Businesses must constantly change and develop to keep up with customer needs and changes in the market. Not being able to adapt to change or not being ready enough can bring risks. These changes and risks can affect both the process and the outputs of the process. It is essential to be prepared for the possible risks experienced in the operations, especially in project-based, production-to-order enterprises, to meet the customer's demands and to comply with the delivery date. Businesses must implement an effective risk assessment process to achieve this. This study implemented a risk prioritization for a new business project that produces energy storage systems by having to order. Changes must be made in the production process for an additional feature to be added to the product in line with the customer's request. The risks posed by the change and the short deadline were analyzed and prioritized. A new model was developed by developing the classical Decision Matrix Risk Assessment (DMRA) method, one of the risk assessment methods to evaluate the ten identified risks. The "severity" component of the classical DMRA method is divided into three sub-components (the severity of delivery time, the severity of cost, and the severity of quality) to be evaluated more specifically. Moreover, since the weights of these sub-components on the risks are different, the components are weighted with the Fuzzy SWARA method. The weights obtained from the Fuzzy SWARA method are used in the Fuzzy MOORA method, and the risks are prioritized. Thus, the effectiveness of the classical risk assessment approach has increased by detailing the "severity" component of the risk assessment components and weighting and prioritizing the components using multi-criteria decision-making (MCDM) techniques.