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The mean number of failed components in discrete time consecutive k-out-of-n: F system and its application to parameter estimation and optimal age-based preventive replacement

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  • Eryilmaz, Serkan
  • Kan, Cihangir

Abstract

It is important in many respects to have information about the number of failed components in the system when or before a system fails. This paper investigates the mean number of failed components at or before the failure time of the linear consecutive k-out-of-n:F system which is a useful structure to model various engineering systems such as transportation and transmission systems. In particular, closed form expressions for the mean number of failed components within the system that have discretely distributed components lifetimes are obtained. The results are used to estimate the unknown parameter of the components’ lifetime distribution and to find the optimal replacement cycle that minimizes the expected cost per unit of time under a certain age-based replacement policy.

Suggested Citation

  • Eryilmaz, Serkan & Kan, Cihangir, 2025. "The mean number of failed components in discrete time consecutive k-out-of-n: F system and its application to parameter estimation and optimal age-based preventive replacement," Reliability Engineering and System Safety, Elsevier, vol. 263(C).
    • Handle: RePEc:eee:reensy:v:263:y:2025:i:c:s0951832025004302
    DOI: 10.1016/j.ress.2025.111229
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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. Davies, Katherine & Dembińska, Anna, 2019. "On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 47-61.
    3. Serkan Eryilmaz & Fatih Tank, 2023. "Optimal age replacement policy for discrete time parallel systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 475-490, October.
    4. Sheldon M. Ross & Mehrdad Shahshahani & Gideon Weiss, 1980. "On the Number of Component Failures in Systems Whose Component Lives are Exchangeable," Mathematics of Operations Research, INFORMS, vol. 5(3), pages 358-365, August.
    5. Eryilmaz, Serkan, 2023. "Age based preventive replacement policy for discrete time coherent systems with independent and identical components," Reliability Engineering and System Safety, Elsevier, vol. 240(C).
    6. Eryilmaz, Serkan, 2020. "Age-based preventive maintenance for coherent systems with applications to consecutive-k-out-of-n and related systems," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    7. Eryilmaz, Serkan, 2024. "Reliability and performance evaluation of weighted k-out-of-n:G system consisting of components with discrete lifetimes," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    8. Dui, Hongyan & Tian, Tianzi & Zhao, Jiangbin & Wu, Shaomin, 2022. "Comparing with the joint importance under consideration of consecutive-k-out-of-n system structure changes," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    9. Goroncy, Agnieszka & Jasiński, Krzysztof & Korejwo, Faustyna & Rudzate, Marta, 2025. "Lost capacity of the weighted k-out-of-n system with discrete component lifetimes," Reliability Engineering and System Safety, Elsevier, vol. 259(C).
    10. Eryilmaz, Serkan & Yalcin, Femin, 2022. "The number of failed components upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    11. Wang, Fang & Bai, Jie & Liu, Linlin & Ye, Tianyuan, 2024. "Temporal noisy-adder of bayesian network for scalable consecutive-k-out-of-n:F system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    12. Alkaff, Abdullah, 2021. "Discrete time dynamic reliability modeling for systems with multistate components," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    13. 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.
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    Cited by:

    1. Ye, Tianyuan & Liu, Linlin & Zhou, Yuan & Gao, Haiyang, 2026. "Effective Noisy-matrix of Bayesian network for scalable m-consecutive-k-out-of-n: F models with overlapping from -1 to k-1," Reliability Engineering and System Safety, Elsevier, vol. 265(PA).
    2. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2026. "Evaluation of joint reliability of linear two-dimensional consecutive k-type systems in a zigzag structure," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).

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