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

• Record Nr.: UNINA9910555198203321
• Autore: Zhou Shiyu <1970->
• Pubbl/distr/stampa: Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2021]; ©2021
• ISBN: 1-5231-4353-3; 1-119-66630-9; 1-119-66627-9; 1-119-66629-5
• Descrizione fisica: 1 online resource (353 pages)
• Disciplina: 658.00727
• Soggetti: Random data (Statistics); Industrial management - Mathematics; Industrial engineering - Statistical methods; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Industrial Data Analytics for Diagnosis and Prognosis -- Contents -- Preface -- Acknowledgments -- Acronyms -- Table of Notation -- 1 Introduction -- 1.1 Background and Motivation -- 1.2 Scope and Organization of the Book -- 1.3 How to Use This Book -- Bibliographic Note -- Part 1 Statistical Methods and Foundation for Industrial Data Analytics -- 2 Introduction to Data Visualization and Characterization -- 2.1 Data Visualization -- 2.1.1 Distribution Plots for a Single Variable -- 2.1.2 Plots for Relationship Between Two Variables -- 2.1.3 Plots for More than Two Variables -- 2.2 Summary Statistics -- 2.2.1 Sample Mean, Variance, and Covariance -- 2.2.2 Sample Mean Vector and Sample Covariance Matrix -- 2.2.3 Linear Combination of Variables -- Bibliographic Notes -- Exercises -- 3 Random Vectors and the Multivariate Normal Distribution -- 3.1 Random Vectors -- 3.2 Density Function and Properties of Multivariate Normal Distribution -- 3.3 Maximum Likelihood Estimation for Multivariate Normal Distribution -- 3.4 Hypothesis Testing on Mean ; Vectors -- 3.5 Bayesian Inference for Normal Distribution -- Bibliographic Notes -- Exercises -- 4 Explaining Covariance Structure: Principal Components -- 4.1 Introduction to Principal Component Analysis -- 4.1.1 Principal Components for More Than Two Variables -- 4.1.2 PCA with Data Normalization -- 4.1.3 Visualization of Principal Components -- 4.1.4 Number of Principal Components to Retain -- 4.2 Mathematical Formulation of Principal Components -- 4.2.1 Proportion of Variance Explained -- 4.2.2 Principal Components Obtained from the Correlation Matrix -- 4.3 Geometric Interpretation of Principal Components -- 4.3.1 Interpretation Based on Rotation -- 4.3.2 Interpretation Based on Low-Dimensional Approximation -- Bibliographic Notes -- Exercises.; 5 Linear Model for Numerical and Categorical Response Variables -- 5.1 Numerical Response - Linear Regression Models -- 5.1.1 General Formulation of Linear Regression Model -- 5.1.2 Significance and Interpretation of Regression Coefficients -- 5.1.3 Other Types of Predictors in Linear Models -- 5.2 Estimation and Inferences of Model Parameters for Linear Regression -- 5.2.1 Least Squares Estimation -- 5.2.2 Maximum Likelihood Estimation -- 5.2.3 Variable Selection in Linear Regression -- 5.2.4 Hypothesis Testing -- 5.3 Categorical Response - Logistic Regression Model -- 5.3.1 General Formulation of Logistic Regression Model -- 5.3.2 Significance and Interpretation of Model Coefficients -- 5.3.3 Maximum Likelihood Estimation for Logistic Regression -- Bibliographic Notes -- Exercises -- 6 Linear Mixed Effects Model -- 6.1 Model Structure -- 6.2 Parameter Estimation for LME Model -- 6.2.1 Maximum Likelihood Estimation Method -- 6.2.2 Distribution-Free Estimation Methods -- 6.3 Hypothesis Testing -- 6.3.1 Testing for Fixed Effects -- 6.3.2 Testing for Variance-Covariance Parameters -- Bibliographic Notes -- Exercises -- Part 2 Random Effects Approaches for Diagnosis and Prognosis -- 7 Diagnosis of Variation Source Using PCA -- 7.1 Linking Variation Sources to PCA -- 7.2 Diagnosis of Single Variation Source -- 7.3 Diagnosis of Multiple Variation Sources -- 7.4 Data Driven Method for Diagnosing Variation Sources -- Bibliographic Notes -- Exercises -- 8 Diagnosis of Variation Sources Through Random Effects Estimation -- 8.1 Estimation of Variance Components -- 8.2 Properties of Variation Source Estimators -- 8.3 Performance Comparison of Variance Component Estimators -- Bibliographic Notes -- Exercises -- 9 Analysis of System Diagnosability -- 9.1 Diagnosability of Linear Mixed Effects Model -- 9.2 Minimal Diagnosable Class.; 9.3 Measurement System Evaluation Based on System Diagnosability -- Bibliographic Notes -- Exercises -- Appendix -- 10 Prognosis Through Mixed Effects Models for Longitudinal Data -- 10.1 Mixed Effects Model for Longitudinal Data -- 10.2 Random Effects Estimation and Prediction for an Individual Unit -- 10.3 Estimation of Time-to-Failure Distribution -- 10.4 Mixed Effects Model with Mixture Prior Distribution -- 10.4.1 Mixture Distribution -- 10.4.2 Mixed Effects Model with Mixture Prior for Longitudinal Data -- 10.5 Recursive Estimation of Random Effects Using Kalman Filter -- 10.5.1 Introduction to the Kalman Filter -- 10.5.2 Random Effects Estimation Using the Kalman Filter -- Biographical Notes -- Exercises -- Appendix -- 11 Prognosis Using Gaussian Process Model -- 11.1 Introduction to Gaussian Process Model -- 11.2 GP Parameter Estimation and GP Based Prediction -- 11.3 Pairwise Gaussian Process Model -- 11.3.1 Introduction to Multi-output Gaussian Process -- 11.3.2 Pairwise GP Modeling Through Convolution Process -- 11.4 Multiple Output Gaussian Process for Multiple Signals -- 11.4.1 Model Structure -- 11.4.2 Model Parameter Estimation and Prediction -- 11.4.3 Time-to-Failure Distribution Based ; on GP Predictions -- Bibliographical Notes -- Exercises -- 12 Prognosis Through Mixed Effects Models for Time-to-Event Data -- 12.1 Models for Time-to-Event Data Without Covariates -- 12.1.1 Parametric Models for Time-to-Event Data -- 12.1.2 Non-parametric Models for Time-to-Event Data -- 12.2 Survival Regression Models -- 12.2.1 Cox PH Model with Fixed Covariates -- 12.2.2 Cox PH Model with Time Varying Covariates -- 12.2.3 Assessing Goodness of Fit -- 12.3 Joint Modeling of Time-to-Event Data and Longitudinal Data -- 12.3.1 Structure of Joint Model and Parameter Estimation -- 12.3.2 Online Event Prediction for a New Unit.; 12.4 Cox PH Model with Frailty Term for Recurrent Events -- Bibliographical Notes -- Exercises -- Appendix -- Appendix: Basics of Vectors, Matrices, and Linear Vector Space -- References -- Index.