Statistics in Practice

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Marian Scott

University of Glasgow, UK

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University of Maryland, USA

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Nottingham Trent University, UK

Statistics in Practice is an important international series of texts which provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study.

With sound motivation and many worked practical examples, the books show in down-to-earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title's special topic area.

The books provide statistical support for professionals and research workers across a range of employment fields and research environments. Subject areas covered include medicine and pharmaceutics; industry, finance and commerce; public services; the earth and environmental sciences, and so on.

The books also provide support to students studying statistical courses applied to the above areas. The demand for graduates to be equipped for the work environment has led to such courses becoming increasingly prevalent at universities and colleges.

It is our aim to present judiciously chosen and well-written workbooks to meet everyday practical needs. Feedback of views from readers will be most valuable to monitor the success of this aim.

A complete list of titles in this series appears at the end of the volume.

This edition first published 2012

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Library of Congress Cataloging-in-Publication Data

Kruger, Uwe, Dr.

Advances in statistical monitoring of complex multivariate processes : with applications in industrial process control / Uwe Kruger and Lei Xie.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-02819-3 (hardback)

1. Multivariate analysis. I. Xie, Lei. II. Title.

QA278.K725 2012

519.5′35—dc23

2012016445

A catalogue record for this book is available from the British Library.

ISBN: 978-0-470-02819-3

Dedicated to Dr. Xun Wang, my wife, and Melanie Kruger, my daughter, whose abundant support has made this book possible.

Uwe Kruger

Without the dedication and support of my wife, Jingjing Sha, this book would never have been possible.

Lei Xie

Preface

This book provides a timely reference text for academics, undergraduate and graduate students, and practitioners alike in the area of process monitoring and safety, as well as product quality assurance using multivariate statistics. The rapid evolution of this research area over the past 20 years is mainly driven by significant advances in computer horsepower and the ever growing demand from industry to effectively and efficiently monitor production processes. As an example, Nimmo (1995) outlined that the US-based petrochemical industry could save an estimated $10 bn annually if abnormal conditions could be detected, diagnosed and appropriately dealt with. Moreover, the demand from the oil and gas industry, other chemical engineering and general manufacturing industries is also a result of ever tighter government legislation on emissions and increased safety standards of their products.

The wide range of applications of multivariate statistics for process monitoring, safety and product quality is of considerable interest to the readership in chemical, mechanical, manufacturing, electrical and electronic, industrial and other related engineering and science disciplines. This research text serves as a reference for introductory and advanced courses on process safety, process monitoring and product quality assurance, total quality management of complex technical systems and is a supplementary text for courses on applied statistics and process systems engineering. As a textbook and reference, this book pays particular attention to a balanced presentation between the required theory and the industrial exploitation of statistical-based process monitoring, safety and quality assurance.

To cater for the different audiences with their partially conflicting demands, the scope of the book is twofold. The main thrust lies on outlining the relevant and important fundamental concept of multivariate statistical process control or, in short, MSPC and to demonstrate the working of this technology using recorded data from complex process systems. This addresses the needs for the more how-does-it-work and what-does-it-do oriented readership of this book, which includes undergraduate students, industrial practitioners and industrially oriented researchers. The second pillar is the theoretical analysis of the underlying MSPC component technology, which is important for the more research-oriented audience including graduate students and academicians.

The twofold coverage of the material results from the research background of both authors, which is centered on academic research in process monitoring, safety, product quality assurance and general process systems engineering, and their participation in numerous industrial R&D projects, including consultancy concerning the application of MSPC and the development of commercial software packages. As this book carefully outlines and discusses, the main advantage of the MSPC technology is its simplicity and reliance on recorded data and some a priori knowledge regarding the operation of the process system. On the other hand, this simplicity comes at the expense of stringent assumptions, including that the process is stationary and time-invariant, and that the process variables follow a Gaussian distribution.

With this in mind and based on academic and industrial R&D experience, the authors are convinced that MSPC technology has the potential to play an important role in commercial applications of process monitoring, safety and product quality assurance. This view is also supported by the arrival of software that entered the value-added market for commercially available packages, which includes AspenMultivariate™, Wonderware, SIMCA-P (to name but a few), consultancy companies, such as Perceptive Engineering Ltd., Eigenvector Research Inc. and statistical data analysis software, e.g. STATISTICA, SAS®.

