scholarly journals Multivariate Six Sigma: A Case Study in Industry 4.0

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1119 ◽  
Author(s):  
Daniel Palací-López ◽  
Joan Borràs-Ferrís ◽  
Larissa Thaise da Silva de Oliveria ◽  
Alberto Ferrer
Keyword(s):  
Least Squares ◽  
Six Sigma ◽  
Latent Variables ◽  
Industry 4.0 ◽  
Principal Component ◽  
Complex Data ◽  
Multivariate Statistical ◽  
Least Squares Techniques ◽  
Powerful Process

The complex data characteristics collected in Industry 4.0 cannot be efficiently handled by classical Six Sigma statistical toolkit based mainly in least squares techniques. This may refrain people from using Six Sigma in these contexts. The incorporation of latent variables-based multivariate statistical techniques such as principal component analysis and partial least squares into the Six Sigma statistical toolkit can help to overcome this problem yielding the Multivariate Six Sigma: a powerful process improvement methodology for Industry 4.0. A multivariate Six Sigma case study based on the batch production of one of the star products at a chemical plant is presented.

scholarly journals Polymethyl Methacrylate Quality Modeling with Missing Data Using Subspace Based Model Identification

Processes ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1691
Author(s):  
Nikesh Patel ◽  
Kavitha Sivanathan ◽  
Prashant Mhaskar
Keyword(s):  
Missing Data ◽  
Least Squares ◽  
Partial Least Squares ◽  
Polymethyl Methacrylate ◽  
Model Identification ◽  
Principal Component ◽  
Quality Modeling ◽  
The Impact ◽  
Quality Measurements

This paper addresses the problem of quality modeling in polymethyl methacrylate (PMMA) production. The key challenge is handling the large amounts of missing quality measurements in each batch due to the time and cost sensitive nature of the measurements. To this end, a missing data subspace algorithm that adapts nonlinear iterative partial least squares (NIPALS) algorithms from both partial least squares (PLS) and principal component analysis (PCA) is utilized to build a data driven dynamic model. The use of NIPALS algorithms allows for the correlation structure of the input–output data to minimize the impact of the large amounts of missing quality measurements. These techniques are utilized in a simulated case study to successfully model the PMMA process in particular, and demonstrate the efficacy of the algorithm to handle the quality prediction problem in general.

Advanced PLS Techniques in Chemometrics and Their Applications to Molecular Design

2011 ◽  
pp. 145-168 ◽  
Author(s):  
Kiyoshi Hasegawa ◽  
Kimito Funatsu
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Molecular Design ◽  
Review Article ◽  
Complex Data ◽  
Quantitative Structure ◽  
Multivariate Statistical ◽  
Diagnostic Plots ◽  
Statistical Measures ◽  
Prediction Regions

In quantitative structure-activity/property relationships (QSAR and QSPR), multivariate statistical methods are commonly used for analysis. Partial least squares (PLS) is of particular interest because it can analyze data with strongly collinear, noisy and numerous X variables, and also simultaneously model several response variables Y. Furthermore, PLS can provide us several prediction regions and diagnostic plots as statistical measures. PLS has evolved or changed for copying with sever demands from complex data X and Y structure. In this review article, the authors picked up four advanced PLS techniques and outlined their algorithms with representative examples. Especially, the authors made efforts to describe how to disclose the embedded inner relations in data and how to use their information for molecular design.

In-Line Monitoring of Polymer Processing. II: Spectral Data Analysis

2002 ◽  
Vol 56 (10) ◽  
pp. 1268-1274 ◽  
Author(s):  
Francesca Apruzzese ◽  
Ramin Reshadat ◽  
Stephen T. Balke
Keyword(s):  
Least Squares ◽  
Latent Variables ◽  
Near Infrared ◽  
Scatter Correction ◽  
Principal Component ◽  
Ordinary Least Squares ◽  
Polymer Processing ◽  
Near Infrared Spectra ◽  
Scattering Effects ◽  
Spectral Data Analysis

The objective of this work was to examine the application of various multivariate methods to determine the composition of a flowing, molten, immiscible, polyethylene–polypropylene blend from near-infrared spectra. These spectra were acquired during processing by monitoring the melt with a fiber-optic-assisted in-line spectrometer. Undesired differences in spectra obtained from identical compositions were attributed to additive and multiplicative light scattering effects. Duplicate blend composition data were obtained over a range of 0 to 100% polyethylene. On the basis of previously published approaches, three data preprocessing methods were investigated: second derivative of absorbance with respect to wavelength (d2), multiplicative scatter correction (MSC), and a combination consisting of MSC followed by d2. The latter method was shown to substantially improve superposition of spectra and principal component analysis (PCA) scores. Also, fewer latent variables were required. The continuum regression (CR) approach, a method that encompasses ordinary least squares (OLS), partial least squares (PLS), and principle component regression (PCR) models, was then implemented and provided the best prediction model as one based on characteristics between those of PLS and OLS models.

