This approach might be potentially useful for:
Testing on material from a process that has changes over time that can be modeled. (e.g., sinusoidal, linear, or other pattern)
Tests that result in deformative measurements, where the characteristic being measured is affected by and changes over repeated measurements, or changes over time during the test.
The modeling approach example given in Mawby is based on an established pattern in the manufacturing variation that is present in the material.
However, I believe that this same approach could be used to account for patterns of change created by repeated (multiple) measurements on specimens during a GR&R study that have little to do with variation in the material (from the manufacturing process), variation attributed to test system operators, or variation related to gauge repeatability.
See also ANCOVA
References