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Some properties of the cumulative residual entropy of coherent and mixed systems

Part of: Survival analysis and censored data Communication, information

Published online by Cambridge University Press:  22 June 2017

A. Toomaj ,
S. M. Sunoj  and
J. Navarro
A. Toomaj*
Affiliation:
Gonbad Kavous University
S. M. Sunoj*
Affiliation:
Cochin University of Science and Technology
J. Navarro*
Affiliation:
Universidad de Murcia
*
* Postal address: Department of Statistics, Gonbad Kavous University, Gonbad Kavous, Iran. Email address: [email protected]
** Postal address: Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India. Email address: [email protected]
*** Postal address: Facultad de Matematicas, Universidad de Murcia, 30100 Murcia, Spain. Email address: [email protected]
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Abstract

Recently, Rao et al. (2004) introduced an alternative measure of uncertainty known as the cumulative residual entropy (CRE). It is based on the survival (reliability) function F̅ instead of the probability density function f used in classical Shannon entropy. In reliability based system design, the performance characteristics of the coherent systems are of great importance. Accordingly, in this paper, we study the CRE for coherent and mixed systems when the component lifetimes are identically distributed. Bounds for the CRE of the system lifetime are obtained. We use these results to propose a measure to study if a system is close to series and parallel systems of the same size. Our results suggest that the CRE can be viewed as an alternative entropy (dispersion) measure to classical Shannon entropy.

Keywords

Coherent systemcumulative residual entropystochastic ordersystem signature

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 94A17: Measures of information, entropy
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 379 - 393
Copyright
Copyright © Applied Probability Trust 2017 

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