A rash of motor failures has afflicted your plant. Your plant engineer read some application notes from the Web site of a test instrument manufacturer and subsequently used a power analyzer on the feeders of these motors. There were some anomalies, but nothing that explains these failures.
These failures are occurring in a few unrelated systems: the plant HVAC, a process exhaust hood, a scrap grinder, a conveyor system, and a wash tank. These same systems keep having motor failures. What should you look at to get to the bottom of this problem?
Your biggest clue here is the localized failures, which tell you it's not a systemic issue such as voltage distortion. Your second biggest clue is that they are repeating. When you combine the two clues, you can conclude that something is happening in these specific systems.
If you understand that improper repairs lead to repeated failures, then you understand that the most likely cause of this rash of motor failures is improper repair. If it was a motor maintenance issue, then it would be affecting other equipment as well. However, the problem is limited to equipment that has undergone repair.
To solve this issue, look for errors in the repair process. One thing you can do is to see if the repair procedure provides (or refers to) the torque spec for the mounting of each motor. If this information isn't readily available, then you have identified one likely cause.
To identify other potential causes, walk down each step from replacement motor specification to startup of that motor. Any step along the way could be responsible for premature failure of replacement motors.