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On the number of failed components in a coherent operating system


  • Asadi, Majid
  • Berred, Alexandre


In this paper, we investigate the number of failed components in a coherent system. We consider an (n−m+1)-out-of-n system and we compute the probability that there are exactly i failures, i=0,…,m−1, in the system under the condition that it is operating at time t. Several properties of the proposed time dependent probabilities are studied. The results are then extended to coherent systems consisting of n components with an arbitrary signature vector.

Suggested Citation

  • Asadi, Majid & Berred, Alexandre, 2012. "On the number of failed components in a coherent operating system," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2156-2163.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2156-2163
    DOI: 10.1016/j.spl.2012.07.010

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    References listed on IDEAS

    1. Navarro, Jorge & Spizzichino, Fabio & Balakrishnan, N., 2010. "Applications of average and projected systems to the study of coherent systems," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1471-1482, July.
    2. Mahdi Tavangar & Majid Asadi, 2010. "A study on the mean past lifetime of the components of (n − k + 1)-out-of-n system at the system level," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 59-73, July.
    3. Navarro, Jorge & Ruiz, Jose M. & Sandoval, Carlos J., 2005. "A note on comparisons among coherent systems with dependent components using signatures," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 179-185, April.
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