Stress Failures vs. Fatigue Failures
The chart at right shows the number of failures vs. the number of running hours. Notice that a relatively high number of failures occur during the first hours of runtime. These failures are known as 'infant mortality' because they occur shortly after start-up. In other words, a machine that is new or rebuilt is started up and has severe problems. Within a few hours, days or possibly weeks, a catastrophic failure occurs. If the failure is mechanical in nature (it could also be electrical or lubrication related), stress will often be a primary cause of failure - components being bent back and forth so much that something simply breaks.
However, once a machine runs for a certain number of hours (rotations), it becomes stress relieved and the likelihood of failure changes to fatigue - a component wearing out. Of course, if the movement (vibration) is high but not quite high enough to cause an 'infant mortality' stress failure, the fatigue failure will still occur in a relatively short period of time (which is one reason why the number of failures on the curve doesn't ever quite get to zero).
So if displacement is sensitive to stress, and velocity is sensitive to fatigue, where do the acceleration amplitude units fit in ?