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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. 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.
    2. 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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    5. 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.
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    2. EryIlmaz, Serkan, 2010. "On system reliability in stress-strength setup," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 834-839, May.
    3. 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).
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    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. 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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