Scalar-On-Function Regression Control Chart Based on a Functional Neural Network

Modern data acquisition systems allow for collecting signals that can be suitably modelled as functions over a continuum (e.g., time or space) and are usually referred to as profiles or functional data. Statistical process monitoring applied to these data is accordingly known as profile monitoring. The aim of this research is to introduce a new profile monitoring strategy based on a functional neural network (FNN) that is able to adjust a scalar quality characteristic for any influence by one or more covariates in the form of functional data. FNN is the name for a neural network able to learn a possibly nonlinear relationship which involves functional data. A Monte Carlo simulation study is performed to assess the monitoring performance of the proposed control chart in terms of the out-of-control average run length with respect to competing methods that already ap peared in the literature before. Furthermore, a case study in the railway industry, courtesy of Hitachi Rail Italy, demonstrates the potentiality and practical applicability in industrial scenarios