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Birnbaum Importance Measure (IM) allows ranking the components of a system with respect to the impact that their failures have on the system's performance, e.g., its reliability or availability. Such ranking is done in industry to efficiently manage Operation and Maintenance (O&M) activities, and to optimize plant design. In the computation of the Birnbaum IM of the components, uncertainty in the parameters of the system model is often neglected. This neglect may lead to erroneous, possibly non-conservative ranking. In this work, we develop a method based on Possibility Theory (PT) for giving due account to epistemic uncertainties in Birnbaum IMs. An example is given with reference to the components of the Auxiliary FeedWater System (AFWS) of a Nuclear Power Plant.