Profile control charts based on nonparametric LL-1 regression methods

Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric $L$-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by three individual metrics. The proposed approach is applied to the previously analyzed vertical density profile data, leading to some interesting insights.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS501 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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.This study has been funded by the eCOAR project (PC18/03) of CITIC. The work of Salvador Naya, Javier Tarrío-Saavedra, Miguel Flores and Rubén Fernández-Casal has been supported by MINECO grants MTM2014-52876-R, MTM2017-82724-R, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015, and Centro Singular de Investigación de Galicia ED431G/01 2016-19), through the ERDF. The research of Miguel Flores has been partially supported by Grant PII-DM-002-2016 of Escuela Politécnica Nacional of EcuadorXunta de Galicia; ED431C-2016-015Xunta de Galicia; ED431G/01 2016-19Escuela Politécnica Nacional de Ecuador; PII-DM-002-201

Parametric, Nonparametric, and Semiparametric Linear Regression in Classical and Bayesian Statistical Quality Control

Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a practitioner’s guide to provide a stepby- step application for parametric, nonparametric, and semiparametric methods in profile monitoring, creating an in-depth guideline for novice practitioners. We then consider the commonly used cumulative sum (CUSUM), multivariate CUSUM (mCUSUM), exponentially weighted moving average (EWMA), multivariate EWMA (mEWMA) charts under a Bayesian framework for monitoring respiratory disease related hospitalizations and global suicide rates with parametric, nonparametric, and semiparametric linear models

Proceedings of the 8th International Conference on Data Science, Technology and Applications (DATA 2019)

[Abstract] The aim of this work is to propose different statistical and machine learning methodologies for identifying anomalies and control the quality of energy efficiency and hygrothermal comfort in buildings. Companies focused on energy sector for buildings are interested on statistical and machine learning tools to automate the control of energy consumption and ensure quality of Heat Ventilation and Air Conditioning (HVAC) installations. Consequently, a methodology based on the application of the Local Correlation Integral (LOCI) anomaly detection technique has been proposed. In addition, the most critical variables for anomaly detection are identified by using ReliefF method. Once vectors of critical variables are obtained, multivariate and univariate control charts can be applied to control the quality of HVAC installations (consumption, thermal comfort). In order to test the proposed methodology, the companies involved in this project have provided the case study of a store of a clothing brand located in a shopping center in Panama. It is important to note that this is a controlled case study for which all the anomalies have been previously identified by maintenance personnel. Moreover, as an alternatively solution, in addition to machine learning and multivariate techniques, new nonparametric control charts for functional data based on data depth have been proposed and applied to curves of daily energy consumption in HVAC.Ministerio de Asuntos Económicos y Transformación Digital; MTM2014-52876-RMinisterio de Asuntos Económicos y Transformación Digital; MTM2017-82724-RXunta de Galicia; ED431C-2016-015Centro Singular de Investigación de Galicia; ED431G/01 2016-19Centro de Investigación en Tecnoloxías da Información e as Comunicacións da Universidade da Coruña; PC18/03Escuela Politécnica Nacional of Ecuador; PII-DM-002-201

Statistical Methodologies of Functional Data Analysis for Industrial Applications

This thesis stands as one of the first attempt to connect the statistical object oriented data analysis (OODA) methodologies with the industry field. Indeed, the aim of this thesis is to develop statistical methods to tackle industrial problems through the paradigm of the OODA. The new framework of Industry 4.0 requires factories that are equipped with sensor and advanced acquisition systems that acquire data with a high degree of complexity. OODA can be particularly suitable to deal with this increasing complexity as it considers each statistical unit as an atom or a data object assumed to be a point in a well-defined mathematical space. This idea allows one to deal with complex data structure by changing the resolution of the analysis. Indeed, from standard methods where the atom is represented by vector of numbers, the focus now is on methodologies where the objects of the analysis are whole complex objects. In particular, this thesis focuses on functional data analysis (FDA), a branch of OODA that considers as the atom of the analysis functions defined on compact domains. The cross-fertilization of FDA methods to industrial applications is developed into three parts in this dissertation. The first part presents methodologies developed to solve specific applicative problems. In particular, a first consistent portion of this part is focused on \textit{profile monitoring} methods applied to ship CO\textsubscript{2} emissions. A second portion deals with the problem of predicting the mechanical properties of an additively manufactured artifact given the particle size distribution of the powder used for its production. And, a third portion copes with the cluster analysis for the quality assessment of metal sheet spot welds in the automotive industry based on observations of dynamic resistance curve. Stimulated by these challenges, the second part of this dissertation turns towards a more methodological line that addresses the notion of \textit{interpretability} for functional data. In particular, two new interpretable estimators of the coefficient function of the function-on-function linear regression model are proposed, which are named S-LASSO and AdaSS, respectively. Moreover, a new method, referred to as SaS-Funclust, is presented for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. In the last part, two ongoing researches on FDA methods for industrial application are presented. In particular, the first one regards the definition of a new robust nonparametric functional ANOVA method (Ro-FANOVA) to test differences among group functional means by being robust against the presence of outliers with an application to additive manufacturing. The second one sketches a new methodological framework for the real-time profile monitoring

A comparison study of distribution-free multivariate SPC methods for multimode data

The data-rich environments of industrial applications lead to large amounts of correlated quality characteristics that are monitored using Multivariate Statistical Process Control (MSPC) tools. These variables usually represent heterogeneous quantities that originate from one or multiple sensors and are acquired with different sampling parameters. In this framework, any assumptions relative to the underlying statistical distribution may not be appropriate, and conventional MSPC methods may deliver unacceptable performances. In addition, in many practical applications, the process switches from one operating mode to a different one, leading to a stream of multimode data. Various nonparametric approaches have been proposed for the design of multivariate control charts, but the monitoring of multimode processes remains a challenge for most of them. In this study, we investigate the use of distribution-free MSPC methods based on statistical learning tools. In this work, we compared the kernel distance-based control chart (K-chart) based on a one-class-classification variant of support vector machines and a fuzzy neural network method based on the adaptive resonance theory. The performances of the two methods were evaluated using both Monte Carlo simulations and real industrial data. The simulated scenarios include different types of out-of-control conditions to highlight the advantages and disadvantages of the two methods. Real data acquired during a roll grinding process provide a framework for the assessment of the practical applicability of these methods in multimode industrial applications

Profile monitoring via sensor fusion: The use of PCA methods for multi-channel data

Continuous advances of sensor technology and real-time computational capability are leading to data-rich environments to improve industrial automation and machine intelligence. When multiple signals are acquired from different sources (i.e. multi-channel signal data), two main issues must be faced: (i) the reduction of data dimensionality to make the overall signal analysis system efficient and actually applicable in industrial environments, and (ii) the fusion of all the sensor outputs to achieve a better comprehension of the process. In this frame, multi-way principal component analysis (PCA) represents a multivariate technique to perform both the tasks. The paper investigates two main multi-way extensions of the traditional PCA to deal with multi-channel signals, one based on unfolding the original data-set, and one based on multi-linear analysis of data in their tensorial form. The approaches proposed for data modelling are combined with appropriate control charting to achieve multi-channel profile data monitoring. The developed methodologies are demonstrated with both simulated and real data. The real data come from an industrial sensor fusion application in waterjet cutting, where different signals are monitored to detect faults affecting the most critical machine components