Nonparametric predictive inference for failure times of systems with exchangeable components

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

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.
• Public URL: https://durham-repository.worktribe.com/output/1489780