Robust Bayesian reliability for complex systems under prior-data conflict.

Abstract

This paper considers the quantification of system reliability in scenarios in which data, that is, failures or the absence of failures, occurring from the system’s use over time, are considered surprising from the perspective of prior information. A generalized, or imprecise, Bayesian approach is presented for general system structures in which the component lifetimes have Weibull distributions with a known shape parameter. For the scale parameter, a specific set of prior distributions is assumed that enables the prior-data conflict to be reflected through the increased imprecision in the posterior reliability bounds.