italia,
This is a great discussion, I am hoping we have not strayed too deep, or too far from the original question.
My original thought, after reading through the posts, was the confusion about RAIM, RAIM prediction, and what it means.
Yes, the unit will do an automatic RAIM check at 2nm from the FAF, to let you go to approach mode, in reality, the unit is checking RAIM all of the time. The check at 2nm is to verify that there is sufficient sat coverage, and HIL (or HPL), required for approach. The approach requirements vary, RNP level, APV, LPV, for example, have different required accuracy limits for these modes.
The tools mentioned, such as AUGER, are pre-flight checks, and conditions can change during the actual flight, but what really matters is what the ac has real-time.
You mentioned NOTAMS, the WAAS system is CONUS only, so the WAAS NOTAM system is not supported outside that area, and I dont believe NavCanada has a similar system.
The RAIM level relates to the number of sats the unit can see. From before, you need at least 4 sats for 3d flight, 5 sats for Fault Detection, and 6 sats for Fault detection and exclusion. RAIM prediction tools will simply show you the predicted coverage, ie number of sats, based on a 5 minute outage.
I would have to disagree on some points, RAIM is simply a part of the system, and provides error checking and error correction of the sat signals. It does nothing else but monitor the integrity of the sat signals, and produces the HIL. HIL and HPL are the same term.
The HIL is generated by the RAIM system, creating a sphere to estimate to true vs calc position of the ac. The size of the sphere in m is the HIL. One alarm is when HIL>HAL, and HAL varies between units and modes.
The alarm timeframes differ as well. When GPS integrity is lost, the unit will create an artificial or equivalent HIL based on internal IRS drift models.
Under ACCUR, you see the required value and the estimated value, or EPE. This is not HIL, but EPE uses HFOM, latency of the FMC, ground speed, and bleed error. HFOM is a function of the IRU.
TSE is a much different animal...
HCE is the horizontal coupling error (along track error on descent)
FTE is the flight technical error (perf of system to control ac on vertical path)
ASE is the altimetry system error.
RNP, well...that is for another day....