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When conducting safety assessment for safety-critical systems, epistemic uncertainty is an ever-present challenge when reasoning about the safety concerns and causal relationships related to hazards. Uncertainty around this causation thus needs to be managed well. Unfortunately, existing safety assessment tends to ignore unknown uncertainties, and stakeholders rarely track known uncertainties well through the system lifecycle. In this thesis, an approach is described for managing epistemic uncertainties about the system and safety causal models that are applied in a safety assessment. First, the principles that define the requirements for the approach are introduced. Next, these principles are used to construct three distinct steps that constitute an approach to manage such uncertainties. These three steps involve identifying, documenting and tracking the uncertainties throughout the system lifecycle so as to enable intervention to address the uncertainties. The approach is evaluated by integrating it with two existing safety assessment techniques, one using models from a system viewpoint and the other with models from a component viewpoint. This approach is also evaluated through peer reviews, semi-structured interviews with practitioners, and by review against requirements derived from the principles. Based on the evaluation results, it is plausible that our approach can provide a feasible and systematic way to manage epistemic uncertainties in safety assessment for safety-critical systems.