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Nonparametric predictive inference for failure times of systems with exchangeable components

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  • F P A Coolen
  • 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 j th 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.

Suggested Citation

  • F P A Coolen & A H Al-nefaiee, 2012. "Nonparametric predictive inference for failure times of systems with exchangeable components," Journal of Risk and Reliability, , vol. 226(3), pages 262-273, June.
    • Handle: RePEc:sae:risrel:v:226:y:2012:i:3:p:262-273
    DOI: 10.1177/1748006X11418430
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    References listed on IDEAS

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    1. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, December.
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    Cited by:

    1. Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2016. "The structure function for system reliability as predictive (imprecise) probability," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 180-187.
    2. Janurová, Kateřina & Briš, Radim, 2014. "A nonparametric approach to medical survival data: Uncertainty in the context of risk in mortality analysis," Reliability Engineering and System Safety, Elsevier, vol. 125(C), pages 145-152.

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