Short answers, pulled from the story.
Engineering tolerance is the permissible limit or limits of variation allowed in a physical dimension, a measured value, a material property, or a physical space. A variation that goes beyond that limit, such as a temperature that is too hot or too cold, is called noncompliant, rejected, or exceeding the tolerance.
Genichi Taguchi compared traditional two-sided tolerancing to goal posts in a football game, where any value between the limits is treated as equally acceptable. His alternative, the Taguchi loss function, holds that loss increases as a measurement drifts from its exact target, and it is the key principle behind inertial tolerancing.
For a 10 mm sliding fit, the shaft might be specified from 9.964 to 10 mm, a lower deviation of 0.036 mm with zero fundamental deviation. The matching hole might be specified from 10.04 to 10.076 mm, producing a clearance fit between 0.04 mm (Maximum Material Condition) and 0.112 mm (Least Material Condition).
H7/h6 is a common International Tolerance grade combination that produces a tight fit between a hole and a shaft. An H7 hole may run up to 0.015 mm larger than its base dimension and never smaller, while a matching h6 shaft may run up to 0.009 mm smaller than its base dimension and never larger, as set out in ISO 286-1:2010.
A resistor labeled 100 ohms with a stated tolerance of plus or minus 1 percent is considered acceptable anywhere between 99 and 101 ohms. Critical components may also need to stay within tolerance across a specified temperature range and over a specified lifetime.
In civil engineering, clearance refers to the difference between the loading gauge and the structure gauge for railroad cars and trams, or the difference between a vehicle's size and the width or height of doors, overpasses, or tunnels. It also covers the air draft under a bridge, the width of a lock, and the difference between a vessel's deep draft and the stream bed or sea bed beneath it.