  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 called prior-data conflict then can arise: observed
data seem very surprising from the viewpoint of the prior, i.e., information
from data is in conflict with prior assumptions. 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. An approach to mitigate this issue
is presented, by considering sets of prior distributions to model limited
knowledge on Weibull distributed component lifetimes, treating systems with
arbitrary layout using the survival signature. This approach can be seen as a
robust Bayesian procedure or imprecise probability method that reflects
surprisingly early or late component failures by wider system reliability
bounds.
