Phase I monitoring via generalized scalar-on-function regression model

Some processes or products are characterized by a scalar quality characteristic, influenced by smooth functional covariates called profiles. In particular, when the scalar quality characteristic can be suitably described by a distribution of the linear exponential family, the generalized scalar-on-function regression model can adequately represent the relationship between the scalar response variable and the functional covariates. In this model, the parameter vector is hybrid as it is based on a real parameter vector and several smooth functions. For Phase I monitoring of the hybrid parameter vector, two T2 control charts are suggested. Through a simulation study, which includes process drift, step shift, and outliers, the signal probability measures the performance of the new charts. An example illustrates the application of the suggested control charts.