Domain-selective functional analysis of variance for supervised statistical profile monitoring of signal data

In many applications, process monitoring has to deal with functional responses, which are also known as profile data. In these scenarios, a relevant industrial problem consists of detecting faults by combining supervised learning with functional data analysis and statistical process monitoring. Supervised learning is usually applied to the whole signal domain, with the aim of discovering the features that are affected by the faults of interest. We explore a different perspective, which consists of performing supervised learning to select inferentially the parts of the signal data that are more informative in terms of underlying fault factors. The procedure is based on a non-parametric domain-selective functional analysis of variance and allows us to identify the specific subintervals where the profile is sensitive to process changes. Benefits achieved by coupling the proposed approach with profile monitoring are highlighted by using a simulation study. We show how applying profile monitoring only to the identified subintervals can reduce the time to detect the out-of-control state of the process. To illustrate its potential in industrial applications, the procedure is applied to remote laser welding, where the main aim is monitoring the gap between the welded plates through the observation of the emission spectra of the welded material.