carry on/of

No, it's not a typo. "Carry" has nothing to do with it. While an inspection of something may be more common, an inspection on something is not incorrect.

Thank you~very helpful~

Maybe. Matter of opinion. I wouldn't go into the correct/incorrect lobbies on this, but I would always use of.

Carry out work on something, yes. Maintenence of, inspection of, sounds better to me.

Google advance search - English only

"an inspection of the equipment"
About 5,480,000 results

"an inspection on the equipment"
About 7 results

We need to carry out an inspection, carefully, of the equipment.

We need to carry out a careful inspection of the equipment.