Agree shared criteria
Consider the impact on safety, process continuity and available alternatives. A situation requiring immediate action under site procedures must not wait for an ordinary system queue review.
For other work, use a small number of understandable categories and concrete allocation rules. A long list of similar priority levels often makes selection harder.
Urgency does not define duration
A short intervention and a lengthy repair can have similar importance while needing different preparation. Technician availability, parts and access to the machine all matter.
Distinguish the decision about order from the time when work can start. Otherwise, a high priority becomes an implied promise of immediate completion that the team cannot meet.
Make changes understandable
A new event may justify postponing scheduled work. Explain the reason and the next planned step to the people affected. Deferred work should not simply disappear from attention.
For a plant director, this creates a practical discussion about real constraints. CMMS brings priorities and status together, but production and maintenance still need to agree the criteria and who can change the sequence.