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- Status: Published
Bayesian networks generalize fault trees by allowing components and subsystems to be related by conditional probabilities instead of deterministic relationships; thus, they provide analytical advantages to the situation when the failure structure is not well understood, especially during the product design stage. In order to tackle this problem, one needs to utilize auxiliary information such as the reliability information from similar products and domain expertise. For this purpose, a Bayesian network approach is proposed to incorporate data from functional analysis and parent products. The functions with low reliability and their impact on other functions in the network are identified, so that design changes can be suggested for system reliability improvement.
A complex system does not necessarily have all components being monitored at the same time, causing another challenge in the reliability assessment problem. Sometimes there are a limited number of sensors deployed in the system to monitor the states of some components or subsystems, but not all of them. Data simultaneously collected from multiple sensors on the same system are analyzed using a Bayesian network approach, and the conditional probabilities of the network are estimated by combining failure information and expert opinions at both system and component levels. Several data scenarios with discrete, continuous and hybrid data (both discrete and continuous data) are analyzed. Posterior distributions of the reliability parameters of the system and components are assessed using simultaneous data.
Finally, a Bayesian framework is proposed to incorporate different sources of prior information and reconcile these different sources, including expert opinions and component information, in order to form a prior distribution for the system. Incorporating expert opinion in the form of pseudo-observations substantially simplifies statistical modeling, as opposed to the pooling techniques and supra Bayesian methods used for combining prior distributions in the literature.
The methods proposed are demonstrated with several case studies.
Single molecule FRET experiments are important for studying processes that happen on the molecular scale. By using pulsed illumination and collecting single photons, it is possible to use information gained from the fluorescence lifetime of the chromophores in the FRET pair to gain more accurate estimates of the underlying FRET rate which is used to determine information about the distance between the chromophores of the FRET pair. In this paper, we outline a method that utilizes Bayesian inference to learn parameter values for a model informed by the physics of a immobilized single-molecule FRET experiment. This method is unique in that it combines a rigorous look at the photophysics of the FRET pair and a nonparametric treatment of the molecular conformational statespace, allowing the method to learn not just relevant photophysical rates (such as relaxation rates and FRET rates), but also the number of molecular conformational states.