"I think it depends on the RNP of the airway. If you have RNP 5 , then you have a 5 NM buffer left or right of the airway axis. So if you will deviate more you must advice ATC."
That is a dangerous answer. If you are yourself RNP 5, this means you will keep within 5 nm of the track you think you are on 95%. This means every intentional deviation will rapidly increase the percent of time you spend outside of these 5 nm.
If you have RNP 3, you will be within 3 nm of the track you think you are on 95% of the time. Very little time will be spent outside of the 5 nm boundary. However, if you deviate 2 nm you will spend 2.5% of your time outside the 5 nm boundary on the side to which you deviated. Any further deviation and you are back to the rapidly increasing percentage of time you'd have seen had you been on RNP 5 and deviated.
Assuming a distribution (e g gaussian) you can crunch the numbers and figure out the odds of the gamble it is to start deviating without advising ATC. You're playing the statistics which are intended to keep your aircraft and other aircraft safely separated.
With any RNP, if your equipment tells you you are on the edge of the airway you are in fact outside of the airway 50% of the time.
You may (or may not) understand this, but you never know about the guy with a fresh instrument rating reading your answer. He may take it as gospel and start spending 30% of his time in the air right at the edge of the glossy purple corridor depicted on the GPS screen - thus being outside the airway 15 percent of the time in the air.