Prioritizing the risk factors in production and service processes has a great importance since limited resources must be well managed. Classical Failure Mode and Effects Analysis (FMEA) is the most used method for this purpose in the literature. However, it handles a small number of parameters and assigns them equal weights. To overcome this inadequacy, we introduce a more comprehensive FMEA method which allows to assign different weights to the risk parameters. The new FMEA model includes nine risk parameters each having a different weight obtained from CRiteria Importance Through Intercriteria Correlation (CRITIC) method. The paper also introduces a fuzzy version of the proposed CRITIC Based Weighted Failure Mode and Effects Analysis (CBW-FMEA) method, which employs triangular and trapezoidal fuzzy numbers. All the proposed models are applied to COVID-19 blood testing process and the results are presented comparatively.