Critical DME has to do with your RNAV Capabilities and availability for the STAR/SID. Japan has not quite embraced pure GPS navagation so for RNAV aircraft you must also have ground based navaids for backup position recognition. So. To answer your question Lets go though the chart. Lets take the Celes Rnav Arrival to RWY 34.
In this case the box on the lower left hand corner (if using Jepps) shows the Critical DME. Let's take the Kajiki VOR for example. it has a DME Gap of 12.5 NM, so basically if the KGE VOR is inop, somewhere in this arrival there would be a 12.5nm gap in coverage of the ground based navaids to calculate DME/DME for your RNAV equipment. Obviously this is probably not a problem because most transport catagory aircraft use a FMS that has GPS/GPS or GPS/DME calculations so you're navigation performance is not degraded significantly. Most operators in Japan have a DME Gap limit for each type of aircraft flown. My aircraft for example has a max DME Gap of 14.0 nm, so if the KGE VOR (which is most restrictive) is INOP I am still ok to fly this arrival. Hope I made it clear as Mud!
