1. A method for detecting a fault in a machine used in a process, comprising: developing a model of said process; generating predicted values for a predetermined number of operating parameters of said process and a predetermined number of vibration parameters of said machine using said model; comparing the value predicted by said model for each of said predetermined number of vibration and operating parameters to a corresponding actual measured value for each of said vibration and operating parameters; and determining whether differences between said predicted and actual measured values for one or more of said predetermined number of vibration and operating parameters exceeds a configured statistical limit using numerical methods.