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Application of On-line Data
Analytics to a Continuous
Process Polybutene Unit
An In-Depth Discussion on Model Building

1
Presenters




Efren Hernandez



Robert Wojewodka



2

QiWei Li

Terry Blevins
Introduction




Continuous data analytics provides online prediction
of quality parameters and detection of fault conditions
Topics
–
–
–
–
–

3

Introduction of continuous data analytics (CDA)
Model building techniques and examples
On-line view platform implementation
Benefits and achievements
Q&A
The Lubrizol Corporation Segments
Lubrizol Additives Lubrizol Advanced Materials
•
•
•

Advanced chemical technology for global transportation, industrial and
consumer markets
Unique, hard-to-duplicate formulations resulting in successful solutions
for our customers
A talented and committed global work force delivering growth through
skill, knowledge and imagination

The Right Mix of People, Ideas and Market Knowledge
4
Lubrizol Leading Market Positions

5
Emerson and Lubrizol Objectives
Lubrizol






6

Evaluate the performance of quality
parameter predictions using data
analytics in comparison to the on-line
analyzers in a continuous
polymerization process unit.
Develop simple and informative user
platform for continuous performance
monitoring and data analysis
Evaluate process quality control
schemes based on parameter
predictions using data analytics

Emerson


Support ALL Lubrizol objectives



Test CDA prototype functionality in
collecting data, developing models and
on-line operation



Developing recommendations for
enhancing CDA prototype and future
CDA product



Providing Lubrizol field trial feedback
on CDA for DeltaV product planning
group

Key Goal:
Collaborate to develop and improve the Continuous
Data Analytics software package.
General Concepts – A Process
PROCESS
INPUTS

OUTPUTS

Very much like batch processing, continuous
process applications can be simplified down to
these major blocks of activity
7

Generic continuous process flow diagram.
General Concepts – A Process
Initial Conditions
Feed Stock Analysis

Measurements reflecting operating
conditions that impact product quality
(X Parameters, In-Process Y Parameters)

Lab Analysis of
Product Quality
(Y Parameter)

Generic continuous process flow diagram.

8
General Concepts – Univariate SPC Charts
SPC Chart for Variable 2

SPC Chart for Variable 1
12

98

UCL = 96.5239
10
CTR = 90.0907
LCL = 83.6576
8

95

X

92

6

89

4
86

2

83

0
0

10

20

30

40

50

60

0

10

Observation
Anything atypical
with this point?
9

20

30

40

Observation
Anything atypical
with this point?

50

60
UCL = 11.5478
CTR = 5.9426
LCL = 0.3374

Statistic – Multi-Variant Analysis
Control Ellipse
50

SPC Chart for Variable 2

60

14

40
30

8

20

5

Observation

Variable 2

Variable 2

11

10

2

0

2

4

6

8

10

12

0

-1

98

SPC Chart for Variable 1

82

86

90
Variable 1

95

X

98

X

92

94

89
86
83
0

10

10

20

30

40

Variable 1

Observation

50

60

UCL = 96.5239
CTR = 90.0907
LCL = 83.6576
Basic Concepts
Multivariate Control Chart

Multivariate SPC Chart
UCL = 10.77
24

T-Squared

20
16
12
8
4
0
0

10

20

30
40
Observation

…. Time ….
11

50

60
Online Data Analytics


Through the use of Principal Component Analysis (PCA) it is
possible to detect abnormal operations resulting from both
measured and unmeasured faults.
– Measured disturbances – may be quantified through the application of
Hotelling’s T2 statistic.
• The T2 plot characterizes the amount of process variation that can be explained by the
model and how it compares to “typical” operation.

– Unmeasured disturbances – The Q statistic, also known as the Squared
Prediction Error (SPE) or DMODX, may be used.
• The Q plot characterizes the amount of process variation that cannot be explained by the
model.



12

Projection to latent structures, also known as partial least
squares (PLS) is used to provide operators with continuous
prediction of quality parameters.
The Nature of Continuous Data
Process

M1
M2
M3
M4

Online
Measurements

M5
M6

Q1 Quality
Q2 Parameters from
Q3 Lab
...

