The number of failed components in a conditional coherent operating system
Received:November 13, 2018  Revised:August 20, 2019
Key Word: Coherent system   Stochastic order   Mean   IFR   Signature.  
Fund ProjectL:The National Natural Science Foundation of China
Author NameAffiliationE-mail
洁 文 熊 Lanzhou Jiaotong University 
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      Coherent systems are very important in reliability, survival analysis and other life sciences. In this paper, we consider the number of failed components in an (n-k+1)-out-of-n system, given that at least m components have failed before time t, and the system is still working at time t. First the reliability and several stochastic properties are obtained. Furthermore, we extend the results to general coherent systems with absolutely continuous and exchangeable components.
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