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The Joint Signature of Coherent Systems with Shared Components

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Jorge Navarro ,
Francisco J. Samaniego  and
N. Balakrishnan
Jorge Navarro*
Affiliation:
Universidad de Murcia
Francisco J. Samaniego*
Affiliation:
University of California, Davis
N. Balakrishnan*
Affiliation:
McMaster University
*
∗Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain. Email address: jorgenav@um.es
∗∗Postal address: University of California, Davis, 1 Shields Avenue, Davis, CA 96616, USA. Email address: fjsamaniego@ucdavis.edu
∗∗∗Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada. Email address: bala@mcmaster.ca
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Abstract

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System signatures are useful tools in the study and comparison of coherent systems. In this paper, we define and study a similar concept, called the joint signature, for two coherent systems which share some components. Under an independent and identically distributed assumption on component lifetimes, a pseudo-mixture representation based on this joint signature is obtained for the joint distribution of the lifetimes of both systems. Sufficient conditions are given based on the respective joint signatures of two pairs of systems, each with shared components, to ensure various forms of bivariate stochastic orderings between the joint lifetimes of the two pairs of systems.

Keywords

Coherent systemk-out-of-n systemorder statisticssignaturesingular distributionmatrix orderingsbivariate stochastic orderings

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 235 - 253
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

Visiting Professor at King Saud University (Saudi Arabia) and National Central University (Taiwan).

References

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