Chatter vibration in turning and milling operations is one of the most critical problems that causes low workpiece quality and manufacturing efficiency. Therefore, the determination of stable cutting depths is crucial for these operations. Several vibrational characteristics [natural frequency (omega(n)), stiffness coefficient (k), and damping coefficient (s)] affect stable cutting depths. The vibration characteristics of these operations show randomness for every setup condition. For this reason, the randomness of the vibration characteristics should be modeled. In this study, a probabilistic approach and regression model are combined for turning operation. Also, a probabilistic approach and analytical model are integrated for milling operation. The purpose of these models is to establish confidence intervals for stability diagrams. As a result, the operators can work in a secure region during the operations.