I have an old, very loose 8" Howa on the 1986 Mazak, which makes great parts. The avatar is the chuck holding a set of 15" jaws. It was loose before I got it, but this probably doesn't do it any favors.
I can hold 0.0005" runout on OD and 0.0005" parallel on those big ass jaws (Hast X rings) in this machine using this method:
Clean jaws, grease chuck, take file card and clean the serrations well in the aluminum jaws with the wire brush side. File out any nicks in the teeth with a 60° needle file or metric thread file.
For gripping on OD parts: After jaws are on tight, set chucking to ID. Set jaw pressure to same setting you are going to run the job. Open chuck. Manually bore the ID to 0.050" larger in diameter than a small, round ring or plug. Stop spindle.
Do NOT use adjustable spiders. They cause the jaws to rock unevenly--especially on loosy goose chucks.
Blow out jaws and flip the chucking switch from ID to OD. Clamp on ring. Jaws will have 0.050" stroke from top of travel. Bore jaws in dedicated jaw boring program (work #1) using same chuck pressure and RPM you will use to run the part. Bore the ID of the jaws 0.000" to 0.002" smaller than your part.
Important--Be sure to undercut the ID corner of the jaws--easily done using the necking feature when using a TPG boring bar.
Never try to check the fit by sliding the part into the chuck with chuck still clamped on ring. If part fits, jaws are bored too big and will only touch on 3 points.
Open Jaws, remove ring. Clean jaws and then wipe them with a clean shop rag. Blowing them off is not enough--especially for pie jaws.
Chuck part.
Lightly tap part into face of jaws with 1lb deadblow hammer to seat part. Verify runout is dead nuts. Make chips. Sell finished part.