M7

X - space

M8

Y - space

M9

13

Time Delays
....
In a continuous process there can be a significant differences in the
time required for each on-line measurement to impact processing or
a measured quality parameter.
Model Building
Define

• the process overview and identify the input, process, and output
measurements

Create

• a module that contains a Continuous Data Analytics block and configure for
measurements that may impact quality

Download
Collect

• the module that contains the CDA block and the continuous data historian
and begin entering lab data
• process data over the full dynamic operating range

Analyze
Generate

14

• the selected historian data in the CDA application, clean up the data, and
perform a sensitivity analysis

• a model by selecting the state parameter and method. Validate the model
for prediction accuracy using data then download the module

Launch

• the web browser to view on-line fault detection and quality parameter
prediction; revalidate further once on-line
Model Building


Learning from Data
– Define the key operating regime parameter in the model as the “state
parameter”
– All variables that impact the quality parameter must be captured
– All variations of the typical operating conditions must be captured

Quality Parameter
State Parameter
Variable X

15
Lubrizol Field Trial Scope
Dynamic
Compressor
Efficiency

Refrigeration System

2+ Hours
A

Operation 1

Reaction

Operation 3

Operation 4

Polybutene Unit
16

Product
Bulk
Viscosity
Refrigeration Model


Quality parameter: Compressor Efficiency
– Maximize compression efficiency
– Detect fault processing conditions




12 out of 22 process inputs incorporated into model
ℎ
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 100 ∗
No process delay
ℎ

𝑝2 , 𝑠1 − ℎ 𝑝1 , 𝑡1
𝑝2 , 𝑡2 − ℎ 𝑝1 , 𝑡1

Where,
h(p2,s1 )=isentropic enthalpy for suction entropy
s1 and discharge pressure p2
h(p2,t2 )=enthalpy at discharge pressure p2 and
temperature t2
h(p1,t1 )=enthalpy at suction pressure p1 and
temperature t1

17

s1=entropy at suction pressure p1 and
temperature t1
Model Improvement – Example 1




Below models cross verifies predicted (green) against actual (blue)
efficiency
Variation in operating condition lowered model effectiveness

2012 Model

r2=0.97
18

2013 Model

r2=0.60
Model Improvement – Example 1



19

Fault in model contributed by change in feed composition
Re-trained model to reflect feed composition variation in 2013
Model Improvement – Example 2




The adjacent compressor’s activity had a direct impact on
existing model
Re-train not recommended due to higher frequency of changes
2 Active Compressor

r2=0.92

20

1 Active Compressor

r2=0.05
Model Improvement – Example 2





21

Defined the number of compressors active as “state parameter”
Collect data to cover all process condition variations
Re-train model
Refrigeration Model Exhibition


2013 Compressor Efficiency Model

r2=0.97

22
Combined Viscosity Model


Quality parameter: Finished product viscometer output
– Distinguish high and low viscosity cuts
– Detect abnormal shift in viscosity
– Detect faulty processing conditions




11 out of 28 process inputs incorporated into model
2+ hour process time delay
Low Vis Input

23

High Vis Input
Model Improvement – Example 3





24

Quality parameter (green trend) failed to trigger the selector logic
because the low range viscosity meter’s top limit in the field was lowered
to a value below the selector trigger point
Issue resolved after modifying logic statements
Intimate process knowledge are great supplements for model integrity
upkeep
Model Improvement – Sensitivity Analysis


Multiple Variables
– Multiple dimensions of data analysis (Time range, time delay, # of
principle components, etc.)
– One variable is changed at a time to define the optimized model

X Hour Delay

r2=0.79
25

Y Hour Delay

r2=0.94
Combined Viscosity Model Exhibition


26

2013 Combined Viscometer Model (Cross Verification)
Lab Viscosity Model


Quality parameter: Finished product lab analyzed viscosity
– Verify viscometer’s accuracy





20 out of 28 process inputs incorporated into model
2-3 hour process time delay
Samples are taken every 2 hours (non-continuous)

420/636 sample points used in model
Jan 6

27

Jan

Mar 1

Mar
Lab Viscosity Model – Self Verification



Models are good fit for self verification with existing data
However, next slide’s cross-verification shows weaker
extrapolation compared to previously displayed models

2012 Model

28

2013 Model
Lab Viscosity Model




29

Compared to the compressor and combined vis models, the
2013 lab viscosity model requires much more work ahead
Possible causes for deviation includes fewer sample points,
additional lab sample delay, missing input variables, etc.
Pureweb On-line View


Pureweb on-line view web interface developed by Emerson
– Web interface deployed in process unit for operator to use
– Quality prediction, fault detection, and deviation alarm are featured



Operator Feedbacks:
– “Our plant is getting younger as more experienced operators retire
and new hires come in. The prediction tool will give new operators
a good idea of what they’re making in the reactor and reduce the
chances of making off spec material.”
– “Poly Plant is a complex system. With all the temperature,
pressure, level, and other variables, it is sometimes overwhelming
to run the board. Data analytics will help us focus on the more
important factors that drive the reaction and allow us to make an
informed decision before making a system change.”

