Multivariate Statistical Process Control with Industrial Application 1st Edition by Robert Mason, John Young ISBN 978-0898714968 0898714966
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Product details:
ISBN 10:0898714966
ISBN 13: 978-0898714968
Author: Robert L. Mason, John C. Young
This applied, self-contained text provides detailed coverage of the practical aspects of multivariate statistical process control (MVSPC) based on the application of Hotelling’s T2 statistic. MVSPC is the application of multivariate statistical techniques to improve the quality and productivity of an industrial process. The authors, leading researchers in this area who have developed major software for this type of charting procedure, provide valuable insight into the T2 statistic. Intentionally including only a minimal amount of theory, they lead readers through the construction and monitoring phases of the T2 control statistic using numerous industrial examples taken primarily from the chemical and power industries. These examples are applied to the construction of historical data sets to serve as a point of reference for the control procedure and are also applied to the monitoring phase, where emphasis is placed on signal location and interpretation in terms of the process variables.
Table of contents:
1 Introduction to the T2 Statistic
1.1 Introduction
1.2 Univariate Control Procedures
1.3 Multivariate Control Procedures
1.4 Characteristics of a Multivariate Control Procedure
1.5 Summary
2 Basic Concepts about the T2 Statistic
2.1 Introduction
2.2 Statistical Distance
2.3 T2 and Multivariate Normality
2.4 Student t versus Hotelling’s T2
2.5 Distributional Properties of the T2
2.6 Alternative Covariance Estimators.
2.7 Summary.
2.8 Appendix: Matrix Algebra Review
2.8.1 Vector and Matrix Notation
2.8.2 Data Matrix
2.8.3 The Inverse Matrix
2.8.4 Symmetric Matrix.
2.8.5 Quadratic Form
2.8.6 Wishart Distribution
3 Checking Assumptions for Using a T2 Statistic
3.1 Introduction
3.2 Assessing the Distribution of the T2
3.3 The T2 and Nonnormal Distributions
3.4 The Sampling Distribution of the T2 Statistic
3.5 Validation of the T2 Distribution
3.6 Transforming Observations to Normality
3.7 Distribution-Free Procedures
3.8 Choice of Sample Size.
3.9 Discrete Variables
3.10 Summary
3.11 Appendix: Confidence Intervals for UCL
4 Construction of Historical Data Set
4.1 Introduction
4.2 Planning
4.3 Preliminary Data
4.4 Data Collection Procedures
4.5 Missing Data.
4.6 Functional Form of Variables.
4.7 Detecting Collinearities
4.8 Detecting Autocorrelation
4.9 Example of Autocorrelation Detection Techniques
4.10 Summary
4.11 Appendix
4.11.1 Eigenvalues and Eigenvectors
4.11.2 Principal Component Analysis
5 Charting the T2 Statistic in Phase I
5.1 Introduction
5.2 The Outlier Problem
5.3 Univariate Outlier Detection
5.4 Multivariate Outlier Detection
5.5 Purging Outliers: Unknown Parameter Case
5.5.1 Temperature Example
5.5.2 Transformer Example….
5.6 Purging Outliers: Known Parameter Case
5.7 Unknown T2 Distribution
5.8 Summary
6 Charting the T2 Statistic in Phase II
6.1 Introduction
6.2 Choice of False Alarm Rate
6.3 T2 Charts with Unknown Parameters
6.4 T2 Charts with Known Parameters
6.5 T2 Charts with Subgroup Means
6.6 Interpretive Features of T2 Charting
6.7 Average Run Length (Optional)
6.8 Plotting in Principal Component Space (Optional)
6.9 Summary
7 Interpretation of T2 Signals for Two Variables
7.1 Introduction
7.2 Orthogonal Decompositions
7.3 The MYT Decomposition.
7.4 Interpretation of a Signal on a T2 Component
7.5 Regression Perspective
7.6 Distribution of the T2 Components
7.7 Data Example
7.8 Conditional Probability Functions (Optional)
7.9 Summary.
7.10 Appendix: Principal Component Form of T2
8 Interpretation of T2 Signals for the General Case
8.1 Introduction
8.2 The MYT Decomposition..
8.3 Computing the Decomposition Terms
8.4 Properties of the MYT Decomposition
8.5 Locating Signaling Variables
8.6 Interpretation of a Signal on a T2 Component
8.7 Regression Perspective
8.8 Computational Scheme (Optional).
8.9 Case Study.
. 8.10 Summary
9 Improving the Sensitivity of the T2 Statistic
9.1 Introduction
9.2 Alternative Forms of Conditional Terms
9.3 Improving Sensitivity to Abrupt Process Changes
9.4 Case Study: Steam Turbine
9.4.1 The Control Procedure
9.4.2 Historical Data Set
9.5 Model Creation Using Expert Knowledge
9.6 Model Creation Using Data Exploration
9.7 Improving Sensitivity to Gradual Process Shifts
9.8 Summary.
10 Autocorrelation in T2 Control Charts
10.1 Introduction.
10.2 Autocorrelation Patterns in T2 Charts
10.3 Control Procedure for Uniform Decay
10.4 Example of a Uniform Decay Process
10.4.1 Detection of Autocorrelation
10.4.2 Autoregressive Functions
10.4.3 Estimates
10.4.4 Examination of New Observations
10.5 Control Procedure for Stage Decay Processes.
10.6 Summary.
11 The T2 Statistic and Batch Processes
11.1 Introduction
11.2 Types of Batch Processes.
11.3 Estimation in Batch Processes
11.4 Outlier Removal for Category 1 Batch Processes
11.5 Example: Category 1 Batch Process.
11.6 Outlier Removal for Category 2 Batch Processes
11.7 Example: Category 2 Batch Process
11.8 Phase II Operation with Batch Processes
11.9 Example of Phase II Operation
11.10 Summary
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Tags: Robert Mason, John Young, Multivariate Statistical, Process Control, Industrial Application