A system for monitoring vibrations in a machine having a rotating element, the system comprising: a vibration measurement device, the vibration measurement device adapted to measure composite vibrations in the machine and output composite digital vibration signals corresponding to the composite vibrations measured; an operating condition sensor, the operating condition sensor measuring operating conditions of the machine; a processor, the processor adapted to receive and filter the composite digital vibration signals into first vibration vector signals and second vibration vector signals, the processor also adapted to receive the measured operating conditions; a storage unit, the storage unit storing said first vibration signals, said second vibration signals, and said operating conditions; a display device, the display device displaying said first vibration signals in association with said operating conditions; wherein a plurality of composite vibration measurements equaling N are measured over time by the vibration measurement device, the N measurements being output as N composite digital vibration signals; the processor thereby receiving and filtering said N measurements into N first vibration vector signals and N second vibration vector signals, the processor determining a mean value and standard deviation of said N first vibration vector signals; wherein the processor receives and filters an N+1 composite vibration measurement measured at a later time into an N+1 first vibration vector signal and an N+1 second vibration vector signal; characterized in that upon the occurrence of said N+1 first vibration vector exceeding a first threshold value related to said mean value and standard deviation of said N first vibration vector signals, said processor activates a first action; wherein said first action is an audible alarm. a vibration measurement device, the vibration measurement device adapted to measure composite vibrations in the machine and output composite digital vibration signals corresponding to the composite vibrations measured; an operating condition sensor, the operating condition sensor measuring operating conditions of the machine; a processor, the processor adapted to receive and filter the composite digital vibration signals into first vibration vector signals and second vibration vector signals, the processor also adapted to receive the measured operating conditions; a storage unit, the storage unit storing said first vibration signals, said second vibration signals, and said operating conditions; a display device, the display device displaying said first vibration signals in association with said operating conditions; wherein a plurality of composite vibration measurements equaling N are measured over time by the vibration measurement device, the N measurements being output as N composite digital vibration signals; the processor thereby receiving and filtering said N measurements into N first vibration vector signals and N second vibration vector signals, the processor determining a mean value and standard deviation of said N first vibration vector signals; wherein the processor receives and filters an N+1 composite vibration measurement measured at a later time into an N+1 first vibration vector signal and an N+1 second vibration vector signal; characterized in that upon the occurrence of said N+1 first vibration vector exceeding a first threshold value related to said mean value and standard deviation of said N first vibration vector signals, said processor activates a first action; wherein said first action is an audible alarm.