Bayesian inference with overlapping data: methodology for reliability estimation of multi-state on-demand systems

Abstract

A Bayesian system reliability analysis methodology for multiple overlapping higher level data sets within complex multi-state on-demand systems is presented in this paper. Data sets are overlapping if they are drawn from the same process at the same time, with reliability data from sensors attached to a system being a prime example. Treating overlapping data as non-overlapping loses or incorrectly infers information. The approach generated in this paper is able to incorporate overlapping data from multi-state on-demand systems with a detailed understanding of the 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.