The failure mode causes and effects analysis (FMCEA) is a commonly used reliability approach. It identifies, predicts, and analyzes potential failure modes affecting the proper function of equipment or the process under study, along with their roots and consequences. FMCEA aims to evaluate and assess the risks resulting from their occurrence, intending to suggest corresponding repair, adjustment, and precautionary measures to be planned during the conception, instruction, or implementation stages. However, the FMCEA has been criticized in the literature for its many inherent shortcomings related to risk assessment and prioritization. Therefore, this study presents an enhanced FMCEA method to address the deficiencies of the traditional risk priority number (RPN) and improve the reliability of risk assessments and corrective actions. A data envelopment analysis (DEA), as a non-parametric method, is used to evaluate the efficiency of these failures by considering their fixing time and cost and deciding on their final priority ranks. Sub-failure modes and their interrelationships are also taken into account. The radio frequency identification (RFID) system was chosen as an example due to its core role in Industry 4.0 and the Internet of Things (IoT) to demonstrate the effectiveness and usefulness of the proposed method. A total of 67 failures related to both hardware and software parts, including the environmental impacts of this technology, have been disclosed. The results of the conventional and the suggested FMCEA methods are found to be considerably different, with ten failure modes classified as being the most efficient.