The first thrust of MSPC work for monitoring complex process systems emerged in the late 1980 and the early 1990s and lays out a statistically sound concept under these basic assumptions. It is important to note, however, that if a process ‘unfortunately forgets’ to meet the above assumptions, the corresponding monitoring charts may produce false alarms or the sensitivity in detecting minor upsets is compromised. From the end of the 1990s until now, research work that has enhanced the core MSPC methodology has removed some of these stringent assumptions. This, in turn, allows the enhanced MSPC technology to be applicable in a more practically relevant environment.

Besides the required theoretical foundation of the MSPC methodology, this book also includes a detailed discussion of these advances, including (i) the monitoring of time-variant process systems, where the mean and variance of the recorded variables, and the relationship between and among these sets, change over time, (ii) the development and application of more practically relevant data structures for the underlying MSPC monitoring models and (iii) the development of a different construction of monitoring statistics and charts which significantly improves their sensitivity in detecting incipient fault conditions.

This book ideally supplements the good number of research texts available on multivariate statistics, statistical process control, process safety and product quality assurance. In particular, the research text brings together the theory of MSPC with industrial applications to demonstrate its usefulness. In particular, the mix of theory and practice in this area is rare; (exceptions include Mason and Young (2001)). Moreover, good and solid reference that address the theory as well as the application of component technology are rarely written for the industrial practitioner whose experience is pivotal in any process monitoring, safety and product quality assurance application.

To comprehend the content of this book, the readership is expected to possess basic knowledge of calculus including differentiation, integration and matrix computation. For the application study, a basic understanding of principles in physics and chemistry is helpful in following the analysis of the application studies and particularly the diagnosis of the recorded fault conditions. To enhance the understanding of the presented material and to improve the learning experience, each chapter presenting theoretical material, except the last two, includes a tutorial session which contains questions and homework-style projects. The questions assist with the familiarization of the covered material and the projects help the reader to understand the underlying principles through experimenting and discovering the facts and findings presented in this book either through self-study reports or team-based project reports. The calculations can be carried out using standard computational software, for example Matlab®.

Acknowledgements

This book would not have been possible without encouragement, dedicated help and constructive comments from a large number of people. We would like to thank SupCon Software Co Ltd., Hangzhou, P.R. China, for providing access to the data sets used in Chapters 7 and 8. We particularly thank Dr. Yong Gu and Mr. Yanhui Zhang for technical advice regarding these data sets and for interpreting associated results. Our thanks also extend to Dr. Jian Chu, Dr. Hongye Su and Dr. Shuqing Wang for facilitating numerous research visits by Dr. Uwe Kruger to the Institute of Cyber Systems and Control, Zhejiang University, P.R. China, from 2006 onwards.

Dr. Xie is grateful for financial support from the National Science Foundation of China (Grant No. 60904039, 61134007) and the Fundamental Research Funds for the Central Universities. Furthmore, Dr. Kruger would like to acknowledge the financial support of the Ministry Of Education Program of Introducing Talents of Discipline (111 Project, Grant No. B07031).

With regards to the recorded data from the chemical reaction process in Chapter 4, Dr. Uwe Kruger is grateful to Dr. Keith Smith for advice on how to interpret the process data, and ICI Polymer Chemicals for providing access to the operating data used and for the permission to present associated results in Kruger et al (2001). Dr. Kruger would also like to thank Mr. Steve Robinson for providing helpful advice in analyzing and interpreting the process data of the distillation process and is grateful to BP Amoco Scotland for providing access to the operating data used in Chapter 5 and for the permission to present associated results in Wang et al (2003). We wish to acknowledge the contribution of Dr. Randall C. McFarlane, who introduced the mechanistic simulator of the fluid catalytic cracking unit and for offering helpful advice regarding the generation of realistic operating scenarios for the application study in Chapter 7.

