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Title: A control chart methodology for functional data Authors:  Miguel Flores - Escuela Politecnica Nacional (Ecuador)
Salvador Naya - University of A Coruna (Spain)
Javier Tarrio-Saavedra - Universidade da Coruna (Spain) [presenting]
Ruben Fernandez Casal - Universidade da Coruna (Spain)
Veronica Bolon - Universidade da Coruna (Spain)
Carlos Eiras - Universidade da Coruna (Spain)
Abstract: Anomaly detection in the industry and the control of the quality of products and services have usually been developed by the application of univariate and multivariate control charts. However, the problem of ongoing monitoring of data (due to the advances in sensoring in the framework of the Industry 4.0) requires more sophisticated tools that can be applied to autocorrelated critical to quality variables. Many of these new data, generally curves, can be studied as functional data. This is the case of energy consumption, temperatures and relative humidity among other variables, measured in buildings. These new complex data require of innovative solutions by researchers in statistical quality control based on the application of functional data analysis techniques (FDA. A methodology to build process control charts for functional data is proposed. The control consists of two phases: Phase I of process calibration and Phase II of process monitoring. For Phase I, a control chart for functional data based on functional data depth and outlier detection is developed. In Phase II, another control chart based on rank control charts and functional depth is also proposed to monitor the process. A comprehensive simulation study and real data application have been performed. Variable selection methods are also studied in advance to FDA control charts.