scholarly journals Regression-Based Methods for Finding Coupled Patterns

2008 ◽  
Vol 21 (17) ◽  
pp. 4384-4398 ◽  
Author(s):  
Michael K. Tippett ◽  
Timothy DelSole ◽  
Simon J. Mason ◽  
Anthony G. Barnston
Keyword(s):  
Least Squares ◽  
Linear Prediction ◽  
Prediction Models ◽  
Principal Component Regression ◽  
Principal Component ◽  
Multivariate Statistical ◽  
Maximum Covariance Analysis ◽  
Least Squares Estimate ◽  
Common Framework ◽  
Value Decomposition

Abstract There are a variety of multivariate statistical methods for analyzing the relations between two datasets. Two commonly used methods are canonical correlation analysis (CCA) and maximum covariance analysis (MCA), which find the projections of the data onto coupled patterns with maximum correlation and covariance, respectively. These projections are often used in linear prediction models. Redundancy analysis and principal predictor analysis construct projections that maximize the explained variance and the sum of squared correlations of regression models. This paper shows that the above pattern methods are equivalent to different diagonalizations of the regression between the two datasets. The different diagonalizations are computed using the singular value decomposition of the regression matrix developed using data that are suitably transformed for each method. This common framework for the pattern methods permits easy comparison of their properties. Principal component regression is shown to be a special case of CCA-based regression. A commonly used linear prediction model constructed from MCA patterns does not give a least squares estimate since correlations among MCA predictors are neglected. A variation, denoted least squares estimate (LSE)-MCA, is suggested that uses the same patterns but minimizes squared error. Since the different pattern methods correspond to diagonalizations of the same regression matrix, they all produce the same regression model when a complete set of patterns is used. Different prediction models are obtained when an incomplete set of patterns is used, with each method optimizing different properties of the regression. Some key points are illustrated in two idealized examples, and the methods are applied to statistical downscaling of rainfall over the northeast of Brazil.

scholarly journals Source Identification of Cd and Pb in Typical Farmland Topsoil in the Southwest of China: A Case Study

2021 ◽  
Vol 13 (7) ◽  
pp. 3729
Author(s):  
Junji Zhang ◽  
Zeming Shi ◽  
Shijun Ni ◽  
Xinyu Wang ◽  
Chao Liao ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Phosphate Rock ◽  
Flow Direction ◽  
Isotope Analysis ◽  
Principal Component ◽  
Pb Isotope ◽  
Multivariate Statistical ◽  
Potential Toxic Metals ◽  
Linear Correlation Analysis

Cd and Pb in farmland topsoil are controlled by many factors. To identify the source of potential toxic metals in the farmland topsoil around Mianyuan River, the chemical analysis and multivariate statistical analysis are performed in this study. The results indicate the following: (1) The concentration of Cd and Pb in soil exceed the background value of Chinese soil elements. (2) Cd is significantly enriched in the whole region and Pb is locally enriched, both of them are more or less influenced by human activities. (3) The contents of Cd and Pb increase significantly following the flow direction of river. (4) Pb isotope analysis indicates that the main source of Pb in the soil include the air dust, coal and phosphate plant, and the contribution of them decreases successively. (5) Linear correlation analysis and principal component analysis show that the main sources of Cd in the soil are mining phosphate rock, air dust, phosphate plant and coal mining.

scholarly journals An Exploratory Multivariate Statistical Analysis to Assess Urban Diversity

2019 ◽  
Vol 11 (14) ◽  
pp. 3812 ◽  
Author(s):  
Lorena Salazar-Llano ◽  
Marti Rosas-Casals ◽  
Maria Isabel Ortego
Keyword(s):  
Statistical Analysis ◽  
Multivariate Statistical Analysis ◽  
Principal Component ◽  
Urban Systems ◽  
Multivariate System ◽  
Multiple Factor Analysis ◽  
Multivariate Statistical ◽  
Sustainability Challenges ◽  
The City

Understanding diversity in complex urban systems is fundamental in facing current and future sustainability challenges. In this article, we apply an exploratory multivariate statistical analysis (i.e., Principal Component Analysis (PCA) and Multiple Factor Analysis (MFA)) to an urban system’s abstraction of the city’s functioning. Specifically, we relate the environmental, economical, and social characters of the city in a multivariate system of indicators by collecting measurements of those variables at the district scale. Statistical methods are applied to reduce the dimensionality of the multivariate dataset, such that, hidden relationships between the districts of the city are exposed. The methodology has been mainly designed to display diversity, being understood as differentiated attributes of the districts in their dimensionally-reduced description, and to measure it with Euclidean distances. Differentiated characters and distinctive functions of districts are identifiable in the exploratory analysis of a case study of Barcelona (Spain). The distances allow for the identification of clustered districts, as well as those that are separated, exemplifying dissimilarity. Moreover, the temporal dependency of the dataset reveals information about the district’s differentiation or homogenization trends between 2003 and 2015.

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