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Probabilistic modeling is widespread in engineering practices, mainly to evaluate the safety, risk analysis, and reliability of complex systems. However, insufficient data makes it difficult to estimate the state probability of components or the global system in dynamic complex systems. Furthermore, conventional methods for dependability analysis typically have little capacity to cope with dependence, failure behavior, epistemic uncertainty, and common cause failure simultaneously. This paper presents the application of an extended discrete-time dynamic evidential network (DEN) model to assess the availability of complex systems. The model application combines Dempster-Shafer's theory to treat epistemic uncertainty over a new state-space reconstruction of components and the dynamic Bayesian network to present multi-state system dependability. This model is demonstrated in a real case study of a water deluge system installed as a safety barrier from Algeria's oil and gas plant. The results show the significant influence of these factors on the system's availability. The goal of this modeling is to assure the high availability of a safety barrier in a volatile setting by providing a decision-making tool to prioritize maintenance tasks, preventing the failure of complicated redundant systems, and recommending alterations to the design.

The dependability occupies a strong place in the performance achievement of the system. It describes the mechanisms that lead to failures of systems. Failure mode and effects, analysis (FMEA) is a classical safety technique widely used in several safety critical industries. This method uses the risk priority number (RPN) to assess the criticality value and prioritize failure modes. However, it suffers from some drawbacks regarding the situation where the in-formation provided is ambiguous or uncertain. Thus, in this work, a fuzzy criticality assessment based approach is carried out to evaluate the failure modes of the relevant system and gives an alternate prioritizing to that obtained by the conventional method. In addition, a novel hybrid approach is proposed that combines the grey relational approach (GRA) and fuzzy analytic hierarchy process. This approach offers a new ranking of failure modes by solving the shortcoming concerning the lack of established rules of inference system which necessitate a lot of experience and shows the weightage or importance to the three parameters severity, detection, and frequency, which are considered to have equal importance in the traditional method. A real case study from a gas turbine system provides encouraging results regarding the risk evaluation and prioritizing failures mode with handling different forms of ambiguity, uncertainty, and divergent judgments of experts.

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