I wouldn't think chuck run out would be an issue on a turned piece unless it's an absolute junk chuck and the bore through the jaws is crooked. Now if a test bar is simply being chucked up and measured that's a different story, but the way I read the original post it was after taking cuts so 'normal' run out disappears.
You may be right but the only way that parallelism can be achieved in a worn or mis-aligned lathes is with a boring bar- and used 'between centres'. Well, this is the way that I have machined to accommodate parallel round PGMS bars in say 'Quorn' Tool and cutter grinder. Professor Chaddock and George H Thomas in the MoModel Engineers Workshop Manual report. As a mere amateur, I have to agree.
A ga in, taking what is said to be 'a normal cut' if the lathe is worn or incorrectly aligned. Mathematically, my experience suggests that wear or mis-alignment can cause an error of THREE times the measured error/wear.
This, is Pi but it gets worse when the actual wear is about 6 inches from the spindle and or the chuck jaws.
This is why a lot of so called measurement is done now with laser alignment. Earlier it was done with a wire and clock gauges, running between centers and clocked using the carriage.
Clears throat a bit and would mention a failed machine tool factory-- and obviously worthless share certificates.
Actually there were 3 but - the rst of the shares in 'other factories' are still a success.
However, I am 'Connolly Man' but note that others may not share my views.
Digressing further, I have 'special equipment' and several of my lathes over the years have been mounted - without twist, using cheap studding, penny washers and cheap nuts. My surface plate was nothing more than a piece of plate glass and I scrapped with a worn out old file using engineers blue. Initially, I got 'near' using strips of cigarette rolling papers. Years before I made wartime models with used single bladed safety razor blades honed on the inside of glass tumblers.
My experiences- but my I found my late wife's ruler yesterday. It was a 6" wooden one and despite having a list of degrees working down from a Fellowship, that is what she still used from when she was- a school girl.
I have Dad's folding 2 foot brass rule. My son has still my slide rule. Such is Life.
I digressed- sorry
Normani