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Comparisons of k-out-of-n systems with heterogenous components


  • Ding, Weiyong
  • Zhang, Yiying
  • Zhao, Peng


The k-out-of-n structure is a very popular type of redundancy in fault-tolerant systems which has been widely applied in reliability engineering and system security. In this paper, we carry out stochastic comparisons between k-out-of-n systems with independent heterogeneous components with respect to various stochastic orders such as hazard rate order, mean residual life order, and reversed hazard rate order. Moreover, we also establish likelihood ratio ordering results of series and parallel systems in multiple-outlier models.

Suggested Citation

  • Ding, Weiyong & Zhang, Yiying & Zhao, Peng, 2013. "Comparisons of k-out-of-n systems with heterogenous components," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 493-502.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:493-502 DOI: 10.1016/j.spl.2012.10.012

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    References listed on IDEAS

    1. Huaihou Chen & Taizhong Hu, 2008. "Multivariate likelihood ratio orderings between spacings of heterogeneous exponential random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(1), pages 17-29, June.
    2. Proschan, F. & Sethuraman, J., 1976. "Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 608-616, December.
    3. Misra, Neeraj & Misra, Amit Kumar, 2012. "New results on stochastic comparisons of two-component series and parallel systems," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 283-290.
    4. Zhao, Peng & Li, Xiaohu & Balakrishnan, N., 2009. "Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 952-962, May.
    5. Kochar, Subhash & Rojo, Javier, 1996. "Some New Results on Stochastic Comparisons of Spacings from Heterogeneous Exponential Distributions," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 272-281, November.
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    Cited by:

    1. Rezapour, Mohsen & Alamatsaz, Mohammad Hossein, 2014. "Stochastic comparison of lifetimes of two (n−k+1)-out-of-n systems with heterogeneous dependent components," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 240-251.
    2. Yang, Jianping & Zhuang, Weiwei, 2014. "A note on likelihood ratio ordering of order statistics from two samples," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 135-139.


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