Reliability Analysis with Ill-Known Probabilities and Dependencies

In this work, we are interested in estimating the uncertainty that a system will work, given the probabilities that its components will be either failing or working. Usually, this estimation is done by propagating the component uncertainties through a structure function. This problem is well-studied when component probabilities are known and when the componenst are assumed to be independent. In this paper, we first recall some results obtained when considering that probabilities are unknown and when one either assumes component independence or no knowledge about the component's dependence. We also explore some structures not studied up to now, such as consecutive k-out-of-n structures.