A successful staircase is one that is easy to walk up and down. The rise, run and tread width (depth) have to be within certain guidelines, often dictated by your local jurisdiction. Since this is a safety issue, you don't have much room for latitude or interpretation.
The uniformity of the steps is as important as their rise and run. It is not unusual for the top or bottom step to have a different rise than the rest. This can be a trip hazard and is most serious if it's the top step.
The standards for rise, run and tread width vary slightly from area to area. You should find out what is acceptable in your area. Rise is usually 8 inches maximum, and runs are typically 9 to 11 inches minimum. The tread width is usually one inch more than the run. In some areas, this is called tread depth; in others it is head width. This is accomplished by adding a one-inch nosing to the tread.
Problems with rise, run, tread width , uniformity and slope may be caused by
the way it was built
settlement or heaving
Stairs that have settled or heaved may have a slope. Generally speaking, any slope is dangerous. This is a safety issue. People may fall on stairs that are improperly arranged.