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Mathematics
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Functional Statistics: Outliers Detection and Quality Control
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Functional Statistics: Outliers Detection and Quality Control

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 October 2020) | Viewed by 29762

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Javier Martínez Torres

E-Mail Website
Guest Editor
Escuela Superior de Ingeniería y Tecnología. Universidad Internacional de La Rioja, 26006 Logroño, Spain
Interests: functional statistics; functional outlier; quality control; process control; capability; functional data
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

At present, a large amount of data can be approached from the functional prism and in a multitude of fields such as engineering, medicine, etc. An example of this, which is very important to the engineering (mechanical, electronic, environmental, etc.) field, is quality control, which is based on the classical Schewart methodology or WECO rules.

However, while application is important, a comparison between methods, and the design and construction of a new model, univariable or multivariable, based on depth, non-parametric, etc., is also important. Thus, in this Special Issue, different articles are collected with new models of detection of functional outliers, or applications thereof, on different areas of quality control and process capability control.

Prof. Dr. Javier Martínez Torres
Guest Editor

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Keywords

  • Functional outliers
  • Functional depth
  • SPC
  • Capability
  • Control process

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Published Papers (7 papers)

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Research

12 pages, 371 KiB  
Article
Functional Location-Scale Model to Forecast Bivariate Pollution Episodes
by Manuel Oviedo-de La Fuente, Celestino Ordóñez and Javier Roca-Pardiñas
Mathematics 2020, 8(6), 941; https://doi.org/10.3390/math8060941 - 8 Jun 2020
Viewed by 1995
Abstract
Predicting anomalous emission of pollutants into the atmosphere well in advance is crucial for industries emitting such elements, since it allows them to take corrective measures aimed to avoid such emissions and their consequences. In this work, we propose a functional location-scale model [...] Read more.
Predicting anomalous emission of pollutants into the atmosphere well in advance is crucial for industries emitting such elements, since it allows them to take corrective measures aimed to avoid such emissions and their consequences. In this work, we propose a functional location-scale model to predict in advance pollution episodes where two pollutants are involved. Functional generalized additive models (FGAMs) are used to estimate the means and variances of the model, as well as the correlation between both pollutants. The method not only forecasts the concentrations of both pollutants, it also estimates an uncertainty region where the concentrations of both pollutants should be located, given a specific level of uncertainty. The performance of the model was evaluated using real data of SO 2 and NO x emissions from a coal-fired power station, obtaining good results. Full article
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control)
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21 pages, 2132 KiB  
Article
Application of Functional Data Analysis and FTIR-ATR Spectroscopy to Discriminate Wine Spirits Ageing Technologies
by Ofélia Anjos, Miguel Martínez Comesaña, Ilda Caldeira, Soraia Inês Pedro, Pablo Eguía Oller and Sara Canas
Mathematics 2020, 8(6), 896; https://doi.org/10.3390/math8060896 - 2 Jun 2020
Cited by 20 | Viewed by 4233
Abstract
Fourier transform infrared spectroscopy (FTIR) with Attenuated Total Reflection (ATR) combined with functional data analysis (FDA) was applied to differentiate aged wine spirits according to the ageing technology (traditional using 250 L wooden barrels versus alternative using micro-oxygenation and wood staves applied in [...] Read more.
Fourier transform infrared spectroscopy (FTIR) with Attenuated Total Reflection (ATR) combined with functional data analysis (FDA) was applied to differentiate aged wine spirits according to the ageing technology (traditional using 250 L wooden barrels versus alternative using micro-oxygenation and wood staves applied in 1000 L stainless steel tanks), the wood species used (chestnut and oak), and the ageing time (6, 12, and 18 months). For this purpose, several features of the wine spirits were examined: chromatic characteristics resulting from the CIELab method, total phenolic index, concentrations of furfural, ellagic acid, vanillin, and coniferaldehyde, and total content of low molecular weight phenolic compounds determined by HPLC. FDA applied to spectral data highlighted the differentiation between all groups of samples, confirming the differentiation observed with the analytical parameters measured. All samples in the test set were differentiated and correctly assigned to the aged wine spirits by FDA. The FTIR-ATR spectroscopy combined with FDA is a powerful methodology to discriminate wine spirits resulting from different ageing technologies. Full article
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control)
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17 pages, 5354 KiB  
Article
Outliers Detection Models in Shewhart Control Charts; an Application in Photolithography: A Semiconductor Manufacturing Industry
by Ishaq Adeyanju Raji, Muhammad Hisyam Lee, Muhammad Riaz, Mu’azu Ramat Abujiya and Nasir Abbas
Mathematics 2020, 8(5), 857; https://doi.org/10.3390/math8050857 - 25 May 2020
Cited by 16 | Viewed by 4636
Abstract
Shewhart control charts with estimated control limits are widely used in practice. However, the estimated control limits are often affected by phase-I estimation errors. These estimation errors arise due to variation in the practitioner’s choice of sample size as well as the presence [...] Read more.
Shewhart control charts with estimated control limits are widely used in practice. However, the estimated control limits are often affected by phase-I estimation errors. These estimation errors arise due to variation in the practitioner’s choice of sample size as well as the presence of outlying errors in phase-I. The unnecessary variation, due to outlying errors, disturbs the control limits implying a less efficient control chart in phase-II. In this study, we propose models based on Tukey and median absolute deviation outlier detectors for detecting the errors in phase-I. These two outlier detection models are as efficient and robust as they are distribution free. Using the Monte-Carlo simulation method, we study the estimation effect via the proposed outlier detection models on the Shewhart chart in the normal as well as non-normal environments. The performance evaluation is done through studying the run length properties namely average run length and standard deviation run length. The findings of the study show that the proposed design structures are more stable in the presence of outlier detectors and require less phase-I observation to stabilize the run-length properties. Finally, we implement the findings of the current study in the semiconductor manufacturing industry, where a real dataset is extracted from a photolithography process. Full article
