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Reliability modelling and analysis of client–server system using Gumbel–Hougaard family copula

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Abstract

The present paper deals with the reliability analysis of a computer network system as series parallel system consisting of two subsystems. Subsystem I consist of four homogeneous clients while subsystem II consist of two homogeneous servers. Both clients and servers have exponential failure whereas repairs follow two types of distributions that are general and Gumbel–Hougaard family copula. The network under consideration has three states: normal, partial failure state and complete failure state. From the transition diagram, the system of first-order partial differential equations is derived and solved using a supplementary variable technique and Laplace transforms. The system is analyzed using Laplace transforms to solve the mathematical equations. The results obtained are presented in tables and graphs. Some important measures of reliability such as availability of system, reliability of the system, MTTF, sensitivity and cost analysis have been discussed. Some particular cases have also been derived and examined to see the practical effect of the model.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Ibrahim Yusuf

  2. Department of Mathematics, Kano State College of Education and Preliminary Studies, Kano, Nigeria

    Abdulkareem Lado Ismail

  3. Department of Mathematics, Kano University of Science and Technology, Wudil, Kano, Nigeria

    Muhammad Auwal Lawan

  4. Department of Mathematics, Federal University, Dutse, Nigeria

    U. A. Ali

  5. Department of Computer Science, Bayero University, Kano, Nigeria

    Sufi Nasir

Authors
  1. Ibrahim Yusuf
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  2. Abdulkareem Lado Ismail
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  3. Muhammad Auwal Lawan
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  4. U. A. Ali
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  5. Sufi Nasir
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Correspondence to Ibrahim Yusuf.

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Yusuf, I., Ismail, A.L., Lawan, M.A. et al. Reliability modelling and analysis of client–server system using Gumbel–Hougaard family copula. Life Cycle Reliab Saf Eng 10, 235–248 (2021). https://doi.org/10.1007/s41872-020-00159-4

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