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On the number of failed components in a series–parallel system upon system failure when the lifetimes are DNID discrete random variables

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  • Krzysztof Jasiński

    (Nicolaus Copernicus University)

Abstract

In this paper, we study properties of a series–parallel system. The component lifetimes may be dependent and non-identically distributed (DNID) discrete random variables. We consider the number of failed components upon system failure. We derive the probability mass function and the expected value of this quantity. In addition, we find the conditional probabilities corresponding to this variate given some partial information about the system failure. We also provide a numerical example to demonstrate the theoretical results.

Suggested Citation

  • Krzysztof Jasiński, 2024. "On the number of failed components in a series–parallel system upon system failure when the lifetimes are DNID discrete random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(2), pages 183-200, February.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:2:d:10.1007_s00184-023-00909-1
    DOI: 10.1007/s00184-023-00909-1
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    References listed on IDEAS

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    1. Eryilmaz, Serkan, 2018. "The number of failed components in a k-out-of-n system consisting of multiple types of components," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 246-250.
    2. M. Kelkinnama & M. Asadi, 2019. "Stochastic and ageing properties of coherent systems with dependent identically distributed components," Statistical Papers, Springer, vol. 60(3), pages 805-821, June.
    3. Fatih Tank & Serkan Eryilmaz, 2015. "The distributions of sum, minima and maxima of generalized geometric random variables," Statistical Papers, Springer, vol. 56(4), pages 1191-1203, November.
    4. Maryam Kelkinnama & Serkan Eryilmaz, 2023. "Some reliability measures and maintenance policies for a coherent system composed of different types of components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 57-82, January.
    5. Achintya Roy & Nitin Gupta, 2020. "Reliability of a coherent system equipped with two cold standby components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 677-697, August.
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