But sure there is not perfect thing in the world. Thank you very much for your time. I shall try to answer your questions. It is generally performed on assemblies. As the parts are assembled, the dimensional variations due to manufacturing processes accumulate statistically and propagate through the assembly kinematically.
Tolerances are just the specified design limits of variation.
They are not statistical quantities. Variation results in a statistical distribution, usually Normal or Gaussian, represented graphically by a histogram or bell-shaped curve. Then he can add tolerances the same way he would add variations, as an estimate of the assembly variation. I have seen tolerance analysis applied to single parts to estimate the accumulation of process variation as the part is produced. For example, it could be used to estimate the accumulation from multiple passes on a lathe to predict whether there will be enough material remaining to be removed by the final cut.