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Constructing a Control Chart Using Functional Data

Author

Listed:
  • Miguel Flores

    (MODES Group, Department of Mathematics, Escuela Politécnica Nacional, 170517 Quito, Ecuador)

  • Salvador Naya

    (MODES Group, CITIC, ITMATI, Department of Mathematics, Escola Politécnica Superior, Campus Industrial, Universidade da Coruña, Mendizábal s/n, 15403 Ferrol, Spain)

  • Rubén Fernández-Casal

    (MODES Group, CITIC, Department of Mathematics, Faculty of Computer Science, Campus de Elviña, Universidade da Coruña, 15008 A Coruña, Spain)

  • Sonia Zaragoza

    (PROTERM Group, Department of Naval and Industrial Engineering, Campus Industrial, Universidade da Coruña, Mendizábal s/n, 15403 Ferrol, Spain)

  • Paula Raña

    (MODES Group, CITIC, Department of Mathematics, Faculty of Computer Science, Campus de Elviña, Universidade da Coruña, 15008 A Coruña, Spain)

  • Javier Tarrío-Saavedra

    (MODES Group, CITIC, Department of Mathematics, Escola Politécnica Superior, Campus Industrial, Universidade da Coruña, Mendizábal s/n, 15403 Ferrol, Spain)

Abstract

This study proposes a control chart based on functional data to detect anomalies and estimate the normal output of industrial processes and services such as those related to the energy efficiency domain. Companies providing statistical consultancy services in the fields of energy efficiency; heating, ventilation and air conditioning (HVAC); installation and control; and big data for buildings, have been striving to solve the problem of automatic anomaly detection in buildings controlled by sensors. Given the functional nature of the critical to quality (CTQ) variables, this study proposed a new functional data analysis (FDA) control chart method based on the concept of data depth. Specifically, it developed a control methodology, including the Phase I and II control charts. It is based on the calculation of the depth of functional data, the identification of outliers by smooth bootstrap resampling and the customization of nonparametric rank control charts. A comprehensive simulation study, comprising scenarios defined with different degrees of dependence between curves, was conducted to evaluate the control procedure. The proposed statistical process control procedure was also applied to detect energy efficiency anomalies in the stores of a textile company in the Panama City. In this case, energy consumption has been defined as the CTQ variable of the HVAC system. Briefly, the proposed methodology, which combines FDA and multivariate techniques, adapts the concept of the control chart based on a specific case of functional data and thereby presents a novel alternative for controlling facilities in which the data are obtained by continuous monitoring, as is the case with a great deal of process in the framework of Industry 4.0.

Suggested Citation

  • Miguel Flores & Salvador Naya & Rubén Fernández-Casal & Sonia Zaragoza & Paula Raña & Javier Tarrío-Saavedra, 2020. "Constructing a Control Chart Using Functional Data," Mathematics, MDPI, vol. 8(1), pages 1-26, January.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:58-:d:304423
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    References listed on IDEAS

    as
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