Applying risk assessment approaches to improve quality in enterprises is of great importance especially for sectors that are labor-intensive and thus frequently encountered failures. One of the methods frequently used to take precautions against failures caused by high variability in this type of sector is failure mode and effects analysis (FMEA). In this study, a hybrid FMEA approach is proposed so as to take measures against failures in the textile sector where there are high-quality differences due to its structure and failures frequently occurred. Since the different combinations of risk parameters' scores may produce the same risk degree based on the function of the FMEA's basis, misleading results for the risk analysis in the practical risk management can be occurred. Moreover, the risk priority number (RPN) function has a limitation in the weight determining process, since it assigns the equal weight for each risk parameter in the classical FMEA. To overcome these shortcomings in the RPN calculation for the risks in the FMEA approach, a multi-criteria decision-making (MCDM) approach is applied under the framework of fuzzy logic. Through that, in this study, we aimed to prove an expert system based on the rules that specifically focusing on the risk sources of the woven fabric industry. To create such a rule-based system, inputs are generated using fuzzy AHP and modified fuzzy TOPSIS. A case study is carried out with the method proposed in a textile mill, and it is determined which risks arising from failures are higher. For the validation of the results, a comparative analysis is conducted. Moreover, for the robustness of the decisions, one-at-a-time sensitivity analysis with respect to different scenarios are applied. As a result of the analyses, it is shown that our proposed model can be used as an efficient proactive risk calculator for the managers or researchers to make useful inferences, judgments, and decisions of the production processes for eliminating the shortcomings of the traditional FMEA.