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Coverage modeling of fault-tolerant system under copula and waiting repair policy

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Abstract

This paper is related to the reliability of a three-unit repairable system having the concept of two types of repairs with waiting repair time and imperfect coverage. The concept of imperfect coverage for switching failed components is taken into account. If any unit fails, it is immediately repaired with the coverage probability c but, if the repair facility is not available instantly, then it has to wait for repairs and when the system waits for repairs, it is repaired by two types of repair facility. The Markov process is used to model the system mathematically to get the transient probabilities related to the system states. Laplace transform is utilized to assess the transient probabilities, which are additionally used to assess some reliability qualities such as availability, mean time to failure (MTTF), expected profit, and sensitivity. The failure time of the units is assumed to follow an exponential distribution whereas, the time to repair follows the general and Gumbel–Hougaard family of copula distribution. Numerical simulations have been taken to explore the availability, MTTF, profit, and sensitivity associated with the system. Results and conclusions are made for the system based on the graphical study.

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Authors and Affiliations

  1. Department of Applied Science & Humanities, ABES Institute of Technology, Ghaziabad, Uttar Pradesh, India

    Vaishali Tyagi

  2. Department of Mathematics, Computer Science and Engineering, Graphic Era Deemed to Be University, Dehradun, Uttarakhand, India

    Mangey Ram

  3. Department of Mathematics and Statistics, Kanya Gurukul Campus (Haridwar), Gurukul Kangri Deemed to be University, Haridwar, Uttarakhand, India

    Ritu Arora

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  1. Vaishali Tyagi
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  2. Mangey Ram
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  3. Ritu Arora
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Correspondence to Mangey Ram.

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Tyagi, V., Ram, M. & Arora, R. Coverage modeling of fault-tolerant system under copula and waiting repair policy. Life Cycle Reliab Saf Eng 13, 1–14 (2024). https://doi.org/10.1007/s41872-024-00241-1

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