When building things it is best to not rely on “habit” to keep things together.
Why these stairs have not collapsed yet can only be attributed to luck and habit.
Looking at the pictures, it should be pretty self-explanatory what is wrong and yet, it certainly was not self-explanatory to whoever built the stairs. The blue line with the black stripe represents the “effective” strength of the stringer that supports the treads. The minimum depth of the remaining portion of the stringer is supposed to be 5” for the given span of the stairs. These stairs, as you can see measure 3-1/2 inches.
So to begin with the stringers are WAY undersized but then the top was notched to allow for installation of the wrong type of hanger which results in further reducing that 3-1/2” distance to 1-3/4 inches.
This leaves the “effective” or “functional” strength of the stringer at 1-3/4 inches. To make things even worse at one of the tread's notches that entire 1-3/4 distance is filled by a knot.
There are too many other things wrong with these stairs to go into here but this single defect is enough to require that the entire stairs (actually whole deck) be replaced by someone that makes a habit of knowing what they are doing.
Charles Buell, Real Estate Inspections in Seattle
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WA State, Home Inspector Advisory Licensing Board