30
On-Line View – Quality Prediction

• Prediction is expected to fall within the
confidence bands
• Auto-scaling zooms in to increase
resolution

31
On-Line View – Fault Detection

• Fault is significant if either indicator exceeds a value of 1.0
• Clicking the left field shows deviations for individual variables

32
Layers of Network Architecture
Remote Desktop
Access - Citrix

Beta Team – Model Building using remote desktop,
On-line monitoring using Web Browser/ remote desktop.

A Plant Management - On-line
monitoring using Web Browser

(existing)

PI
(existing)

PI LAB DATA
(Matrikon/opc Tunneller)

Web Server
Access

(existing)

Corporate
Level 4

Poly Control Room - On-line
monitoring using Web
Browser

(existing)

A Plant

Level 3

Continuous Data Analytics
IIS Server
PureWeb

Level 2,5
DMZ 2.5
DMZ 2

Measurements
(Matrikon/opcTunneller)

Application Station
(existing)

33

Level 2

Production Control Network
Business Results Achieved


Product Integrity and Productivity Improvement
– Quality prediction promotes product integrity
– Fault detection improves mechanical reliability and prevent
production time lost



Personnel & Process Safety
– Fault detection can recognize abnormal system behaviors and act
as secondary safety safeguards in addition to alarms

Production

34

Detects
Deviation

Respond to
Deviation

Avoid Lost
Production
Time
Business Results Achieved


Operation Efficiency
– A quick glance informs the operators on the state of the process
– Operators can utilize future viscosity predictions to reduce transition
time in between product grades



Training
– The web interface is an easy-to-learn training module for less
experienced operators
– CDA provides experienced operator with another layer knowledge
on the intermittent relationship of over 10 variables in a continuous
process

35
Summary









36

Continuous Data Analytics has successfully provided
Lubrizol, Deer Park TX with quality prediction and fault
detection capabilities
With the combined effort of Lubrizol and Emerson
representatives, four analytical models were developed for
the compressors and the production unit
These four models were deployed into unit operation
CDA model’s quality prediction and fault detection features
received positive feedback from operations
Extensive knowledge on CDA and model building is gained
Data Analytics Workshops
Learn more about continuous and batch data analytics by
attending the following workshops at this year’s Emerson
Exchange:




8-4342 How to install Batch Analytics on a non-V12
DeltaV system



37

8-4775 Challenges and Solutions in Data Analytics
Application for a Distillation Column

8-4240 Application of On-line Data Analytics to a
Continuous Process Polybutene Unit
Where To Get More Information


Regina, Sansoni, T., Blevins, Application of Online Data Analytics to a Continuous Process Polybutene
Unit, October, 2012



Terrence Blevins, Willy K. Wojsznis and Mark Nixon Advanced Control Foundation – Tools, Techniques,
and Applications, ISA, 2013



Dunia, R., Edgar, T., Blevins, T., Wojsznis, W., Multistate PLS for Continuous Process Monitoring, ACC,
March, 2012



J.V. Kresta, J.F. MacGregor, and T.E. Marlin., Multivariate Statistical Monitoring of Process Operating
Performance. Can. J. Chem.Eng. 1991; 69:35-47



Dunia, R., Edgar, T., Blevins, T., Wojsznis, W., Multistate Analytics for Continuous Processes, Journal of
Process Control, 2012



MacGregor J.F., Kourti T., Statistical process control of multivariate processes. Control Engineering
Practice 1995; 3:403-414



Kourti, T. Application of latent variable methods to process control and multivariate statistical process
control in industry. International Journal of Adaptive Control and Signal Processing 2005; 19:213-246



Kourti T, MacGregor J.F. Multivariate SPC methods for process and product monitoring, Journal of
Quality Technology 1996; 28: 409-428

