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Efficient reliability computation of consecutive- k -out-of- n : F systems with shared components

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  • Juan Yin
  • Narayanaswamy Balakrishnan
  • Lirong Cui

Abstract

Consecutive- k systems have been studied extensively in reliability engineering. Linear and circular consecutive- k -out-of- n : F systems with shared component(s) have been studied recently by Lin et al. and Yin and Cui . They considered two adjacent subsystems overlapping with one (multiple) shared component(s), respectively, and obtained system reliability formulas by summing the reliability values for all disjoint cases. As their method is computationally intensive, it would be of interest to develop a simpler and more efficient method for the computation of the reliability function of such systems instead of requiring to list all disjoint cases. In this work, by employing the finite Markov chain imbedding approach, we develop unified formulas as products of matrices for evaluating system reliabilities by redefining the state space of the Markov chain. The results developed here decrease the complexity in the computation of system reliability. Furthermore, the new method is also employed to obtain reliability formulas for Markov-dependent cases. A case study of communication systems is finally presented and some numerical examples are presented to illustrate the developed model and the corresponding results.

Suggested Citation

  • Juan Yin & Narayanaswamy Balakrishnan & Lirong Cui, 2024. "Efficient reliability computation of consecutive- k -out-of- n : F systems with shared components," Journal of Risk and Reliability, , vol. 238(1), pages 122-135, February.
    • Handle: RePEc:sae:risrel:v:238:y:2024:i:1:p:122-135
    DOI: 10.1177/1748006X221130540
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    References listed on IDEAS

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    1. Xiang, Yanping & Levitin, Gregory, 2012. "Combined m-consecutive and k-out-of-n sliding window systems," European Journal of Operational Research, Elsevier, vol. 219(1), pages 105-113.
    2. Stathis Chadjiconstantinidis & Markos V. Koutras, 1999. "Measures of component importance for markov chain imbeddable reliability structures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 613-639, September.
    3. Zarezadeh, S. & Mohammadi, L. & Balakrishnan, N., 2018. "On the joint signature of several coherent systems with some shared components," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1092-1100.
    4. Yin, Juan & Cui, Lirong & Balakrishnan, Narayanaswamy, 2022. "Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
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