Constructing a Control Chart Using Functional Data

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.

Anomaly detection for aircraft electrical generator using machine learning in a functional data framework

“…The warning should raise the probability and the remaining time to get a failure. The concept of our DT can be adapted to other fields and especially for the industrial maintenance (see [6], [3], [7] and [11]). The most important is to identify the features that are correlated with the process under study and have a labeled dataset with abnormal and normal behaviors.…”

Statistical Quality Control with the qcr Package

“…When the processes are defined by functional data, the authors encourage to apply control charts based on Functional Data Analysis (FDA) in order to implement control and improvement tasks. In this section, the use of control charts presented in Flores et al (Flores et al, 2020). Summarizing, this methodology consists of the proposal of new Phase I and Phase II control charts to be applied in those case study in which the datum unit is a curve.…”

A Control Chart for Exponentially Distributed Characteristics Using Modified Multiple Dependent State Sampling

“…In this section, the efficiency of the proposed t-chart under MMDS sampling is evaluated compared to the t-chart under the MDS and GMDS sampling schemes. In many studies, a simulation approach is extensively employed to demonstrate the performance and effectiveness of control charts [27][28][29][30][31]. Using simulated data is convenient and is usually done when exact statistics of the proposed process are not available.…”