For those using Petzl Rigs in Tyrolleans (and other applications!) the following set of recent tests by Petzl on a range of different ropes (looks like American tests and ropes) may be of interest. Shows how the rope diameter plays a part in the slippage rates.
Worth highlighting that these slip rates were likely from test conditions rather than the wet and grubby ropes we’re likely to be dealing with!!
https://www.petzl.com/US/en/Professional/Tests?ProductName=RIG