Recent Advances in Statistical
Quality Control
Prof. Fugee Tsung
Hong Kong University
of Science and Technology
Email: season@ust.hk
Quality Lab: http://qlab.ieem.ust.hk
INFORMS International, Hong Kong 2006
Dr. Fugee Tsung, HKUST
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Outline
I.
II.
III.
IV.
SPC for profiles
SPC for engineering controlled
processes
SPC for multistage processes
Quality techniques in service industry
Dr. Fugee Tsung, HKUST
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How to Handle Variation
Ignore
Desensitize
Compensate
Reduce/
Eliminate
Dr. Fugee Tsung, HKUST
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Statistical Process Control (SPC):
Role in Six Sigma
Define
Control
Measure
Improve

Analyze
SPC is emphasized as the major tool used to
control and sustain a Six Sigma process
Dr. Fugee Tsung, HKUST
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I. SPC for Profiles
SPC: Basic Idea
yi ~ N ( 1 ,  12 ) for i  1,2,..., ;
yi ~ N (  2 ,  ) for i    1,..., n.
?
y
Sample Mean
2
2
1.5
UCL=1.342
1.0
0.5
0.0
Mean=0
-0.5
-1.0
LCL=-1.342
-1.5
0
10
20
30
Sample Number
In most SPC applications it is assumed that the quality of a process or product
can be adequately represented by the distribution of a univariate quality
characteristic or by the general multivariate distribution of a vector consisting of
several quality characteristics (Woodall et al. 2004).
Dr. Fugee Tsung, HKUST
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SPC: A Different Idea
yi  f ( xi )
1.5
UCL=1.342
x
?
y
Sample Mean
1.0
0.5
0.0
Mean=0
-0.5
-1.0
LCL=-1.342
-1.5
0
10
20
30
Sample Number
In many practical situations, however, the quality of a process or product is
better characterized and summarized by a relationship between a response
variable and one or more explanatory variables (Woodall et al. 2004).
Dr. Fugee Tsung, HKUST
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A Profile Example
Dr. Fugee Tsung, HKUST
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Another Profile Example
Dr. Fugee Tsung, HKUST
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II. SPC for engineering controlled
processes
A Engineering Controlled Process
1.5
UCL=1.342
x
Sample Mean
1.0
y
?
Process
0.5
0.0
Mean=0
-0.5
-1.0
EPC
Controller
LCL=-1.342
-1.5
0
i
xi  k P yi  k I  yi  k Dyi
10
20
30
Sample Number
j 1
kI
xi  k P yi 
yi  k D (1  B) yi
1 B
Dr. Fugee Tsung, HKUST
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Window of Opportunity
(a)
(b)
Tsung, Shi, and Wu (1999, JQT)
Dr. Fugee Tsung, HKUST
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Dynamics and autocorrelation

To monitor the engineering controlled
process, one may consider monitoring a
Dynamic T2 statistic of the form
1
DTt  X  X t
L
where



T
t
Xt = [ yt , xt , yt-1 , xt-1 , …, yt-L , xt-L ]T
 is the covariance matrix of Xt
L is a user-specified time shift factor
Tsung and Apley (2002, IIE Trans.)
Dr. Fugee Tsung, HKUST
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Incoming signal confounding
Model-void assignable causes
Output assignable causes
Input assignable causes
x
?
y
Process
EPC
Controller
Dr. Fugee Tsung, HKUST
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Recent results in SPC/EPC











