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Reliability modeling for repairable circular consecutive-k-out-of-n: F systems with retrial feature

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  • Li, Mingjia
  • Hu, Linmin
  • Peng, Rui
  • Bai, Zhuoxin

Abstract

In this paper, we consider a repairable circular consecutive-k-out-of-n: F retrial system, which can be used to simulate the intelligent closed recurring water cooling automation system in industrial production. We assume that the working time and retrial time of each component obey exponential distributions, and the repair time obeys a general distribution. Based on the generalized transition probability and the key component priority repair rule of the retrial system, the availability and reliability indices of the general repairable circular consecutive-k-out-of-n: F retrial system are derived by using the methods of supplementary variable and Laplace transform. Furthermore, we calculate the explicit expressions of the above indices when n and k are fixed at definite values in the system. The repair time is assumed to follow a Weibull distribution in examples demonstration, and the influence of various parameters on system reliability, steady-state availability and other indices are obtained. The sensitivity and relative sensitivity analysis of the steady-state availability, steady-state failure frequency and mean time to first failure (MTTFF) of the system are also performed.

Suggested Citation

  • Li, Mingjia & Hu, Linmin & Peng, Rui & Bai, Zhuoxin, 2021. "Reliability modeling for repairable circular consecutive-k-out-of-n: F systems with retrial feature," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:reensy:v:216:y:2021:i:c:s0951832021004683
    DOI: 10.1016/j.ress.2021.107957
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    References listed on IDEAS

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    1. Chen, Wu-Lin & Wang, Kuo-Hsiung, 2018. "Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 476-486.
    2. Zhu, Xiaoyan & Boushaba, Mahmoud & Coit, David W. & Benyahia, Azzeddine, 2017. "Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 1-9.
    3. 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).
    4. Dui, Hongyan & Si, Shubin & Yam, Richard C.M., 2018. "Importance measures for optimal structure in linear consecutive-k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 339-350.
    5. Yen, Tseng-Chang & Wang, Kuo-Hsiung, 2020. "Cost benefit analysis of four retrial systems with warm standby units and imperfect coverage," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    6. Gao, Shan & Wang, Jinting, 2021. "Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    7. A. Krishnamoorthy & P. Ushakumari, 1999. "Reliability of ak-out-of-n system with repair and retrial of failed units," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 293-304, December.
    8. Wu, Chia-Huang & Yen, Tseng-Chang & Wang, Kuo-Hsiung, 2021. "Availability and Comparison of Four Retrial Systems with Imperfect Coverage and General Repair Times," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    9. Yang, Dong-Yuh & Tsao, Chih-Lung, 2019. "Reliability and availability analysis of standby systems with working vacations and retrial of failed components," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 46-55.
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    Cited by:

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    2. Ioannis S. Triantafyllou, 2022. "Signature-Based Analysis of the Weighted- r -within-Consecutive- k -out-of- n : F Systems," Mathematics, MDPI, vol. 10(15), pages 1-13, July.
    3. Tian-yuan, Ye & Lin-lin, Liu & He-wei, Pang & Yuan-zi, Zhou, 2023. "Bayesian Networks based approach to enhance GO methodology for reliability modeling of multi-state consecutive-k-out-of-n: F system," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    4. Li, Mingjia & Hu, Linmin & Wu, Shaomin & Zhao, Bing & Wang, Yan, 2023. "Reliability assessment for consecutive-k-out-of-n: F retrial systems under Poisson shocks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    5. 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).
    6. Wang, Yan & Hu, Linmin & Yang, Li & Li, Jing, 2022. "Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    7. Yu, Xiaoyun & Hu, Linmin & Ma, Mengrao, 2023. "Reliability measures of discrete time k-out-of-n: G retrial systems based on Bernoulli shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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