  In many Industry 4.0 data analytics applications, quality characteristic data
acquired from manufacturing processes are better modeled as functions, often
referred to as profiles. In practice, there are situations where a scalar
quality characteristic, referred to also as the response, is influenced by one
or more variables in the form of functional data, referred to as functional
covariates. To adjust the monitoring of the scalar response by the effect of
this additional information, a new profile monitoring strategy is proposed on
the residuals obtained from the functional neural network, which is able to
learn a possibly nonlinear relationship between the scalar response and the
functional covariates. An extensive Monte Carlo simulation study is performed
to assess the performance of the proposed method with respect to other control
charts that appeared in the literature before. Finally, a case study in the
railway industry is presented with the aim of monitoring the heating,
ventilation and air conditioning systems installed onboard passenger trains.
