Profile Monitoring of Probability Density Functions via Simplicial Functional PCA with application to Image Data

The advance of sensor and information technologies is leading to data-rich industrial environments, where large amounts of data are potentially available. This study focuses on industrial applications where image data are used more and more for quality inspection and statistical process monitoring. In many cases of interest, acquired images consist of several and similar features that are randomly distributed within a given region. Examples are pores in parts obtained via casting or additive manufacturing, voids in metal foams and light-weight components, grains in metallographic analysis, etc. The proposed approach summarizes the random occurrences of the observed features via their (empirical) probability density functions (PDFs). In particular, a novel approach for PDF monitoring is proposed. It is based on simplicial functional principal component analysis (SFPCA), which is performed within the space of density functions, that is, the Bayes space B2. A simulation study shows the enhanced monitoring performances provided by SFPCA-based profile monitoring against other competitors proposed in the literature. Finally, a real case study dealing with the quality control of foamed material production is discussed, to highlight a practical use of the proposed methodology. Supplementary materials for the article are available online

Profile Monitoring of Probability Density Functions via Simplicial Functional PCA With Application to Image Data

<p>The advance of sensor and information technologies is leading to data-rich industrial environments, where large amounts of data are potentially available. This study focuses on industrial applications where image data are used more and more for quality inspection and statistical process monitoring. In many cases of interest, acquired images consist of several and similar features that are randomly distributed within a given region. Examples are pores in parts obtained via casting or additive manufacturing, voids in metal foams and light-weight components, grains in metallographic analysis, etc. The proposed approach summarizes the random occurrences of the observed features via their (empirical) probability density functions (PDFs). In particular, a novel approach for PDF monitoring is proposed. It is based on simplicial functional principal component analysis (SFPCA), which is performed within the space of density functions, that is, the Bayes space <i>B</i>². A simulation study shows the enhanced monitoring performances provided by SFPCA-based profile monitoring against other competitors proposed in the literature. Finally, a real case study dealing with the quality control of foamed material production is discussed, to highlight a practical use of the proposed methodology. Supplementary materials for the article are available online.</p

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods