Theoretical and methodological extensions to dynamic reliability analysis:Dissertation

Rigorous analysis of the reliability of a dynamic system calls for modelling of the dynamic behaviour of the system and its interactions. However, traditional and the most frequently used reliability analysis methods, such as fault tree analysis, are static and have only limited capability to represent dynamic systems. Therefore, dynamic reliability analysis methods have been studied since 1990s. Dynamic flowgraph methodology (DFM) is a method for the reliability analysis of dynamic systems containing feedback loops. A DFM model is a dynamic graph representation of the analysed system. DFM has been most often applied to different digital control systems. One reason for this is that a DFM model can represent the interactions between a control system and the controlled process. The main goal of DFM analysis is to identify prime implicants, which are minimal combinations of events and conditions that cause the analysed top event, for example, system failure. This dissertation strengthens the mathematical foundation of DFM by developing an improved definition of a prime implicant. Risk importance measures can be used to identify components and basic events that are most important for the reliability of the system. This dissertation develops new dynamic risk importance measures as generalisations of two traditional risk importance measures for the needs of DFM. Unlike any other importance measure, the dynamic risk importance measures utilise all the information available in prime implicants of DFM. They primarily measure the importances of different states of components and variables of a DFM model. The computation of the dynamic risk importance measures for failure states of components provides significant additional information compared to other importance values.This dissertation also examines common cause failures (CCFs) in dynamic reliability analysis. Taking CCFs into account is important when modelling systems with redundancies. The dissertation extends the DFM by presenting CCF models that take failure times of components into account