Bayesian inference with overlapping data: Reliability estimation of multi-state on-demand continuous life metric systems with uncertain evidence

• Application of Bayesian techniques for the analysis of overlapping multi-state data for both discrete and continuous systems.
• Development of methodology for incorporation of uncertain data.
• Modification of likelihood function for time based continuous systems resulting in substantial mathematical simplification.
• Discussion of uncertain data as it applies to extant forms of analysis and observation error.

A Bayesian system reliability estimation methodology for multiple overlapping uncertain data sets within complex multi-state on-demand and continuous life metric 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 at different functional and physical levels being a prime example. Treating overlapping data as non-overlapping loses or incorrectly infers information on system reliability. Methodologies for system reliability analysis of certain overlapping data sets have previously been proposed. These methodologies, and the approach presented in this paper, are able to incorporate overlapping uncertain evidence from systems with a detailed understanding of the system logic represented using fault-trees, reliability block diagrams or equivalent representations. The method presented here builds on approaches that have already been developed by the authors that allow incorporation of exact or certain data sets.