38
Thank You for Attending!
Enjoy the rest of the conference.

39

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Aplication of on line data analytics to a continuous process polybetene unit

  • 1. Application of On-line Data Analytics to a Continuous Process Polybutene Unit An In-Depth Discussion on Model Building 1
  • 3. Introduction   Continuous data analytics provides online prediction of quality parameters and detection of fault conditions Topics – – – – – 3 Introduction of continuous data analytics (CDA) Model building techniques and examples On-line view platform implementation Benefits and achievements Q&A
  • 4. The Lubrizol Corporation Segments Lubrizol Additives Lubrizol Advanced Materials • • • Advanced chemical technology for global transportation, industrial and consumer markets Unique, hard-to-duplicate formulations resulting in successful solutions for our customers A talented and committed global work force delivering growth through skill, knowledge and imagination The Right Mix of People, Ideas and Market Knowledge 4
  • 6. Emerson and Lubrizol Objectives Lubrizol    6 Evaluate the performance of quality parameter predictions using data analytics in comparison to the on-line analyzers in a continuous polymerization process unit. Develop simple and informative user platform for continuous performance monitoring and data analysis Evaluate process quality control schemes based on parameter predictions using data analytics Emerson  Support ALL Lubrizol objectives  Test CDA prototype functionality in collecting data, developing models and on-line operation  Developing recommendations for enhancing CDA prototype and future CDA product  Providing Lubrizol field trial feedback on CDA for DeltaV product planning group Key Goal: Collaborate to develop and improve the Continuous Data Analytics software package.
  • 7. General Concepts – A Process PROCESS INPUTS OUTPUTS Very much like batch processing, continuous process applications can be simplified down to these major blocks of activity 7 Generic continuous process flow diagram.
  • 8. General Concepts – A Process Initial Conditions Feed Stock Analysis Measurements reflecting operating conditions that impact product quality (X Parameters, In-Process Y Parameters) Lab Analysis of Product Quality (Y Parameter) Generic continuous process flow diagram. 8
  • 9. General Concepts – Univariate SPC Charts SPC Chart for Variable 2 SPC Chart for Variable 1 12 98 UCL = 96.5239 10 CTR = 90.0907 LCL = 83.6576 8 95 X 92 6 89 4 86 2 83 0 0 10 20 30 40 50 60 0 10 Observation Anything atypical with this point? 9 20 30 40 Observation Anything atypical with this point? 50 60
  • 10. UCL = 11.5478 CTR = 5.9426 LCL = 0.3374 Statistic – Multi-Variant Analysis Control Ellipse 50 SPC Chart for Variable 2 60 14 40 30 8 20 5 Observation Variable 2 Variable 2 11 10 2 0 2 4 6 8 10 12 0 -1 98 SPC Chart for Variable 1 82 86 90 Variable 1 95 X 98 X 92 94 89 86 83 0 10 10 20 30 40 Variable 1 Observation 50 60 UCL = 96.5239 CTR = 90.0907 LCL = 83.6576
  • 11. Basic Concepts Multivariate Control Chart Multivariate SPC Chart UCL = 10.77 24 T-Squared 20 16 12 8 4 0 0 10 20 30 40 Observation …. Time …. 11 50 60
  • 12. Online Data Analytics  Through the use of Principal Component Analysis (PCA) it is possible to detect abnormal operations resulting from both measured and unmeasured faults. – Measured disturbances – may be quantified through the application of Hotelling’s T2 statistic. • The T2 plot characterizes the amount of process variation that can be explained by the model and how it compares to “typical” operation. – Unmeasured disturbances – The Q statistic, also known as the Squared Prediction Error (SPE) or DMODX, may be used. • The Q plot characterizes the amount of process variation that cannot be explained by the model.  12 Projection to latent structures, also known as partial least squares (PLS) is used to provide operators with continuous prediction of quality parameters.
  • 13. The Nature of Continuous Data Process M1 M2 M3 M4 Online Measurements M5 M6 Q1 Quality Q2 Parameters from Q3 Lab ... M7 X - space M8 Y - space M9 13 Time Delays .... In a continuous process there can be a significant differences in the time required for each on-line measurement to impact processing or a measured quality parameter.
