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Reliabilities for (n,f,k) systems

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  • Chang, Gerard J.
  • Cui, Lirong
  • Hwang, Frank K.

Abstract

The (n,f,k) system consists of n components ordered in a line or a cycle, while the system fails if, and only if, there exist at least f failed components or at least k consecutive failed components. For the linear (n,f,k) system with equal component reliabilities, the system reliability formula was given by Sun and Liao (1990). In this paper, we obtain the system reliability formulas for the linear and the circular systems with different component reliabilities by means of a Markov chain method.

Suggested Citation

  • Chang, Gerard J. & Cui, Lirong & Hwang, Frank K., 1999. "Reliabilities for (n,f,k) systems," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 237-242, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:3:p:237-242
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    References listed on IDEAS

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    1. M. Chao & James Fu, 1989. "A limit theorem of certain repairable systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 809-818, December.
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    Cited by:

    1. Ioannis S. Triantafyllou, 2023. "Combined m -Consecutive- k -Out-of- n : F and Consecutive k c -Out-of- n : F Structures with Cold Standby Redundancy," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    2. Negi, Seema & Singh, S.B., 2015. "Reliability analysis of non-repairable complex system with weighted subsystems connected in series," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 79-89.
    3. Ioannis S. Triantafyllou, 2020. "On the Consecutive k 1 and k 2 -out-of- n Reliability Systems," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    4. Kirtee Kamalja, 2014. "On the joint distribution of success runs of several lengths in the sequence of MBT and its applications," Statistical Papers, Springer, vol. 55(4), pages 1179-1206, November.
    5. Bartolucci, F., 2001. "Developments of the Markov chain approach within the distribution theory of runs," Computational Statistics & Data Analysis, Elsevier, vol. 36(1), pages 107-118, March.
    6. Yin, Juan & Cui, Lirong, 2021. "Reliability for consecutive-k-out-of-n: F systems with shared components between adjacent subsystems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    7. Gao, Hongda & Cui, Lirong & Yi, He, 2019. "Availability analysis of k-out-of-n: F repairable balanced systems with m sectors," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    8. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2024. "Joint signatures of two or more semi-coherent systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    9. Markos V. Koutras & Ioannis S. Triantafyllou & Serkan Eryilmaz, 2016. "Stochastic Comparisons Between Lifetimes of Reliability Systems with Exchangeable Components," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1081-1095, December.
    10. Ioannis S. Triantafyllou, 2020. "m -Consecutive- k -out-of- n : F Structures with a Single Change Point," Mathematics, MDPI, vol. 8(12), pages 1-14, December.
    11. Ioannis S. Triantafyllou & Miltiadis Chalikias, 2023. "Consecutive- k 1 and k 2 -out-of- n : F Structures with a Single Change Point," Stats, MDPI, vol. 6(1), pages 1-12, March.
    12. Ioannis S. Triantafyllou, 2024. "A Dynamic Reliability Analysis for the Conditional Number of Working Components within a Structure," Stats, MDPI, vol. 7(3), pages 1-18, August.
    13. Gao, Hongda & Tu, Tengfei & Qiu, Qingan, 2024. "Reliability analysis for a generalized sparse connection multi-state consecutive-k-out-of-n linear system," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    14. Yin, Juan & Cui, Lirong & Sun, Yudao & Balakrishnan, Narayanaswamy, 2022. "Reliability modelling for linear and circular k-out-of-n: F systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    15. Cui, Lirong & Kuo, Way & Li, Jinlin & Xie, Min, 2006. "On the dual reliability systems of (n,f,k) and," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1081-1088, June.

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