Failure mode and effects analysis (FMEA) is a critical but labor-intensive process in product development that aims to identify and mitigate potential failure modes to ensure product quality and reliability. In this paper, a novel framework to improve the FMEA process by integrating generative artificial intelligence (AI), in particular large language models (LLMs), is presented. By using these advanced AI tools, we aim to streamline collaborative work in FMEA, reduce manual effort and improve the accuracy of risk assessments. The proposed framework includes LLMs to support data collection, pre-processing, risk identification, and decision-making in FMEA. This integration enables a more efficient and reliable analysis process and leverages the strengths of human expertise and AI capabilities. To validate the framework, we conducted a case study where we first used GPT-3.5 as a proof of concept, followed by a comparison of the performance of three well-known LLMs: GPT-4, GPT-4o and Gemini. These comparisons show significant improvements in terms of speed, accuracy, and reliability of FMEA results compared to traditional methods. Our results emphasize the transformative potential of LLMs in FMEA processes and contribute to more robust design and quality assurance practices. The paper concludes with recommendations for future research focusing on data security and the development of domain-specific LLM training protocols.