  • 14. Model Building Define • the process overview and identify the input, process, and output measurements Create • a module that contains a Continuous Data Analytics block and configure for measurements that may impact quality Download Collect • the module that contains the CDA block and the continuous data historian and begin entering lab data • process data over the full dynamic operating range Analyze Generate 14 • the selected historian data in the CDA application, clean up the data, and perform a sensitivity analysis • a model by selecting the state parameter and method. Validate the model for prediction accuracy using data then download the module Launch • the web browser to view on-line fault detection and quality parameter prediction; revalidate further once on-line
  • 15. Model Building  Learning from Data – Define the key operating regime parameter in the model as the “state parameter” – All variables that impact the quality parameter must be captured – All variations of the typical operating conditions must be captured Quality Parameter State Parameter Variable X 15
  • 16. Lubrizol Field Trial Scope Dynamic Compressor Efficiency Refrigeration System 2+ Hours A Operation 1 Reaction Operation 3 Operation 4 Polybutene Unit 16 Product Bulk Viscosity
  • 17. Refrigeration Model  Quality parameter: Compressor Efficiency – Maximize compression efficiency – Detect fault processing conditions   12 out of 22 process inputs incorporated into model ℎ 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 100 ∗ No process delay ℎ 𝑝2 , 𝑠1 − ℎ 𝑝1 , 𝑡1 𝑝2 , 𝑡2 − ℎ 𝑝1 , 𝑡1 Where, h(p2,s1 )=isentropic enthalpy for suction entropy s1 and discharge pressure p2 h(p2,t2 )=enthalpy at discharge pressure p2 and temperature t2 h(p1,t1 )=enthalpy at suction pressure p1 and temperature t1 17 s1=entropy at suction pressure p1 and temperature t1
  • 18. Model Improvement – Example 1   Below models cross verifies predicted (green) against actual (blue) efficiency Variation in operating condition lowered model effectiveness 2012 Model r2=0.97 18 2013 Model r2=0.60
  • 19. Model Improvement – Example 1   19 Fault in model contributed by change in feed composition Re-trained model to reflect feed composition variation in 2013
  • 20. Model Improvement – Example 2   The adjacent compressor’s activity had a direct impact on existing model Re-train not recommended due to higher frequency of changes 2 Active Compressor r2=0.92 20 1 Active Compressor r2=0.05
  • 21. Model Improvement – Example 2    21 Defined the number of compressors active as “state parameter” Collect data to cover all process condition variations Re-train model
  • 22. Refrigeration Model Exhibition  2013 Compressor Efficiency Model r2=0.97 22
  • 23. Combined Viscosity Model  Quality parameter: Finished product viscometer output – Distinguish high and low viscosity cuts – Detect abnormal shift in viscosity – Detect faulty processing conditions   11 out of 28 process inputs incorporated into model 2+ hour process time delay Low Vis Input 23 High Vis Input
  • 24. Model Improvement – Example 3    24 Quality parameter (green trend) failed to trigger the selector logic because the low range viscosity meter’s top limit in the field was lowered to a value below the selector trigger point Issue resolved after modifying logic statements Intimate process knowledge are great supplements for model integrity upkeep
  • 25. Model Improvement – Sensitivity Analysis  Multiple Variables – Multiple dimensions of data analysis (Time range, time delay, # of principle components, etc.) – One variable is changed at a time to define the optimized model X Hour Delay r2=0.79 25 Y Hour Delay r2=0.94
  • 26. Combined Viscosity Model Exhibition  26 2013 Combined Viscometer Model (Cross Verification)
  • 27. Lab Viscosity Model  Quality parameter: Finished product lab analyzed viscosity – Verify viscometer’s accuracy    20 out of 28 process inputs incorporated into model 2-3 hour process time delay Samples are taken every 2 hours (non-continuous) 420/636 sample points used in model Jan 6 27 Jan Mar 1 Mar
  • 28. Lab Viscosity Model – Self Verification   Models are good fit for self verification with existing data However, next slide’s cross-verification shows weaker extrapolation compared to previously displayed models 2012 Model 28 2013 Model
  • 29. Lab Viscosity Model   29 Compared to the compressor and combined vis models, the 2013 lab viscosity model requires much more work ahead Possible causes for deviation includes fewer sample points, additional lab sample delay, missing input variables, etc.
