Management of Sampling Uncertainty Using Conservative Estimate of Probability in Bayesian Network

Since the safety of a system is often assessed by the probability of failure, it is crucial to calculate the probability accurately in order to achieve the target safety. Despite such importance, calculating the precise probability is not a trivial task due to the inherent aleatory variability and epistemic uncertainty. Therefore the safety is assessed by a conservative estimate of the probability rather than using a single value of the probability. In general, there are two ways to achieve the target probability: Shifting the probability or reducing the uncertainty. In this paper, among various sources of epistemic uncertainty, the uncertainty quantification error from sampling is considered to calculate the conservative estimate of a system probability of failure. To quantify and shape the epistemic uncertainty, Bayesian network is utilized for constituting the relationship between the system probability and component probabilities, while global sensitivity analysis is employed to connect the variance in the probabilities in system level with that in the component level. Based on this, local sensitivity of the conservative estimate with respect to a design change in a component is derived and approximated for a simple numerical calculation using Bayesian network and global sensitivity analysis. This is to show how a design can meet the probabilistic criteria considering propagated uncertainty when the design changes.