Hmm, sorry, I have to take back some of I wrote above.
For RNAV and RNP:
1. Instead of "half-scale deflection", the guidance for established is: "
An aircraft is considered to be established on-course during RNAV and RNP operations anytime it is within 1 times the required accuracy for the segment being flown." (The scale will depend on your FMS but this seems to imply full-scale deflection).
2. Instead of waiting to "pass" the segment's defining fix, the exact standard is: "(a)
Pilots flying FMS equipped aircraft with barometric vertical navigation (Baro-VNAV) may descend when the aircraft is established on-course following FMS leg transition [to the next segment]. Leg transition normally occurs at the turn bisector for a fly-by waypoint [...] (b) Pilots flying TSO-C129 navigation system equipped aircraft without full automation should use normal lead points to begin the turn. Pilots may descend when established on-course on the next segment of the approach."
The italicized quotations are from revised
FAA AIM 5-5-16. RNAV and RNP Operations:
https://www.faa.gov/air_traffic/publ...m/aim0505.html