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Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

Part of: Distribution theory Special processes

Published online by Cambridge University Press:  14 July 2016

Zhengcheng Zhang
Zhengcheng Zhang*
Affiliation:
Lanzhou Jiaotong University
*
∗Postal address: School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, 730070 Lanzhou, P. R. China. Email address: zhangzc@mail.lzjtu.cn
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Abstract

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In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.

Keywords

Coherent systeminactivity timemixture representationsignaturestochastic order

MSC classification

Secondary: 62E15: Exact distribution theory 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 876 - 885
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

Research supported by the Science and Technology Program of Gansu Province, China (project no. 1010RJZA076).

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