This paper presents a novel application of Large Language Models (LLMs) to improve Failure Mode and Effect Analysis (FMEA) for managing risks in technical processes and products. We designed an LLM multi-agent system that utilizes Retrieval Augmented Generation (RAG) for risk analysis and text generation. This system interfaces directly with an FMEA knowledge database to dynamically extract relevant information, perform reasoning based on user input and retrieved information, and generate targeted text recommendations for completing FMEA spreadsheets. By automating the analysis and synthesis of risk information, this system can provide expert knowledge and reduces the cognitive load on users, speeding up the FMEA process. The effectiveness and functionality of this LLM-enhanced FMEA application is demonstrated through a prototype, accessible via a GitHub Repository at: https://github.com/YuchenXia/LLMRiskAnalyzer.