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Nonparametric predictive inference for failure times of systems with exchangeable components

Coolen, F.P.A.; Al-nefaiee, A.H.

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Authors

A.H. Al-nefaiee



Abstract

The theory of system signatures (Samaniego, 2007) provides a powerful framework for reliability assessment for systems consisting of exchangeable components. For a system with m components, the signature is a vector containing the probabilities for the events that the system fails at the moment of the jth ordered component failure time, for all j = 1,…, m. As such, the signature represents the structure of the system. This paper presents how signatures can be used within nonparametric predictive inference, a statistical framework which uses few modelling assumptions enabled by the use of lower and upper probabilities to quantify uncertainty. The main result is the use of signatures to derive lower and upper survival functions for the failure time of systems with exchangeable components, given failure times of tested components that are exchangeable with those in the system. In addition, it is shown how the failure times of two such systems can be compared. This paper is the first in which signatures are combined with theory of lower and upper probabilities; related research challenges are briefly discussed.

Citation

Coolen, F., & Al-nefaiee, A. (2012). Nonparametric predictive inference for failure times of systems with exchangeable components. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 226(3), 262-273. https://doi.org/10.1177/1748006x11418430

Journal Article Type Article
Publication Date Jun 1, 2012
Deposit Date Mar 29, 2013
Publicly Available Date Dec 3, 2014
Journal Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
Print ISSN 1748-006X
Electronic ISSN 1748-0078
Publisher SAGE Publications
Peer Reviewed Peer Reviewed
Volume 226
Issue 3
Pages 262-273
DOI https://doi.org/10.1177/1748006x11418430
Keywords Coherent systems, Exchangeable components, Lower and upper survival functions, Nonparametric predictive inference, Signatures.

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Accepted Journal Article (505 Kb)
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Copyright Statement
Coolen, F.P.A. and Al-nefaiee, A.H. (2012) 'Nonparametric predictive inference for failure times of systems with exchangeable components.', Proceedings of the Institution of Mechanical Engineers, part O : journal of risk and reliability., 226 (3). pp. 262-273. Copyright 2012 © Sage Publications. Reprinted by permission of SAGE Publications.






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