Potentials Method for Threshold Service Strategies [in Russian], LAP Lambert Academic Publishing, Saarbrucken (2015).

    MATH  Google Scholar 

  5. Yu. V. Zhernovyi and K. Yu. Zhernovyi, “Method of potentials for a closed system with queue length dependent service times,” J. Commun. Technol. Electron., Vol. 60, No. 12, 1341–1347 (2015). https://doi.org/https://doi.org/10.1134/S1064226915120219.

  6. Yu. Zhernovyi and B. Kopytko, “The potentials method for a closed queueing system with hysteretic strategy of the service time change,” J. Applied Math. and Comp. Mech., 2015, Vol. 14, Iss. 2, 131–143. https://doi.org/10.17512/jamcm.2015.2.14.

  7. Yu. V. Zhernovyi and K. Yu. Zhernovyi, “Potentials method for M G m / /1/ systems with threshold operating strategies,” Cybern. Syst. Analys, Vol. 52, No. 3, 481–491 (2016). https://doi.org/https://doi.org/10.1007/s10559-016-9849-7.

  8. Yu. V. Zhernovyi, “Potentials method forM G m / /1/ systems with hysteretic operating strategies,” Cybern. Syst. Analysis, Vol. 52, No. 5, 770–781 (2016). https://doi.org/https://doi.org/10.1007/s10559-016-9878-2.

  9. Yu. Zhernovyi, Creating Models of Queueing Systems using GPSS World: Programs, Detailed Explanations and Analysis of Results, LAP Lambert Academic Publishing, Saarbrucken (2015).

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Authors and Affiliations

  1. Ivan Franko National University of Lviv, Lviv, Ukraine

    Yu. V. Zhernovyi

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  1. Yu. V. Zhernovyi
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Correspondence to Yu. V. Zhernovyi.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 4, July–August, 2021, pp. 146–154.

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Zhernovyi, Y.V. Reliability of a Series System with Redundancy and Threshold Recovery Strategies. Cybern Syst Anal 57, 629–637 (2021). https://doi.org/10.1007/s10559-021-00388-0

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  • DOI: https://doi.org/10.1007/s10559-021-00388-0

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