The early detection of incipient failure in a Mechanical System is of great practical importance as it permits scheduled inspections without costly shutdowns and indicates urgency and locations for repair before a system will incur any catastrophic failure. One of the most commonly used approaches in failure detection is vibration signature analysis. This project aims at the development of a joint time-frequency vibration analysis methodology that uses Wigner-Ville Distribution (WVD) function to identify incipient mechanical faults. In order to develop an accurate signature pattern recognition procedure, a complete database of vibration signal has to be generated. Experimentally validated analytical/numerical models will be developed to generate vibration signal database for both normal and abnormal operating conditions (Experimental generation of the database will be too costly). The main thrusts of this study are: a) development of accurate analytical models to simulate a variety of faults in engine and transmission systems and verification of the models using experimental data, b) comparison and verification of analytical simulations with the Wigner-Ville distribution results to experimental WVD results, c) create a comprehensive data base using analytical modeling to supplement the experimental data for fault pattern recognition, and most significantly d) development of a machine health monitoring system for identification of wear and failures in machine components. Some initial success has been accomplished by the P.I. in using the WVD to determine gear surface pitting and tooth fracture -1921 from both experimental and analytical study. However, before an accurate pattern recognition procedure can be developed, a complete vibration signal databa s has to be generated and more in-depth examination of the vibration signature is required.