The management of risks and failures in health systems is considered one of the most efficient solutions for providing care to patients. In practice, this activity also makes it possible to join new corporate opportunities, because it allows preventive measures resulting from social, scientific, and technological developments to be constantly evolving throughout the organization. The aim of the article is to present an application of the failure modes and their health effects analysis model (HFMEA) integrated with Fuzzy logic in three Emergency Care Units (UPAs) in Brazil. This mapping model analyzes and analyzes how failures occurred in the supply chain of UPAs. The methodology used included dividing the study into 4 stages, which were used to prepare the proposed model through the evaluation of failure modes integrated with Fuzzy logic. This work reports as one of the roots of the problems in the studied UPAs: the predominance of processing and creativity waste. These, associated with the factor Management and Leadership for a Lean environment, demonstrate that failures in leadership are linked to the dissatisfaction of management support professionals. In addition, a hierarchical analysis of the failure probabilities and evaluation of the eight Lean wastes found in the UPAs was presented.