The PRISM (partial risk map) methodology is a novel risk assessment method developed as the combination of the failure mode and effect analysis and risk matrix risk assessment methods. Based on the concept of partial risks, three different aggregation functions are presented for assessing incident risks. Since the different aggregation functions give different properties to the obtained PRISM numbers and threshold surfaces (convex, concave, linear), the description of these properties is carried out. Similarity analyses based on the sum of ranking differences (SRD) method and rank correlation are performed and robustness tests are applied related to the changes of the assessment scale lengths. The PRISM method provides a solution for the systematically criticized problem of the FMEA, i.e., it is not able to deal with hidden risks behind the aggregated RPN number, while the method results in an expressive tool for risk management. Applying new aggregation functions, proactive assessment can be executed, and predictions can be given related to the incidents based on the nature of their hidden risk. The method can be suggested for safety science environments where human safety, environmental protection, sustainable production, etc., are highly required.