Dr. Uwe Kruger is indebted to Dr. David J. Sandoz for the mentoring and the care as adviser for his doctorate degree at the University of Manchester and for introducing the area of industrial process control and monitoring during his attachment to the Control Technology Center Ltd. and Predictive Control Ltd. between 1996 and 2000. Dr. Sandoz's leadership and vision has always been a source of inspiration and a reference for technology transfer, improving existing methods and for generating conceptual ideas. In addition, Dr. Kruger would like to acknowledge the mentoring as well as the helpful and constructive advice by Dr. George W. Irwin during his employment at Queen's University Belfast between 2001 and 2007. Dr. Irwin's leadership of the Intelligent Systems and Control Group contributed in large parts to the research work in Chapter 7. During that time, Dr. Kruger's research activities on process monitoring, process safety and quality assurance were financially supported by DuPont (UK) Ltd., Invest Northern Ireland, the Engineering and Physical Science Research Council, the European Social Fund, the Department of Education and Learning, the Center for the Theory and Application of Catalysis and the Virtual Engineering Center. From 2007 to 2012, Dr. Kruger acknowledges financial support from The Petroleum Institute to continue the development of industrially relevant techniques for process monitoring, process safety and product quality assurance. Dr. Kruger would particularly like to acknowledge the helpful assistance by Dr. Cornelis Peters and Dr. Ali Almansoori of the Chemical Engineering Program and the advice by Dr. Jaap Geluk of the Department of Mathematics regarding the central limit theorem.

We are also in debt to many graduate students, colleagues and friends for their encouragement, helpful suggestions and invaluable contributions in generating the research work in this book. As it is difficult to provide an inclusive list of all contributors to our work, we would like to mention in particular the academic colleagues Dr. Xun Wang, Dr. Qian Chen, Dr. Tim Littler, Dr. Barry Lennox, Dr. Günter Wozny, Dr. Sebstian Engell, Dr. Yiqi Zhou, Dr. Enrique Luis Lima, Dr. José Carlos Pinto and Dr. Zhihuan Song. The following former postdoctoral researchers and graduate students strongly contributed to the work in this book: Dr. Zhiqiang Ge, Dr. David Antory, Dr. Dirk Lieftucht, Dr. Yan Zhou, Dr. Xueqin Liu, Dr. Thiago Feital and Dr. Udo Schubert. The authors also want to acknowledge the contribution by the graduate students Mr. Omar AlJaberi, Ms. Zhe Li and Mr. Gui Chen. Dr. Uwe Kruger finally wishes to thank Mr. Marcel Meronk for his support in relation to the application studies in Chapters 4 and 5 and for his friendship and encouragement.

Finally, the authors would like to thank the Wiley team and, in particular, Mr. Richard Davies, Miss. Heather Kay and Mrs. Susan Barclay for their patience, invaluable support and encouragement for drafting and completing this book.

Abbreviations

CLT | Central Limit Theorem
flops | Number of floating point operations
i.d. | Independently distributed
i.i.d. | Identically and independently distributed
LCL | Lower Confidence Limit
LV | Latent Variable
MLPCA | Maximum Likelihood Principal Component Analysis
MLPLS | Maximum Likelihood Partial Least Squares
MRPLS | Maximum Redundancy Partial Least Squares
MSPC | Multivariate Statistical Process Control
MWPCA | Moving Window Principal Component Analysis
OLS | Ordinary Least Squares
PCA | Principal Component Analysis
PDF | Probability Density Function
PLS | Partial Least Squares
RPCA | Recursive Principal Component Analysis
RPLS | Recursive Partial Least Squares
SPC | Statistical Process Control
SVD | Singular Value Decomposition
UCL | Upper Control Limit
w.r.t | with respect to

Symbols

| Estimated variable
∼ | Follows a specific distribution function, e.g. z ∼ F( · )
₀ | Stochastic component of variable
| Mean value of variable
lim | Limit operator, e.g.
⊗ | Kronecker product of two matrices
| Imaginary unit,
a | Vector
A | Matrix
I | Identity matrix
| Diagonal matrix
|A| | Determinant of A, N = M
||a|| | Length of a,
||A|| | Frobenius norm of A,
A† | Generalized inverse of a matrix,
| A†A = I if N > M or AA† = I if N < M
| Orthogonal complement of column or row space of A,
| if N > M or if N < M
trace{A} | Trace of A, , N = M
E{ · } | Expectation operator, e.g. E{z} = 1.2
vec{A} | Vector representation of matrix,