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control)
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20 pages, 9071 KiB  
Article
A Functional Data Analysis for Assessing the Impact of a Retrofitting in the Energy Performance of a Building
by Miguel Martínez Comesaña, Sandra Martínez Mariño, Pablo Eguía Oller, Enrique Granada Álvarez and Aitor Erkoreka González
Mathematics 2020, 8(4), 547; https://doi.org/10.3390/math8040547 - 7 Apr 2020
Cited by 4 | Viewed by 2824
Abstract
There is an increasing interest in reducing the energy consumption in buildings and in improving their energy efficiency. Building retrofitting is the employed solution for enhancing the energy efficiency in existing buildings. However, the actual performance after retrofitting should be analysed to check [...] Read more.
There is an increasing interest in reducing the energy consumption in buildings and in improving their energy efficiency. Building retrofitting is the employed solution for enhancing the energy efficiency in existing buildings. However, the actual performance after retrofitting should be analysed to check the effectiveness of the energy conservation measures. The aim of this work was to detect and to quantify the impact that a retrofitting had in the electrical consumption, heating demands, lighting and temperatures of a building located in the north of Spain. The methodology employed is the application of Functional Data Analyses (FDA) in comparison with classic mathematical techniques such as the Analysis of Variance (ANOVA). The methods that are commonly used for assessing building refurbishment are based on vectorial approaches. The novelty of this work is the application of FDA for assessing the energy performance of renovated buildings. The study proves that more accurate and realistic results are obtained working with correlated datasets than with independently distributed observations of classical methods. Moreover, the electrical savings reached values of more than 70% and the heating demands were reduced more than 15% for all floors in the building. Full article
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control)
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17 pages, 798 KiB  
Article
Classical Lagrange Interpolation Based on General Nodal Systems at Perturbed Roots of Unity
by Elías Berriochoa, Alicia Cachafeiro, Alberto Castejón and José Manuel García-Amor
Mathematics 2020, 8(4), 498; https://doi.org/10.3390/math8040498 - 2 Apr 2020
Cited by 3 | Viewed by 3040
Abstract
The aim of this paper is to study the Lagrange interpolation on the unit circle taking only into account the separation properties of the nodal points. The novelty of this paper is that we do not consider nodal systems connected with orthogonal or [...] Read more.
The aim of this paper is to study the Lagrange interpolation on the unit circle taking only into account the separation properties of the nodal points. The novelty of this paper is that we do not consider nodal systems connected with orthogonal or paraorthogonal polynomials, which is an interesting approach because in practical applications this connection may not exist. A detailed study of the properties satisfied by the nodal system and the corresponding nodal polynomial is presented. We obtain the relevant results of the convergence related to the process for continuous smooth functions as well as the rate of convergence. Analogous results for interpolation on the bounded interval are deduced and finally some numerical examples are presented. Full article
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control)
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19 pages, 1583 KiB  
Article
A Functional Data Analysis Approach for the Detection of Air Pollution Episodes and Outliers: A Case Study in Dublin, Ireland
by Javier Martínez Torres, Jorge Pastor Pérez, Joaquín Sancho Val, Aonghus McNabola, Miguel Martínez Comesaña and John Gallagher
Mathematics 2020, 8(2), 225; https://doi.org/10.3390/math8020225 - 10 Feb 2020
Cited by 33 | Viewed by 5607
Abstract
Ground level concentrations of nitrogen oxide (NOx) can act as an indicator of air quality in the urban environment. In cities with relatively good air quality, and where NOx concentrations rarely exceed legal limits, adverse health effects on the population may still occur. [...] Read more.
Ground level concentrations of nitrogen oxide (NOx) can act as an indicator of air quality in the urban environment. In cities with relatively good air quality, and where NOx concentrations rarely exceed legal limits, adverse health effects on the population may still occur. Therefore, detecting small deviations in air quality and deriving methods of controlling air pollution are challenging. This study presents different data analytical methods which can be used to monitor and effectively evaluate policies or measures to reduce nitrogen oxide (NOx) emissions through the detection of pollution episodes and the removal of outliers. This method helps to identify the sources of pollution more effectively, and enhances the value of monitoring data and exceedances of limit values. It will detect outliers, changes and trend deviations in NO2 concentrations at ground level, and consists of four main steps: classical statistical description techniques, statistical process control techniques, functional analysis and a functional control process. To demonstrate the effectiveness of the outlier detection methodology proposed, it was applied to a complete one-year NO2 dataset for a sub-urban site in Dublin, Ireland in 2013. The findings demonstrate how the functional data approach improves the classical techniques for detecting outliers, and in addition, how this new methodology can facilitate a more thorough approach to defining effect air pollution control measures. Full article
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control)
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26 pages, 2400 KiB  
Article
Constructing a Control Chart Using Functional Data
by Miguel Flores, Salvador Naya, Rubén Fernández-Casal, Sonia Zaragoza, Paula Raña and Javier Tarrío-Saavedra
Mathematics 2020, 8(1), 58; https://doi.org/10.3390/math8010058 - 2 Jan 2020
Cited by 22 | Viewed by 6191
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; [...] Read more.
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. Full article
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control)
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