Abstract
In this note, we consider a coherent system with the property that, upon failure of the system, some of its components remain unfailed in the system. Under this condition, we study the residual lifetime of the live components of the system. Signature based mixture representation of the joint and marginal reliability functions of the live components are obtained. Various stochastic and aging properties of the residual lifetime of such components are investigated. Some characterization results on exponential distributions are also provided.
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Acknowledgments
We would like to thank the editor and the referee for constructive comments which improved the presentation of the paper. M. Asadi’s research was in part supported by a grant from IPM (No. 91620411). Z. Zhang’s research was supported by National Natural Science Foundation of China (11161028).
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Kelkin Nama, M., Asadi, M. & Zhang, Z. On the residual lifelengths of the remaining components in a coherent system. Metrika 76, 979–996 (2013). https://doi.org/10.1007/s00184-012-0427-3
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DOI: https://doi.org/10.1007/s00184-012-0427-3