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In many industrial applications, quality of products or processes is related to profiles. With reference to mechanical components, profiles and surfaces play a relevant role, as shown by the high number of geometric specifications characterizing most of the technical drawings. In this framework, an important step consists in identifying the systematic pattern which characterizes all the profiles machined while the process is in its standard or nominal state. With reference to this aim, this paper focuses on the use of principal component analysis (PCA) for profile data (Functional PCA). Since a usual objection to PCA is that principal components (PCs) are often difficult or impossible to interpret, this paper explores what types of profile features allow one to obtain interpretable PCs. Within the paper, a real case study related to roundness profiles of mechanical components is used as reference. In particular, functional PCA is applied to the set of real profile data to derive the significant PCs and the corresponding eigenfunctions. In order to gain insight into the information behind the retained PCs, both simulations and analytical results are used. In particular, the analytical results, outlined in the literature on functional data analysis, allow one to link the eigenfunctions to specific profile features, given that profile data admit an orthogonal basis series expansion.

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In order to produce products with constant quality, manufacturing systems need to be monitored for any unnatural deviations in the state of the process. Control charts have an important role in solving quality control problems; nevertheless, their effectiveness is strictly dependent on statistical assumptions that in real industrial applications are frequently violated. In contrast, neural networks can elaborate huge amounts of noisy data in real time, requiring no hypothesis on statistical distribution of monitored measurements. This important feature makes neural networks potential tools that can be used to improve data analysis in manufacturing quality control applications. In this paper, a neural network system, which is based on an unsupervised training phase, is presented for quality control. In particular, the adaptive resonance theory (ART) has been investigated in order to implement a model-free quality control system, which can be exploited for recognising changes in the state of a manufacturing process. The aim of this research is to analyse the performances of ART neural network under the assumption that predictable unnatural patterns are not available. To such aim, a simplified Fuzzy ART neural algorithm is firstly discussed, and then studied by means of extensive Monte Carlo simulation. r

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