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Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence

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  • Yin, Juan
  • Cui, Lirong
  • Balakrishnan, Narayanaswamy

Abstract

Multi-state system models are more practical and valuable when describing complex engineering structures than binary-state system models. Modelling of linear consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence is discussed in this work. The proposed model is an extension of both “consecutive-k-out-of-n: F system†and “consecutive-k-out-of-n: F system with shared components between adjacent subsystems†. All the components in the system are assumed to have three states and are non-homogeneous Markov-dependent. Using the method of sum of disjoint products (SDP), the system reliability formula is derived by summing the reliability values for all disjoint cases. The well-known finite Markov chain imbedding approach (FMCIA) is used for deriving the reliability formula for each disjoint case. For the special cases of systems with homogeneous Markov-dependent or independent components, the corresponding results are deduced. Finally, some numerical examples are presented to illustrate all the results developed here.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:224:y:2022:i:c:s0951832022002009
    DOI: 10.1016/j.ress.2022.108549
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    3. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
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    6. Zhu, Xiaojun & Balakrishnan, N., 2023. "Non-parametric inference based on reliability life-test of non-identical coherent systems with application to warranty time," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    7. Xiahou, Tangfan & Zheng, Yi-Xuan & Liu, Yu & Chen, Hong, 2023. "Reliability modeling of modular k-out-of-n systems with functional dependency: A case study of radar transmitter systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    8. 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.
    9. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2024. "Joint reliability of linear consecutive k-type systems with shared components in a zigzag structure," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    10. Zhao, Xian & Qi, Xin & Wang, Xiaoyue, 2023. "Reliability assessment for coherent systems operating under a generalized mixed shock model with multiple change points of the environment," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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