The damages to the structural elements, viz., inner race, outer race, rollers, cage, etc., of rolling contact bearings if not detected in time can cause tragic failures of the machineries supported by these bearings. The operating parameters like variations in the machinery speed, unbalance, operating load, etc., can cause a bearing to vibrate at higher energy levels and consequently will accelerate its wear. An attempt is made in this study, and a generalized model is developed using matrix method of dimensional analysis (MMDA) that predicted the response and correlated the dependent parameter, i.e., response with the significant independent parameters. Combined use of response surface methodology (RSM) is made to explore the dependence of various factors such as size of the defect, unbalance, speed, and their interactions on the vibration characteristics of the bearings. It is observed from the study that the model developed based on the MMDA has provided an efficient approach in recognizing the damaged bearing state, which can be easily implemented in the condition-based preventive maintenance strategies. Also, the effectiveness of MMDA as compared to the conventional Buckingham's pi theorem in the dimensional analysis (DA) practice, especially in the problems involving multiple variables, is shown in this study.