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A Note on the Mixture Representation of the Conditional Residual Lifetime of a Coherent System

Part of: Distribution theory Special processes

Published online by Cambridge University Press:  30 January 2018

Xiuying Feng ,
Shuhong Zhang  and
Xiaohu Li
Xiuying Feng*
Affiliation:
Lanzhou University
Shuhong Zhang*
Affiliation:
Lanzhou University
Xiaohu Li*
Affiliation:
Xiamen University
*
∗ Postal address: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
∗ Postal address: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
∗∗∗ Postal address: School of Mathematics Sciences, Xiamen University, Xiamen 361005, China.
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Abstract

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This paper builds a mixture representation of the reliability function of the conditional residual lifetime of a coherent system in terms of the reliability functions of conditional residual lifetimes of order statistics. Some stochastic ordering properties for the conditional residual lifetime of a coherent system with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors.

Keywords

Coherent systemorder statisticsresidual lifetimesignaturestochastic order

MSC classification

Primary: 62E15: Exact distribution theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 2 , June 2013 , pp. 475 - 485
Copyright
© Applied Probability Trust 

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