  • 30. Pureweb On-line View  Pureweb on-line view web interface developed by Emerson – Web interface deployed in process unit for operator to use – Quality prediction, fault detection, and deviation alarm are featured  Operator Feedbacks: – “Our plant is getting younger as more experienced operators retire and new hires come in. The prediction tool will give new operators a good idea of what they’re making in the reactor and reduce the chances of making off spec material.” – “Poly Plant is a complex system. With all the temperature, pressure, level, and other variables, it is sometimes overwhelming to run the board. Data analytics will help us focus on the more important factors that drive the reaction and allow us to make an informed decision before making a system change.” 30
  • 31. On-Line View – Quality Prediction • Prediction is expected to fall within the confidence bands • Auto-scaling zooms in to increase resolution 31
  • 32. On-Line View – Fault Detection • Fault is significant if either indicator exceeds a value of 1.0 • Clicking the left field shows deviations for individual variables 32
  • 33. Layers of Network Architecture Remote Desktop Access - Citrix Beta Team – Model Building using remote desktop, On-line monitoring using Web Browser/ remote desktop. A Plant Management - On-line monitoring using Web Browser (existing) PI (existing) PI LAB DATA (Matrikon/opc Tunneller) Web Server Access (existing) Corporate Level 4 Poly Control Room - On-line monitoring using Web Browser (existing) A Plant Level 3 Continuous Data Analytics IIS Server PureWeb Level 2,5 DMZ 2.5 DMZ 2 Measurements (Matrikon/opcTunneller) Application Station (existing) 33 Level 2 Production Control Network
  • 34. Business Results Achieved  Product Integrity and Productivity Improvement – Quality prediction promotes product integrity – Fault detection improves mechanical reliability and prevent production time lost  Personnel & Process Safety – Fault detection can recognize abnormal system behaviors and act as secondary safety safeguards in addition to alarms Production 34 Detects Deviation Respond to Deviation Avoid Lost Production Time
  • 35. Business Results Achieved  Operation Efficiency – A quick glance informs the operators on the state of the process – Operators can utilize future viscosity predictions to reduce transition time in between product grades  Training – The web interface is an easy-to-learn training module for less experienced operators – CDA provides experienced operator with another layer knowledge on the intermittent relationship of over 10 variables in a continuous process 35
  • 36. Summary      36 Continuous Data Analytics has successfully provided Lubrizol, Deer Park TX with quality prediction and fault detection capabilities With the combined effort of Lubrizol and Emerson representatives, four analytical models were developed for the compressors and the production unit These four models were deployed into unit operation CDA model’s quality prediction and fault detection features received positive feedback from operations Extensive knowledge on CDA and model building is gained
  • 37. Data Analytics Workshops Learn more about continuous and batch data analytics by attending the following workshops at this year’s Emerson Exchange:   8-4342 How to install Batch Analytics on a non-V12 DeltaV system  37 8-4775 Challenges and Solutions in Data Analytics Application for a Distillation Column 8-4240 Application of On-line Data Analytics to a Continuous Process Polybutene Unit
  • 38. Where To Get More Information  Regina, Sansoni, T., Blevins, Application of Online Data Analytics to a Continuous Process Polybutene Unit, October, 2012  Terrence Blevins, Willy K. Wojsznis and Mark Nixon Advanced Control Foundation – Tools, Techniques, and Applications, ISA, 2013  Dunia, R., Edgar, T., Blevins, T., Wojsznis, W., Multistate PLS for Continuous Process Monitoring, ACC, March, 2012  J.V. Kresta, J.F. MacGregor, and T.E. Marlin., Multivariate Statistical Monitoring of Process Operating Performance. Can. J. Chem.Eng. 1991; 69:35-47  Dunia, R., Edgar, T., Blevins, T., Wojsznis, W., Multistate Analytics for Continuous Processes, Journal of Process Control, 2012  MacGregor J.F., Kourti T., Statistical process control of multivariate processes. Control Engineering Practice 1995; 3:403-414  Kourti, T. Application of latent variable methods to process control and multivariate statistical process control in industry. International Journal of Adaptive Control and Signal Processing 2005; 19:213-246  Kourti T, MacGregor J.F. Multivariate SPC methods for process and product monitoring, Journal of Quality Technology 1996; 28: 409-428 38
  • 39. Thank You for Attending! Enjoy the rest of the conference. 39