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Signature-Based Representations for the Reliability of Systems with Heterogeneous 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 and King Saud University
*
∗ Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain. Email address: jorgenav@um.es
∗∗ Postal address: Department of Statistics, University of California, Davis, 1 Shields Avenue, 95616 Davis, CA, 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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Signature-based representations of the reliability functions of coherent systems with independent and identically distributed component lifetimes have proven very useful in studying the ageing characteristics of such systems and in comparing the performance of different systems under varied criteria. In this paper we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of systems with homogeneous and heterogeneous components.

Keywords

Coherent systemk-out-of-n systemorder statisticsignaturemixturecopulastochastic order

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 856 - 867
Copyright
Copyright © Applied Probability Trust 2011 

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