Nomenclature

, , c, d, ϑ, 7.1 | Constants or correction terms
| Correlation matrix for variable set z₀
χ², | Cumulative chi-squared distribution function and critical value for significance α
| Projection matrix, (PCA model)
δij | Kronecker delta, δij = 1 for i = j and 0 for i ≠ j
e, f, E, F | Residual vectors and matrices for input and output variables (PLS/MRPLS model)
, | Error vector for input and variables (PLS/MRPLS model)
f( · ), F( · ) | Probability density and cumulative distribution function
, | Cumulative distribution and critical value of an F distribution with m₁ and m₂ degrees of freedom and a significance α
g, G | Residual vector and matrix (PCA model)
| Error vector for process variables (PCA model)
Γ(m) | Gamma function, m > 0
H₀,H₁ | Null and alternative hypothesis
i, j | Variable indices, e.g. zi or xj
k, l | Sampling indices, e.g. z(k) is the kth sample of z
| Index set
K, and | Number of reference samples, application delay for adapted MSPC models and length of moving window
Λ, λi | Diagonal matrix of eigenvalues, ith eigenvalue
n | Number of retained pairs of latent variables (PCA and PLS/MRPLS models)
nx, ny and nz | Number of input and output variables (PLS/MRPLS model), and number of process variables (PCA model)
| Cumulative Gaussian distribution function of mean and covariance matrix Szz
Ω, ω | General projection matrix and vector
p, P | Loading vector and matrix for process variables (PCA model) and input variable sets (PLS/MRPLS model)
q, , Q, | Weight and loading vectors and matrices for output variables (PLS/MRPLS model)
Q, Qα | Residual Q statistic and its control limit for significance α
rij | Correlation coefficient between ith and jth variable
r, w, R, W | Loading vectors and matrices for input variables (PLS/MRPLS model)
σ, Σ | Standard deviation and diagonal matrix storing standard deviations
| Covariance matrix of source variables and its eigendecomposition
t, T | Score vector and matrix for data vector of PCA model and input vector of PLS/MRPLS model
T², | Hotelling's T² statistic and control limit for significance α
u, U | Score vector and matrix for output vector (PLS model)
| Fault subspace
w, , W | Weight vectors and matrix for input variables (PLS/MRPLS model)
x, X | Input vector and matrix (PLS/MRPLS model)
Ξ and (, ) | Parameter matrices (PCA and PLS/MRPLS models)
y, Y | Output vector and matrix (PLS/MRPLS model)
z, Z | Data vector and matrix (PCA model)
| Parameter vector determining confidence interval for covariance matrix (Chapter 7)

Metric conversions |
1lb/s | 0.453 kb/s
1scf/s | 0.0283m³/s
1psi/psia | 6894.75732Pa
Degrees in K | (80 × degrees in F − 32)/1.8 + 273.15
1 ICFM | 1.699 m³/h
degrees in C | (80 × degrees in F − 32)/1.8

Introduction

Performance assessment and quality control of complex industrial process systems are of ever increasing importance in the chemical and general manufacturing industries as well as the building and construction industry (Gosselin and Ruel 2007; Marcon et al. 2005; Miletic et al. 2004; Nimmo 1995). Besides other reasons, the main drivers of this trend are: the ever more stringent legislation based on process safety, emissions and environmental pollution (ecological awareness); an increase in global competition; and the desire of companies to present a green image of their production processes and products.

Associated tasks entail the on-line monitoring of production facilities, individual processing units and systems (products) in civil, mechanical, automotive, electrical and electronic engineering. Examples of such systems include the automotive and the aerospace industries for monitoring operating conditions and emissions of internal combustion and jet engines; buildings for monitoring the energy consumption and heat loss; and bridges for monitoring stress, strain and temperature levels and hence assess elastic deformation.

