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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. 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.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:

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    2. 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).
    3. 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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    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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