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.
Highlights
Common-cause failure has been recognized since the time of the Reactor Safety Study [1] as a dominant contributor to the unreliability of redundant systems
As zero counts are generally less of an issue here, we find that the choice of this learning parameter is less crucial
The benefit of the alpha-factor model over the basic parameter model lies in its distinction between the total failure rate of a component qt, for which we generally have a lot of information, and common-cause failures modeled by α, for which we generally have very little information
Summary
Common-cause failure has been recognized since the time of the Reactor Safety Study [1] as a dominant contributor to the unreliability of redundant systems. We follow Troffaes et al [3], and adapt the imprecise Dirichlet model of Walley [4] to represent epistemic uncertainty in the alpha-factors. In this approach the analyst specifies lower or upper expectations (or both) for each alphafactor, along with a learning parameter, which determines how quickly the prior distribution learns from observed data. Similar to the procedure for the alpha-factors, we can model epistemic uncertainty on the marginal failure rate by considering lower and upper expected prior failure rates, along with a learning parameter that determines how quickly the prior distribution learns from observed data. It is sensible to reparameterize the model in terms of parameters that can be more estimated, as follows
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
