Efficient reliability and sensitivity analysis of complex systems and networks with imprecise probability

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Complex systems and networks, such as grid systems and transportation networks, are backbones of our society, so performing RAMS (Reliability, Availability, Maintainability, and Safety) analysis on them is essential. The complex system consists of multiple component types, which is time consuming to analyse by using cut sets or system signatures methods. Analytical solutions (when available) are always preferable than simulation methods since the computational time is in general negligible. However, analytical solutions are not always available or are restricted to particular cases. For instance, if there exist imprecisions within the components' failure time distributions, or empirical distribution of components failure times are used, no analytical methods can be used without resorting to some degree of simplification or approximation. In real applications, there sometimes exist common cause failures within the complex systems, which make the components' independence assumption invalid. In this dissertation, the concept of survival signature is used for performing reliability analysis on complex systems and realistic networks with multiple types of components. It opens a new pathway for a structured approach with high computational efficiency based on a complete probabilistic description of the system. An efficient algorithm for evaluating the survival signature of a complex system bases on binary decision diagrams is introduced in the thesis. In addition, the proposed novel survival signature-based simulation techniques can be applied to any systems irrespectively of the probability distribution for the component failure time used. Hence, the advantage of the simulation methods compared to the analytical methods is not on the computational times of the analysis, but on the possibility to analyse any kind of systems without introducing simplifications or unjustified assumptions. The thesis extends survival signature analysis for application to repairable systems reliability as well as illustrates imprecise probability methods for modelling uncertainty in lifetime distribution specifications. Based on the above methodologies, this dissertation proposes applications for calculation of importance measures and performing sensitivity analysis. To be specific, the novel methodologies are based on the survival signature and allow to identify the most critical component or components set at different survival times of the system. The imprecision, which is caused by limited data or incomplete information on the system, is taken into consideration when performing a sensitivity analysis and calculating the component importance index. In order to modify the above methods to analyse systems with components that are subject to common cause failures, $\alpha$-factor models are presented in this dissertation. The approaches are based on the survival signature and can be applied to complex systems with multiple component types. Furthermore, the imprecision and uncertainty within the $\alpha$-factor parameters or component failure distribution parameters is considered as well. Numerical examples are presented in each chapter to show the applicability and efficiency of the proposed methodologies for reliability and sensitivity analysis on complex systems and networks with imprecise probability.