Machine learning applications have seen an exponential rise in prevalence across many different industries including healthcare, banking, manufacturing, and defense. While there is a lot of potential for machine learning applications, successful development and productionization is not assured. To prevent failures and ensure success, a Machine Learning Operations (MLOps) Failure Modes and Effects Analysis (FMEA) is proposed as a proactive structured approach for risk identification and mitigation. The MLOps FMEA framework demonstrates an approach to enumerate, prioritize, and mitigate potential failure modes, which spans the entire MLOps lifecycle. The MLOps FMEA framework tailors the classical FMEA to address the risk assessment needs for machine learning projects. This work proposes developing templated MLOps failure modes by utilizing the CRISP-ML(Q) as a standardized representation of the MLOps workflow to identify categories of MLOps failure modes, and the NIST Artificial Intelligence Risk Management Framework (AI RMF 1.0) as the basis for principled MLOps Design Patterns to derive specific failure modes. Together, these standards establish a methodological and comprehensive foundation to identify and establish templated failure modes in the MLOps lifecycle. This work also proposes adaptations to the classical FMEA workflow and risk prioritization to support the MLOps FMEA framework. For prioritizing MLOps failure modes, MLOps-centric Severity, Occurrence, & Detection tables were proposed, Consequence Levels (Safe vs. Unsafe) were incorporated, and risks are categorized by intentional and unintentional failure modes. As a machine learning project transitions from a proof of concept to a production solution, the MLOps FMEA framework is applied at each Machine Learning Technology Maturity Level (MLTRL). The MLOps FMEA framework is demonstrated with a predictive maintenance case study. This framework has aided the organization in increasing the successful delivery of impactful machine learning solutions to production, as well as providing the added benefit of increased machine learning awareness and maturity in the organizational culture.