Industrial Data Analytics for Diagnosis and Prognosis. Yong Chen

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Industrial Data Analytics for Diagnosis and Prognosis

      A Random Effects Modelling Approach

       Shiyu Zhou

       University of Wisconsin – Madison

       Yong Chen

       University of Iowa

Copyright © 2021 by John Wiley & Sons, Inc. All rights reserved.

      Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

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       Library of Congress Cataloging-in-Publication Data:

      Names: Zhou, Shiyu, 1970- author. | Chen, Yong (Professor of industrial and systems engineering), author.

      Title: Industrial data analytics for diagnosis and prognosis : a random effects modelling approach / Shiyu Zhou, Yong Chen.

      Description: Hoboken. NJ : John Wiley & Sons, Inc., 2021. | Includes bibliographical references and index.

      Identifiers: LCCN 2021000379 (print) | LCCN 2021000380 (ebook) | ISBN 9781119666288 (hardback) | ISBN 9781119666295 (pdf) | ISBN 9781119666301 (epub) | ISBN 9781119666271 (ebook)

      Subjects: LCSH: Industrial engineering--Statistical methods. | Industrial management--Mathematics. | Random data (Statistics) | Estimation theory.

      Classification: LCC T57.35 .Z56 2021 (print) | LCC T57.35 (ebook) | DDC 658.0072/7--dc23

      LC record available at https://lccn.loc.gov/2021000379

      LC ebook record available at https://lccn.loc.gov/2021000380

      Cover image: © monsitj/ iStock/Getty Images

      Cover design by Wiley

      Set in 9.5/12.5pt STIX Two Text by Integra Software Services, Pondicherry, India.

To our families:

       Yifan and LauraJinghui, Jonathan, and Nathan

Contents

      1  Cover

      2  Title page

      3  Copyright

      4  Dedication

      5  Preface

      6  Acknowledgments

      7  Acronyms

      8  Table of Notation

      9 Chapter 1: Introduction1.1 Background and Motivation1.2 Scope and Organization of the Book1.3 How to Use This BookBibliographic Notes

      10 Part 1 Statistical Methods and Foundation for Industrial Data AnalyticsChapter 2: Introduction to Data Visualization and Characterization2.1 Data Visualization2.1.1 Distribution Plots for a Single Variable2.1.2 Plots for Relationship Between Two Variables2.1.3 Plots for More than Two Variables2.2 Summary Statistics2.2.1 Sample Mean, Variance, and Covariance2.2.2 Sample Mean Vector and Sample Covariance Matrix2.2.3 Linear Combination of VariablesBibliographic NotesExercisesChapter 3: Random Vectors and the Multivariate Normal Distribution3.1 Random Vectors3.2 Density Function and Properties of Multivariate Normal Distribution3.3 Maximum Likelihood Estimation for Multivariate Normal Distribution3.4 Hypothesis Testing on Mean Vectors3.5 Bayesian Inference for Normal DistributionBibliographic NotesExercisesChapter 4: Explaining Covariance Structure: Principal Components4.1 Introduction to Principal Component Analysis4.1.1 Principal Components for More Than Two Variables4.1.2 PCA with Data Normalization4.1.3 Visualization of Principal Components4.1.4 Number of Principal Components to Retain4.2 Mathematical Formulation of Principal Components4.2.1 Proportion of Variance Explained4.2.2 Principal Components Obtained from the Correlation Matrix4.3 Geometric Interpretation of Principal Components4.3.1 Interpretation Based on Rotation4.3.2 Interpretation Based on Low-Dimensional ApproximationBibliographic NotesExercisesChapter 5: Linear Model for Numerical and Categorical Response Variables5.1 Numerical Response – Linear Regression Models5.1.1 General Formulation of Linear Regression Model5.1.2 Significance and Interpretation of Regression Coefficients5.1.3 Other Types of Predictors in Linear Models5.2 Estimation and Inferences of Model Parameters for Linear Regression5.2.1 Least Squares Estimation5.2.2 Maximum Likelihood Estimation5.2.3 Variable Selection in Linear Regression5.2.4 Hypothesis Testing5.3 Categorical Response – Logistic Regression Model5.3.1 General Formulation of Logistic Regression Model5.3.2 Significance and Interpretation of Model Coefficients5.3.3 Maximum Likelihood Estimation for Logistic RegressionBibliographic NotesExercisesChapter 6: Linear Mixed Effects Model6.1