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Ordered properties on the residual life and inactivity time of (n-k+1)-out-of-n systems under double monitoring

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  • Zhang, Zhengcheng
  • Yang, Yonghong

Abstract

The (n-k+1)-out-of-n system is an important structure of the reliability of technical systems. In this paper, we consider the residual lifetime and the inactivity time of the system consisting of independent and identically distributed components, under the condition that the total number of failures of the components at time t1 is r (r t1) the system is still working or it has failed. Under these conditions, some ordered properties of one system or between two systems with two sets of independent components are obtained both for the hazard rate order and the likelihood ratio order. The results obtained here are stronger than the results included in Poursaeed (in press).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:711-717
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    References listed on IDEAS

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    1. Xiaohu Li & Zhengcheng Zhang, 2008. "Some stochastic comparisons of conditional coherent systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 541-549, November.
    2. Navarro, Jorge & Balakrishnan, N., 2010. "Study of some measures of dependence between order statistics and systems," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 52-67, January.
    3. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
    4. Bhattacharya, Debasis & Samaniego, Francisco J., 2008. "On the optimal allocation of components within coherent systems," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 938-943, May.
    5. 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.
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    Cited by:

    1. 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.
    2. Funda Iscioglu & Aysegul Erem, 2021. "Reliability analysis of a multi-state system with identical units having two dependent components," Journal of Risk and Reliability, , vol. 235(2), pages 241-252, April.
    3. EryIlmaz, Serkan, 2010. "On system reliability in stress-strength setup," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 834-839, May.
    4. Bayramoglu, Ismihan, 2020. "Joint distribution of a random sample and an order statistic: A new approach with an application in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    5. Li, Chen & Li, Xiaohu, 2023. "On k-out-of-n systems with homogeneous components and one independent cold standby redundancy," Statistics & Probability Letters, Elsevier, vol. 203(C).
    6. Sareh Goli, 2019. "On the conditional residual lifetime of coherent systems under double regularly checking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 352-363, June.

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