Tsung, F., Wu, H. and Nair, V.N., "On Efficiency and Robustness of Discrete
Proportional-Integral Control Schemes," Technometrics, 40, 214-222, 1998.
Tsung, F., Shi, J. and Wu, C.F.J., "Joint Monitoring of PID Controlled Processes,"
Journal of Quality Technology, 31, 275-285, 1999.
Tsung, F. and Shi, J., "Integrated Design of Run-to-Run PID Controller and SPC
Monitoring for Process Disturbance Rejection," IIE Transactions, 31, 517-527, 1999.
Tsung, F., "Improving Automatic-Controlled Process Quality Using Adaptive Principal
Component Monitoring," Quality and Reliability Engineering International, 15, 135144, 1999
Tsung, F., "On Three-Term Adjustment Schemes for Statistical Process Control,"
International Journal of Industrial Engineering, 6, 161-170, 1999.
Tsung, F., "Statistical Monitoring and Diagnosis of Automatic Controlled Processes
Using Dynamic PCA," International Journal of Production Research, 38, 625-637,
2000.
Tsung, F., "A Note on Statistical Monitoring of Engineering Controlled Processes,"
International Journal of Reliability, Quality and Safety Engineering, 8, 1-14, 2001.
Tsung, F. and Apley, D.W., " The Dynamic T-squared Chart for Monitoring FeedbackControlled Processes," IIE Transactions, 34, 1043-1054, 2002.
Shi, D. and Tsung, F., " Modeling and Diagnosis of Feedback-Controlled Processes
Using Dynamic PCA and Neural Networks," International Journal of Production
Research, 41, 365-380, 2003.
Tsung, F. and Tsui, K.-L., "A Mean Shift Pattern Study on Integration of SPC and APC
for Process Monitoring," IIE Transactions, 35, 231-242, 2003.
Tseng, S.-T., Yeh, A. B., Tsung, F., and Chan Y.-Y., " A Study of Variable EWMA
Controller," IEEE Transactions on Semiconductor Manufacturing, 16, 633-643, 2003.
Dr. Fugee Tsung, HKUST
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III. SPC for Multistage processes
A Multistage Process
Stage 1
Stage k-1
Stage k
Stage N
1.5
UCL=1.342
yk-1
?
Sample Mean
1.0
yk
0.5
0.0
Mean=0
-0.5
-1.0
LCL=-1.342
-1.5
yk  Ak 1 yk 1  Bk  k  wk
0
10
20
30
Sample Number
Yk  Ck yk  vk
vk ~ N (0,  v2 ), wk ~ N (0,  w2 )
Dr. Fugee Tsung, HKUST
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Example: Printed Circuit Board Manufacturing
Exposure
Black Oxide
Lay-up
From Ding, Shi, and Ceglarek (2002)
Hot Press
Cutting
Drilling
Inspection
…….
Dr. Fugee Tsung, HKUST
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Multistage Monitoring



The use of single-stage SPC can be misleading and
ineffective as its measure is confounded with the
cumulative effects from previous stages.
Impact of dynamics and autocorrelation due to the
cumulative effects of process dynamics and inertia
of serially dependent stages.
How to make use of SPC information accessible
outside of the individual process to make better
quality control decisions.
Dr. Fugee Tsung, HKUST
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Multistage Diagnosis



It is critical to trace the source of a defect found in
final inspection to a root cause early in the
multistage process -- Traceability (Palm et al. 1997)
How to isolate and identify the sources of an outof-control condition by linking the current stage
signal to information about earlier stages in the
process
Multistage fault/fraud detection/identification
through data mining and knowledge discovery.
Dr. Fugee Tsung, HKUST
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Recent results in Multistage SPC








Tsung, F., "Impact of Information Sharing on Statistical Quality Control,"
IEEE Transactions on Systems, Man, and Cybernetics, 30, 211-216, 2000.
Linn, R., Au, E. and Tsung, F., " Process Capability Improvement for
Multistage Processes," Quality Engineering, 15, 281-292, 2003.
Shu, L. and Tsung, F., " On Multistage Statistical Process Control," Journal of
Chinese Institute of Industrial Engineers, 20, 1-8, 2003.
Shu, L., Tsung, F., and Kapur, K., " Design of Multiple Cause-Selecting
Charts for Multistage Processes with Model Uncertainty," Quality
Engineering, 16, 437-450, 2004.
Sun, R. and Tsung, F., " Change Pattern Discovery in Multistage Statistical
Process Control," International Journal of Industrial Engineering, 11, 261272, 2004.
Shu, L., Tsung, F., and Tsui, K.-L., " Run-Length Performance of Regression
Control Charts with Estimated Parameters," Journal of Quality Technology,
36, 280-292, 2004.
Shu, L., Tsung, F., and Tsui, K.-L., " Effects of Estimation Errors on CauseSelecting Charts," IIE Transactions, 37, 559-567, 2005.
Xiang, L. and Tsung, F., " Statistical Monitoring of Multistage Processes
Based on Engineering Models ," IIE Transactions, in press, 2006.
Dr. Fugee Tsung, HKUST
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Recent results in autocorrelated/dynamic SPC







Apley, D.W. and Tsung, F., "The Autoregressive T-squared Chart for
Monitoring Univariate Autocorrelated Processes," Journal of Quality
Technology, 34, 80-96, 2002.
Shu, L., Apley, D.W. and Tsung, F., " Autocorrelated Process Monitoring
Using Triggered Cuscore Charts," Quality and Reliability Engineering
International, 18, 411-421, 2002.
Jiang, W., Wu, H., Tsung, F., Nair, V.N. and Tsui, K.-L., " PID Charts for
Process Monitoring," Technometrics, 44, 205-214, 2002.
Han, D. and Tsung, F., " A Generalized EWMA Control Chart and Its
Comparison with the Optimal EWMA, CUSUM and GLR Schemes," The
Annals of Statistics, 32, 316-339, 2004.
Han, D. and Tsung, F., " Comparison of the Cuscore, GLRT and CUSUM
Control Charts for Detecting a Dynamic Mean Change," The Annals of the
Institute of Statistical Mathematics, 57, 531-552, 2005.
Castagliola, P. and Tsung, F., " Autocorrelated Statistical Process Control for
Non-Normal Situations," Quality and Reliability Engineering International,
21, 131-161, 2005.
Han, D. and Tsung, F., “A Reference-Free Cuscore Chart for Dynamic Mean
Change Detection and a Unified Framework for Charting Performance
Comparison,” Journal of the American Statistical Association, in press, 2006.
Dr. Fugee Tsung, HKUST
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Recent results in process diagnosis and
improvement





