Review Articles

Time-dependent reliability analysis for repairable consecutive-k-out-of-n:F system

Gökhan Gökdere ,

Department of Statistics, Faculty of Science, Fırat University, Elazıg, Turkey

Hon Keung Tony Ng

Department of Statistical Science, Southern Methodist University, Dallas, TX, USA

Pages 139-147 | Received 27 Jan. 2020, Accepted 08 Aug. 2021, Published online: 13 Sep. 2021,
  • Abstract
  • Full Article
  • References
  • Citations

In a repairable consecutive $C(k,n:F)$ system, after the system operates for a certain time, some components may fail, some failed components may be repaired and the state of the system may change. The models developed in the existing literature usually assume that the state of the system varies over time depending on the values of n and k and the state of the system is known. Since the system reliability will vary over time, it is of great interest to analyse the time-dependent system reliability. In this paper, we develop a novel and simple method that utilizes the eigenvalues of the transition rate matrix of the system for the computation of time-dependent system reliability when the system state is known. In addition, the transition performance probabilities of the system from a known state to the possible states are also analysed. Computational results are presented to illustrate the applicability and accuracy of the proposed method.

References

  • Bollinger, R. C., & Salvia, A. A. (1982). Consecutive-k-out-of-n: F networks. IEEE Transactions on Reliability, R-31(1), 5356. https://doi.org/10.1109/TR.1982.5221227
  • Chang, G. J., Cui, L. R., & Hwang, F. (2000). Reliabilities of consecutive-k-out-of-n:F systems. Kluwer.
  • Cheng, K., & Zhang, Y. L. (2001). Analysis for a consecutive-k-out-of-n: F repairable system with priority in repair. International Journal of Systems Science, 32(5), 591598. https://doi.org/10.1080/00207720119474
  • Chiang, D. T., & Niu, S. C. (1981). Reliability of consecutive-k-out-of-n:F system. IEEE Transactions on Reliability, R-30(1), 8789. https://doi.org/10.1109/TR.1981.5220981
  • Derman, C., Lieberman, G. J., & Ross, S. M. (1982). On the consecutive-k-out-of-n:F system. IEEE Transactions on Reliability, R-31(1), 5763. https://doi.org/10.1109/TR.1982.5221229
  • Eryilmaz, S. (2010). Review of recent advances in reliability of consecutive k-out-of-n and related systems. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 224(3), 225237. https://doi.org/10.1243/1748006XJRR332
  • Eryilmaz, S. (2014). Computing reliability indices of repairable systems via signature. Journal of Computational and Applied Mathematics, 260(2014), 229235. https://doi.org/10.1016/j.cam.2013.09.023
  • Gökdere, G., Gürcan, M., & Kılıç, M. B. (2016). A new method for computing the reliability of consecutive k-out-of-n:F systems. Open Physics, 14(1), 166170. https://doi.org/10.1515/phys-2016-0015
  • Guan, J., & Wu, Y. (2006). Repairable consecutive-k-out-of-n:F system with fuzzy states. Fuzzy Sets and Systems, 157(1), 121142. https://doi.org/10.1016/j.fss.2005.05.025
  • Hongda, G., Lirong, C., & He, Y. (2019). Availability analysis of k-out-of-n:F repairable balanced systems with m sectors. Reliability Engineering and System Safety, 191(2019), 110. https://doi.org/10.1016/j.ress.2019.106572
  • Kontoleon, J. M. (1980). Reliability determination of a r-successive-out-of-n:F system. IEEE Transactions on Reliability, 29(5), 437. https://doi.org/10.1109/TR.1980.5220921
  • Kuo, W., & Zuo, M. (2003). Optimal reliability modeling: principles and applications. Wiley.
  • Lam, Y., & Ng, H. K. T. (2001). A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k-1)-step Markov dependence. European Journal of Operational Research, 129(3), 663682. https://doi.org/10.1016/S0377-2217(99)00474-9
  • Lam, Y., & Zhang, Y. L. (1999). Analysis of repairable consecutive-2-out-of-n: F systems with Markov dependence. International Journal of Systems Science, 30(8), 799809. https://doi.org/10.1080/002077299291921
  • Lam, Y., & Zhang, Y. L. (2000). Repairable consecutive-k-out-of-n:F system with Markov dependence. Naval Research Logistics (NRL), 47(1), 1839. https://doi.org/10.1002/(ISSN)1520-6750
  • R Core Team (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing.
  • Wang, G., Hu, L., Zhang, T., & Wang, Y. (2021). Reliability modeling for a repairable (k1,k2)-out-of-n: G system with phase-type vacation time. Applied Mathematical Modelling, 91(2), 311321. https://doi.org/10.1016/j.apm.2020.08.071
  • Yam, R. C. M., Zuo, M. J., & Zhang, Y. L. (2003). A method for evaluation of reliability indices for repairable circular consecutive-k-out-of-n:F systems. Reliability Engineering and System Safety, 79(1), 19. https://doi.org/10.1016/S0951-8320(02)00204-1
  • Yuan, L., & Cui, Z. D. (2013). Reliability analysis for the consecutive-k-out-of-n: F system with repairmen taking multiple vacations. Applied Mathematical Modelling, 37(7), 46854697. https://doi.org/10.1016/j.apm.2012.09.008
  • Zhang, Y. L., & Lam, Y. (1998). Reliability of consecutive-k-out-of-n: G repairable system. International Journal of Systems Science, 29(12), 13751379. https://doi.org/10.1080/00207729808929623
  • Zhang, Y. L., & Wang, T. P. (1996). Repairable consecutive-2-out-of-n:F system. Microelectronics Reliability, 36(5), 605608. https://doi.org/10.1016/0026-2714(95)00183-2
  • Zhang, Y. L., Wang, T. P., & Jia, J. S. (1998). Reliability analysis of consecutive-k-out-of-n:G repairable system. Chinese Journal of Automation, 10(1998), 181186.
  • Zhang, Y. L., Zuo, M. J., & Yam, R. C. M. (2000). Reliability analysis for a circular consecutive-2-out-of-n:F repairable system with priority in repair. Reliability Engineering and System Safety, 68(2), 113120. https://doi.org/10.1016/S0951-8320(99)00076-9
  • Zuo, M. J., & Kuo, W. (1990). Design and performance analysis of consecutive-k-out-of-n structure. Naval Research Logistics, 37(2), 203230. https://doi.org/10.1002/(ISSN)1520-6750 [Crossref], [Web of Science ®][Google Scholar]

To cite this article: Gökhan Gökdere & Hon Keung Tony Ng (2021): Time-dependent reliability
analysis for repairable consecutive-k-out-of-n:F system, Statistical Theory and Related Fields, DOI:10.1080/24754269.2021.1971489
To link to this article: https://doi.org/10.1080/24754269.2021.1971489