Quality of machined products is often related to the shapes of surfaces
that are constrained by geometric tolerances. In this case, statistical
quality monitoring should be used to quickly detect unwanted deviations
from the nominal pattern. The majority of the literature has focused on
statistical profile monitoring, while there is little research on
surface monitoring. This paper faces the challenging task of moving from
profile to surface monitoring. To this aim, different parametric
approaches and control-charting procedures are presented and compared
with reference to a real case study dealing with cylindrical surfaces
obtained by lathe turning. In particular, a novel method presented in
this paper consists of modeling the manufactured surface via Gaussian
processes models and monitoring the deviations of the actual surface
from the target pattern estimated in phase I. Regardless of the specific
case study in this paper, the proposed approach is general and can be
extended to deal with different kinds of surfaces or profiles