Downwards inference: Bayesian analysis of overlapping higher-level data sets of complex binary-state on-demand systems

A developed Bayesian approach for generating inference from multiple overlapping higher level data sets on component failure probabilities within complex on-demand systems is presented in this paper. Data sets are overlapping if they are drawn from the same process or system at the same time. Alternate methodologies are typically strictly limited to analyzing non-overlapping data, which can both lose or incorrectly infer information if the data is overlapping in nature. The methodology outlined in this paper is based on typical understanding of system logic represented using fault-trees, reliability block diagrams or another equivalent representation. Structure functions of the system at relevant sensor locations (developed from the system logic) in terms of component states are used in conjunction with the probability of all possible system states (or all possible state vectors) to generate the likelihood function of overlapping evidence. This forms the basis of the likelihood function used in the Bayesian analysis of the overlapping data sets.