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On the equivalence of systems of different sizes, with applications to system comparisons

Part of: Survival analysis and censored data Operations research and management science Special processes

Published online by Cambridge University Press:  10 June 2016

Bo H. Lindqvist ,
Francisco J. Samaniego  and
Arne B. Huseby
Bo H. Lindqvist*
Affiliation:
Norwegian University of Science and Technology
Francisco J. Samaniego*
Affiliation:
University of California, Davis
Arne B. Huseby*
Affiliation:
University of Oslo
*
* Postal address: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Email address: [email protected]
** Postal address: Department of Statistics, Mathematical Sciences Building, One Shields Avenue, University of California, Davis, CA 95616, USA.
*** Postal address: Department of Mathematics, University of Oslo, PO Box 1053 Blindern, N-0316 Oslo, Norway.
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Abstract

The signature of a coherent system is a useful tool in the study and comparison of lifetimes of engineered systems. In order to compare two systems of different sizes with respect to their signatures, the smaller system needs to be represented by an equivalent system of the same size as the larger system. In the paper we show how to construct equivalent systems by adding irrelevant components to the smaller system. This leads to simpler proofs of some current key results, and throws new light on the interpretation of mixed systems. We also present a sufficient condition for equivalence of systems of different sizes when restricting to coherent systems. In cases where for a given system there is no equivalent system of smaller size, we characterize the class of lower-sized systems with a signature vector which stochastically dominates the signature of the larger system. This setup is applied to an optimization problem in reliability economics.

Keywords

Coherent systemsystem signaturek-out-of-n systemmixed systemreliability polynomialirrelevant componentcut setcritical path vectorstochastic orderreliability economics

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing 90B50: Management decision making, including multiple objectives
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 2 , June 2016 , pp. 332 - 348
Copyright
Copyright © Applied Probability Trust 2016 

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