Hierarchical Bayesian Reliability Analysis of Complex Dynamical Systems

The Bayesian methods provide additional information about the meaningful parameters in a statistical analysis obtained by combining the prior and sampling distributions to form the posterior distribution of the parameters. The desired inferences are obtained from this joint posterior. An estimation strategy for hierarchical models, where the resulting joint distribution of the associated model parameters cannot be evaluated analytically, is to use sampling algorithms, known as Markov Chain Monte Carlo (MCMC) methods, from which approximate solutions can be obtained. Both serial and parallel configurations of subcomponents are permitted. Components of the system are assumed to be linked through a reliability block diagram and the manner of failure data collected at the component or subcomponent level can be included into the posterior distribution permit the extension of failure information across similar subcomponents within the same or related systems. An effective and flexible event-based model for assessing the reliability of complex systems including multiple components that illustrates the Bayesian approach is presented.