For example Within the next [25 hours] time-in-service (TIS) after the effective date of this AD, unless already done within the last [75 hours] TIS, and thereafter at intervals not to exceed [100 hours] TIS from the last inspection.
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The threshold is the starting base line of the repeat inspection requirement, in this case the calendar date of AD release, and the phase-in is the "grace period" (25 hours) to accommodate airplanes not done yet.
The AD implements a hundred hour repeat inspection. That means that there is a maximum dormancy (potential undetected existence of whatever condition it is) of 100 hours from the last time the condition was confirmed not to exist by that specific inspection. The probability of the condition growing from a detectable level to a dangerous level is acceptably low within 100 hours based on analysis or test.
For airplanes where the condition has never been confirmed not to exist and is unknown, or at least more than 100 hours ago, there is obviously a higher risk profile, and they are not comfortable with waiting more than a full 100 hours of the repeat interval with unknown aircraft. However, they are comfortable with letting unknown aircraft go another 25 hours before the inspection, to avoid grounding everybody until the inspection is done as soon as the AD is released.
So the language says:
You have to inspect at 100 hour intervals going forward, period.
If you've never done the inspection, you can't wait 100 hours and have to do it within the next 25 hours.
If you've already done the inspection for whatever reason before this AD came out, you get credit for that if it meets the maximum 100 hour dormancy. This is where the 75 hours before the AD comes in.
Airplane has 1000 hours when AD is released. Inspection was done 50 hours ago, at 950 total hours, for whatever reason (maybe it was already in place but with a longer interval before, or was a voluntary Service Bulletin, something like that). It's within 75 hours of the AD release so it can be treated as the first inspection of the 100 hour repeats going forward and you can ignore the 25 hour phase in and do the next inspection at 1050.
If the same 1000 hour airplane had the inspection done at 90 hours ago when the AD came out, at 910 hours, you aren't forced to do the repeat in the next 10 hours (the next 100 hour interval), at 1010; you get the benefit of the phase in and can wait up to 25 hours of AD release before doing it, then every 100 hours going forward.