Sun, R. and Tsung, F., " A Kernel-Distance-Based Multivariate Control Chart
using Support Vector Methods," International Journal of Production
Research, 41, 2975-2989, 2003.
Tong, J., Tsung, F., and Yen, B., " A DMAIC Approach for Printed Circuit
Board Quality Improvement," International Journal of Advanced
Manufacturing Technology, 23, 523-531, 2004.
Shi, D., Tsung, F., and Unsworth, P., " Adaptive Time-Frequency
Decomposition for Transient Vibration Monitoring of Rotating Machinery,"
Mechanical Systems and Signal Processing, 18, 127-141, 2004.
Sun, R., Tsung, F., and Qu, L., " Combining bootstrap and genetic
programming for feature discovery in diesel engine diagnosis," International
Journal of Industrial Engineering, 11, 273-281, 2004.
Lee, N., An, Y, and Tsung, F., " Studying Effects of Screw-Fastening Process
On Assembly Accuracy ," International Journal of Advanced Manufacturing
Technology, 25, 493-499, 2005.
Dr. Fugee Tsung, HKUST
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VI. Quality Techniques in Service
Industry
Six Sigma in Financial Service
港基應用「六個標準差」 即時見效
港基公布中期業績，港基因為應用到國際大企業最流行的管理方
法︰「Six Sigma」（六個標準差，統計學用語，目的是減少生產過
程中的錯誤），而在營運開支方面減少 1.4%。
究竟甚麼是六個標準差？對銀行如此有利？
六個標準差源自 1986 年美國 Motorola 公司通訊部門提出的一項嶄新
作法，使公司在 1987 至 1997 年的十年推行期：每年銷售增長五倍；
節省的成本更達 140 億美元。
近年因美國通用電氣（GE）大力推行六個標準差，結果使其獲利屢
創新高，更讓顧客滿意度大幅提升。也因此引起品質管理界所重視，
並開始蔚為風潮。
看似神效無比，相信對近年積極開源節流的本地銀行家來說，也會
對這個妙用無窮的六個標準差極有興趣…
-- 香港經濟日報 2002-08-05
Dr. Fugee Tsung, HKUST
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Six Sigma in Insurance
A Thank You Letter…
Date:Wed, September 14, 2005 11:30 am
Dear Fugee,
I am pleased to let you know that I have joined AIA since March this
year. I am working on a Six Sigma deployment program (They call it
Performance Management Program here) in AIA's six Southeast Asian
operations. Insurance operations are new to me but the underlying
processes and principles are very close to banks. My major
responsibility is to drive and deliver performance metrics as well as
project facilitation. I would like to thank you again for your guidance and
sharing of Six Sigma knowledge.
Best regards,
XXXX XX
--------------------------------------------------------AIA Performance Management Program
Tel. (852) XXXX XXXX
Fax. (852) XXXX XXXX
Dr. Fugee Tsung, HKUST
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Six Sigma in Telecommunication
Service
SIX SIGMA PROJECT COVER SHEET
XXXXXX
Project Name:
Black Belt/Green Belt Leader Dr Fugee Tsung
Business Function: NWTbb Hotline Service Support
Project Initiation Date: 13 Aug 05
DEFINE/MEASURE
ANALYZE
Initial Process Performance (Zigma): 2.64
Process Graph:
Fishbone to determine key process input
Matrix Flow & SIPOC to review the whole service
process
Target Process (Zigma: 3
XXXXXX
Prioritization Tool for x’s: T-Test and DOE
IMPROVE & CONTROL
Vital X
1
2
3
What Tool
SUSTAIN
Previous
setting
New Setting
Control
Procedure
Workflow review
(11 actions)
Details of actions & control mechanism in page 2-3)
Saff skill set
(3 actions)
Details of actions & control mechanism in page 3)
Testing tools
Completion
Dates
Details of actions & control mechanism in page 3)
DEFINE/
MEASURE
Ending Process ