On the use of Principal Component Analysis for identifying and monitoring Geometric Profiles

In many industrial applications, quality of products or processes is related to profiles or curves. Recent literature pointed out that traditional control charting methods can not be applied in these cases and new approaches for profile monitoring are required. With reference to mechanical components, profiles and surfaces play a relevant role, testified by the high number of geometric specifications characterizing most of the technical drawings. In this framework, approaches for profile monitoring can be effectively adopted to quickly detect unusual patterns in the machined profiles. Most of the approaches for profile monitoring are based on combining classical regression to multivariate control charting. Regression is used to describe the profile by means of a relationship between a response variable and one or more explanatory variables or predictors. These predictors have to be properly chosen depending on the specific case faced. A different approach consists in using Principal Component Analysis (PCA) instead of regression to identify patterns in the profile data. However, the use of PCA has been limited to a visual aid in interpreting the systematic behavior underneath collected curves. In this paper, we deepen advantages related with the use of PCA in profile monitoring. In particular, we explore which type of profiles' features allows one to obtain interpretable principal components. We further compare performance of PCA control charting with the one attainable with traditional approaches for profile monitoring. Within the paper, a real case study related to roundness profiles of mechanical components is used as reference.