To address the need for rigorous process monitoring, the level of instrumentation of processing units and general engineering systems, along with the accuracy of the sensor readings, have consequently increased over the past few decades. The information that is routinely collected and stored, for example in distributed control systems for chemical production facilities and the engine management system for internal combustion engines, is then benchmarked against conditions that are characterized as normal and/or optimal.

The data records therefore typically include a significant number of process variables that are frequently sampled. This, in turn, creates huge amounts of process data, which must be analyzed online or archived for subsequent analysis. Examples are reported for:

the chemical industry (Al-Ghazzawi and Lennox 2008; MacGregor et al. 1991; Piovoso and Kosanovich 1992; Simoglou et al. 2000; Wang et al. 2003);

the general manufacturing industry (Kenney et al. 2002; Lane et al. 2003; Martin et al. 2002; Monostori and Prohaszka 1993; Qin et al. 2006);

internal combustion engines (Gérard et al. 2007; Howlett et al. 1999; Kwon et al. 1987; McDowell et al. 2008; Wang et al. 2008);

aircraft systems (Abbott and Person 1991; Boller 2000; Jaw 2005; Jaw and Mattingly 2008; Tumer and Bajwa 1999); and

civil engineering systems (Akbari et al. 2005; Doebling et al. 1996; Ko and Ni 2005; Pfafferott et al. 2004; Westergren et al. 1999).

For the chemical and manufacturing industries, the size of the data records and the ever increasing complexity of such systems have caused efficient process monitoring by plant operators to become a difficult task. This complexity stems from increasing levels of process optimization and intensification, which gives rise to operating conditions that are at the limits of operational constraints and which yield complex dynamic behavior (Schmidt-Traub and Górak 2006). A consequence of these trends is a reduced safety margin if the process shows some degree of abnormality, for example caused by a fault (Schuler 2006).

Examples for monitoring technical systems include internal combustion engines and gearbox systems. Process monitoring of internal combustion engines relates to tackling increasing levels of pollution caused by the emissions of an ever growing number of registered vehicles and has resulted in the introduction of the first on-board-diagnostic (OBD) system in the United States in 1988, and in Europe (EURO1) in 1992. The requirement for more advanced monitoring systems culminated in the introduction of OBDII (1994), EURO2 (1997) and EURO3 (2000) legislation. This trend has the aim of continuously decreasing emissions and is supported through further regulations, which relate to the introduction of OBDIII (considered since 2000), EURO4 (2006) and EURO5 (2009) systems.

Current and future regulations demand strict monitoring of engine performance at certain intervals under steady-state operating conditions. This task entails the diagnosis of any fault condition that could potentially cause the emissions to violate legislated values at the earliest opportunity. With respect to this development, a prediction by Powers and Nicastri (1999) indicated that the integration of model-based control systems and design techniques have the potential to produce safer, more comfortable and manoeuvrable vehicles. According to Kiencke and Nielsen (2000), there are a total of three main objectives that automotive control systems have to adhere to: (i) maintaining efficiency and low fuel consumption, (ii) producing low emissions to protect the environment and (iii) ensuring safety. Additional benefits of condition monitoring are improved reliability and economic operation (Isermann and Ballé 1997) through early fault detection.

For gearbox systems, the early detection of incipient fault conditions is of fundamental importance for their operation. Gearboxes can be found in aerospace, civil and general mechanical systems. The consequences of not being able to detect such faults at early stages can, for example, include reduced productivity in manufacturing processes, reduced efficiency of engines, equipment damage or even failure. Early detection of such faults can therefore provide significant improvements in the reduction of operational and maintenance costs, system down-time, and lead to increased levels of safety, which is of ever growing importance. An incipiently developing fault in a mechanical system usually affects certain parameters, such as vibration, noise and temperature. The analysis of these external variables therefore allows the monitoring of internal components, such as gears, which are usually inaccessible without the dismantling of the system. It is consequently essential to extract relevant information from the recorded signals with the aim of detecting any irregularities that could be caused by such faults.

