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Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties

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Abstract

In this paper, we present several useful mixture representations for the reliability function of the inactivity time of systems with heterogeneous components based on order statistics, signatures and mean reliability functions. Some stochastic comparisons of inactivity times between two systems are discussed. These results form nice extensions of some existing results for the case when the components are independent and identically distributed.

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Acknowledgments

Zhengcheng Zhang’s research was supported by National Natural Science Foundation of China (11161028) while N. Balakrishnan’s research was supported by the Natural Sciences and Engineering Research Council of Canada. The authors are also thankful to the anonymous reviewers and the editor for their helpful comments and suggestions on an earlier version of this manuscript which led to this improved version.

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Authors and Affiliations

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Zhengcheng Zhang

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, L8S 4K1, Canada

    N. Balakrishnan

Authors
  1. Zhengcheng Zhang
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  2. N. Balakrishnan
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Correspondence to Zhengcheng Zhang.

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Zhang, Z., Balakrishnan, N. Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties. Metrika 79, 113–126 (2016). https://doi.org/10.1007/s00184-015-0546-8

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