When designing vehicle vibration monitoring systems for aerospace devices, it is common to use well-established models of vibration features to determine whether failures or defects exist. Most of the algorithms used for failure detection rely on these models to detect significant changes in a flight environment. In actual practice, however, most vehicle vibration monitoring systems are corrupted by high rates of false alarms and missed detections. Research conducted at the NASA Ames Research Center has determined that a major reason for the high rates of false alarms and missed detections is the numerous sources of statistical variations that are not taken into account in the modeling assumptions. In this paper, we address one such source of variations, namely, those caused during the design and manufacturing of rotating machinery components that make up aerospace systems. We present a novel way of modeling the vibration response by including design variations via probabilistic methods. The results demonstrate initial feasibility of the method, showing great promise in developing a general methodology for designing more accurate aerospace vehicle vibration monitoring systems.