The research community has utilized a number of different approaches to monitor complex technical systems. These include model-based approaches (Ding 2008; Frank et al. 2000; Isermann 2006; Simani et al. 2002; Venkatasubramanian et al. 2003) that address a wide spectrum of application areas, signal-based approaches (Bardou and Sidahmed 1994; Chen et al. 1995; Hu et al. 2003; Kim and Parlos 2003) which are mainly applied to mechanical systems, rule-based techniques (Iserman 1993; Kramer and Palowitch 1987; Shin and Lee 1995; Upadhyaya et al. 2003) and more recently knowledge-based techniques (Lehane et al. 1998; Ming et al. 1998; Qing and Zhihan 2004; Shing and Chee 2004) that blend heuristic knowledge into monitoring application. Such techniques have shown their potential whenever cost-benefit economics have justified the required effort in developing applications.

Given the characteristics of modern production and other technical systems, however, such complex technical processes may present a large number of recorded variables that are affected by a few common trends, which may render these techniques difficult to implement in practice. Moreover, such processes often operate under steady-state operation conditions that may or may not be predefined. To some extent, this also applies to automotive systems as routine technical inspections, for example once per year, usually include emission tests that are carried out at a reference steady state operation condition of the engine.

Underlying trends are, for example, resulting from known or unknown disturbances, interactions of the control system with the technical system, and minor operator interventions. This produces the often observed high degree of correlated among the recorded process variables that mainly describe common trends or common cause variation. The sampled data has therefore embedded within it information for revealing the current state of process operation. The difficult issue here is to extract this information from the data and to present it in a way that can be easily interpreted.

Based on the early work on quality control and monitoring (Hotelling 1947; Jackson 1959, 1980; Jackson and Morris 1956, 1957; Jackson and Mudholkar 1979), several research articles around the 1990s proposed a multivariate extension to statistical process control Kresta et al. (1989, 1991) MacGregor et al. (1991) Wise et al. (1989b, 1991) to generate a statistical fingerprint of a technical system based on recorded reference data. Methods that are related to this extension are collectively referred to as multivariate statistical process control or MSPC. The application of MSPC predominantly focussed on the chemical industry (Kosanovich and Piovoso 1991; Morud 1996; Nomikos and MacGregor 1994; Piovoso and Kosanovich 1992; Piovoso et al. 1991) but was later extended to general manufacturing areas (Bissessur et al. 1999; 2000; Lane et al. 2003; Martin et al. 2002; Wikström et al. 1998).

Including this earlier work, the last two decades have seen the development and application of MSPC gaining substantial interest in academe and industry alike. The recipe for the considerable interest in MSPC lies in its simplicity and adaptability for developing monitoring applications, particularly for larger numbers of recorded variables. In fact, MSPC relies on relatively few assumptions and only requires routinely collected operating data from the process to be monitored. The first of four parts of this book outlines and describes these assumptions, and is divided into a motivation for MSPC, a description of the main MSPC modeling methods and the underlying data structures, and the construction of charts to carry out on-line monitoring.

For monitoring processes in the chemical industry, the research community has proposed two different MSPC approaches. The first one relates to processes that produce a specific product on a continuous basis, i.e. they convert a constant stream of inputs into a constant stream of outputs and are referred to as a continuous processes. Typical examples of continuous processes can be found in the petrochemical industry. The second approach has been designed to monitor processes that convert a discontinuous feed into the required product over a longer period of time. More precisely, and different from a continuous process, this type of process receives a feed that remains in the reactor over a significantly longer period of time before the actual production process is completed. Examples of the second type of process can be found in the pharmaceutical industry and such processes are referred to as batch processes. This book focuses on continuous processes to provide a wide coverage of processes in different industries. References that discuss the monitoring of batch processes include Chen and Liu (2004), Lennox et al. (2001), Nomikos and MacGregor (1994, 1995), van Sprang et al. (2002) to name only a few.

