Toward a better monitoring statistic for profile monitoring via variational autoencoders

Wide accessibility of imaging and profile sensors in modern industrial systems created an abundance high-dimensional sensing variables. This led to a growing interest the research process monitoring. However, most approaches literature assume in-control population lie on linear manifold with given basis (i.e., spline, wavelet, kernel, etc) or unknown principal component analysis its variants), which cannot be used efficiently model profiles nonlinear is common many real-life cases. We propose deep probabilistic autoencoders as viable unsupervised learning approach such manifolds. To do so, we formulate extensions monitoring statistics from classical expected reconstruction error (ERE) KL-divergence (KLD) based statistics. Through extensive simulation study, provide insights why latent-space are unreliable residual-space ones typically perform much better for approaches. Finally, demonstrate superiority models via both study case involving images defects hot steel rolling process.