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On the residual lifelengths of the remaining components in an n-k+1 out of n system

Author

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  • Bairamov, Ismihan
  • Arnold, Barry C.

Abstract

Suppose that a system consists of n independent components and that the lifelength of the ith component is a random variable . For k[set membership, variant]{1,2,...,n-1}, denote by , the residual lifelengths of the remaining functioning components following the kth failure in the system. We discuss the joint distribution of these exchangeable random variables. In addition, we identify the conditions sufficient to guarantee the independence of the residual lifelengths.

Suggested Citation

  • Bairamov, Ismihan & Arnold, Barry C., 2008. "On the residual lifelengths of the remaining components in an n-k+1 out of n system," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 945-952, June.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:8:p:945-952
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    Citations

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    Cited by:

    1. Vladimir Rykov & Nika Ivanova & Dmitry Kozyrev & Tatyana Milovanova, 2022. "On Reliability Function of a k -out-of- n System with Decreasing Residual Lifetime of Surviving Components after Their Failures," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    2. Balakrishnan, Narayanaswamy & Barmalzan, Ghobad & Haidari, Abedin, 2016. "Multivariate stochastic comparisons of multivariate mixture models and their applications," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 37-43.
    3. Tavangar, Mahdi & Bairamov, Ismihan, 2015. "On conditional residual lifetime and conditional inactivity time of k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 225-233.
    4. Sadiya & Mangey Ram & Akshay Kumar, 2022. "A New Approach to Compute System Reliability with Three-Serially Linked Modules," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    5. Mangey Ram & Subhi Tyagi & Akshay Kumar, 2024. "Reliability evaluation of a programmable logic controller based system," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(8), pages 3620-3628, August.
    6. EryIlmaz, Serkan, 2010. "On system reliability in stress-strength setup," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 834-839, May.
    7. Francisco J. Samaniego & N. Balakrishnan & Jorge Navarro, 2009. "Dynamic signatures and their use in comparing the reliability of new and used systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 577-591, September.
    8. Tokarev, Daniel V. & Borovkov, Konstantin A., 2009. "On the expectations of maxima of sets of independent random variables," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2381-2388, December.
    9. Serkan Eryılmaz, 2013. "On residual lifetime of coherent systems after the rth failure," Statistical Papers, Springer, vol. 54(1), pages 243-250, February.
    10. Zhang, Zhengcheng & Yang, Yonghong, 2010. "Ordered properties on the residual life and inactivity time of (n-k+1)-out-of-n systems under double monitoring," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 711-717, April.
    11. Eryilmaz, Serkan, 2012. "On the mean residual life of a k-out-of-n:G system with a single cold standby component," European Journal of Operational Research, Elsevier, vol. 222(2), pages 273-277.

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