The second part of this book then presents two application studies of a chemical reaction process and a distillation process. Both applications demonstrate the ease of utilizing MSPC for process monitoring and detecting as well as diagnosing abnormal process behavior. The detection is essentially a boolean decision whether current process behavior still matches the statistical fingerprint describing behavior that is deemed normal and/or optimal. If it matches, the process is in-statistical-control and if it does not the process is out-of-statistical-control. The diagnosis of abnormal events entails the identification and analysis of potential root causes that have led to the anomalous behavior. In other words, it assesses why the current plant behavior deviates from that manifested in the statistical fingerprint, constructed from a historic data record, that characterizes normal process behavior. The second part of this book also demonstrates that the groundwork on MSPC in the early to mid 1990s may rely on oversimplified assumptions that may not represent true process behavior.

The aim of the third part is then to show advances in MSPC which the research literature has proposed over the past decade in order to overcome some of the pitfalls of this earlier work. These advances include:

improved data structures for MSPC monitoring models;

the removal of the assumption that the stochastic process variables have a constant mean and variance, and the variable interrelationships are constant over time; and

a fresh look at constructing MSPC monitoring charts, resulting in the introduction of a new paradigm which significantly improves the sensitivity of the monitoring scheme in detecting incipient fault conditions.

In order to demonstrate the practical usefulness of these improvements, the application studies of the chemical reactor and the distillation processes in the second part of this book are revisited. In addition, the benefits of the adaptive MSPC scheme is also shown using recorded data from a furnace process and the enhanced monitoring scheme is applied to recorded data from gearbox systems.

Finally, the fourth part of this book presents a detailed treatment of the core MSPC modeling methods, including their objective functions, and their statistical and geometric properties. The analysis also includes the discussion of computational issues in order to obtain data models efficiently.

Part I

Fundamentals of Multivariate Statistical Process Control

Chapter 1

Motivation for multivariate statistical process control

This first chapter outlines the basic principles of multivariate statistical process control. For the reader unfamiliar with statistical-based process monitoring, a brief revision of statistical process control (SPC) and its application to industrial process monitoring are provided in Section 1.1.

The required extension to MSPC to address data correlation is then motivated in Section 1.2. This section also highlights the need to extract relevant information from a large dimensional data space, that is the space in which the variation of recorded variables is described. The extracted information is described in a reduced dimensional data space that is a subspace of the original data space.

To help readers unfamiliar with MSPC technology, Section 1.3 offers a tutorial session, which includes a number of questions, small calculations/examples and projects to help familiarization with the subject and to enhance the learning outcomes. The answers to these questions can be found in this chapter. Project 2 to 4 require some self study and result in a detailed understanding on how to interpret SPC monitoring charts for detecting incipient fault conditions.

1.1 Summary of statistical process control

Statistical process control has been introduced into general manufacturing industry for monitoring process performance and product quality, and to observe the general process variation, exhibited in a few key process variables. Although this indicates that SPC is a process monitoring tool, the reference to control (in control engineering often referred to as describing and analyzing the feedback or feed-forward controller/process interaction), is associated with product or, more precisely, process improvement. In other words, the control objective here is to reduce process variation and to increase process reliability and product quality. One could argue that the controller function is performed by process operators or, if a more fundamental interaction with the process is required, a task force of experienced plant personnel together with plant managers. The next two subsections give a brief historical review of its development and outline the principles of SPC charts. The discussion of SPC in this section only represents a brief summary for the reader unfamiliar with this subject. A more in-depth and detailed treatment of SPC is available in references Burr (2005); Montgomery (2005); Oakland (2008); Smith (2003); Thompson and Koronacki (2002).

1.1.1 Roots and evolution of statistical process control

The principles of SPC as a system monitoring tool were laid out by Dr. Walter A. Shewhart during the later stages of his employment at the Inspection Engineering Department of the Western Electric Company between 1918 and 1924 and from 1925 until his retirement in 1956 at the Bell Telephone Laboratories. Shewhart summarized his early work on statistical control of industrial production processes in his book (Shewhart, 1931). He then extended this work which eventually led to the applications of SPC to the measurement processes of science and stressed the importance of operational definitions of basic quantities in science, industry and commerce (Shewhart, 1939). In particular, the latter book has had a profound impact upon statistical methods for research in behavioral, biological and physical sciences, as well as general engineering.

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