When a motor fails, production often stops. If it's a critical line, you can expect plenty of attention from management until the line is back up. Consequently, the tune played during many motor replacement jobs is speed, speed, speed. This is the wrong song. Quite often, haste truly does make waste.
Consider the case of an air compressor motor that failed. A local shop had a replacement motor in stock and rushed it over. What nobody noticed until the techs had spent four hours swapping out the motors was the new motor had a bent shaft. Nobody bothered to run a dial indicator on the shaft once the motor arrived or after it had been transported through the plant to the compressor room. So the plant was down an additional four hours.
If you don't have a motor replacement checklist, you risk replacing a failed motor with one that will fail soon. You should have this checklist in your CMMS so it's available for every motor replacement.
This list needs to include a preliminary investigation. You may not be able to determine why the motor failed in the limited time available, but at least catch the easy stuff. Look for voltage imbalance, load issues, and mounting issues.