Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

A robust Bayesian approach to modelling epistemic uncertainty in common-cause failure models.

Troffaes, Matthias C. M. and Walter, Gero and Kelly, Dana (2014) 'A robust Bayesian approach to modelling epistemic uncertainty in common-cause failure models.', Reliability engineering & system safety., 125 . pp. 13-21.

Abstract

In a standard Bayesian approach to the alpha-factor model for common-cause failure, a precise Dirichlet prior distribution models epistemic uncertainty in the alpha-factors. This Dirichlet prior is then updated with observed data to obtain a posterior distribution, which forms the basis for further inferences. In this paper, we adapt the imprecise Dirichlet model of Walley to represent epistemic uncertainty in the alpha-factors. In this approach, epistemic uncertainty is expressed more cautiously via lower and upper expectations for each alpha-factor, along with a learning parameter which determines how quickly the model learns from observed data. For this application, we focus on elicitation of the learning parameter, and find that values in the range of 1 to 10 seem reasonable. The approach is compared with Kelly and Atwood's minimally informative Dirichlet prior for the alpha-factor model, which incorporated precise mean values for the alpha-factors, but which was otherwise quite diffuse. Next, we explore the use of a set of Gamma priors to model epistemic uncertainty in the marginal failure rate, expressed via a lower and upper expectation for this rate, again along with a learning parameter. As zero counts are generally less of an issue here, we find that the choice of this learning parameter is less crucial. Finally, we demonstrate how both epistemic uncertainty models can be combined to arrive at lower and upper expectations for all common-cause failure rates. Thereby, we effectively provide a full sensitivity analysis of common-cause failure rates, properly reflecting epistemic uncertainty of the analyst on all levels of the common-cause failure model.

Item Type:Article
Keywords:Common-cause failure, Alpha-factor model, Epistemic uncertainty, Conjugate prior, Imprecise Dirichlet model.
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
Download PDF
(327Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.ress.2013.05.022
Publisher statement:© 2013 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).
Date accepted:15 May 2013
Date deposited:14 June 2013
Date of first online publication:25 June 2013
Date first made open access:No date available

Save or Share this output

Export:
Export
Look up in GoogleScholar