Robust Bayesian estimation of system reliability for scarce and surprising data

In reliability engineering, data about failure events is often scarce. To arrive at meaningful estimates for the reliability of a system, it is therefore often necessary to also include expert information in the analysis, which is straightforward in the Bayesian approach by using an informative prior distribution. A problem that then can arise is called prior-data conflict: from the viewpoint of the prior, the observed data seem very surprising, i.e., the information from data is in conflict with the prior assumptions. It has been recognised that models based on conjugate priors can be insensitive to prior-data conflict, in the sense that the spread of the posterior distribution does not increase in case of such a conflict, thus conveying a false sense of certainty by communicating that we can quantify the reliability of a system quite precisely when in fact we cannot. We present an approach to mitigate this issue, by considering sets of prior distributions to model vague knowledge on component lifetimes, and study how surprisingly early or late component failures affect the prediction of the reliability of a simplified parallel system. Our approach can be seen as a robust Bayesian procedure or imprecise probability method that appropriately reflects surprising data in the posterior system survival function or other posterior inferences.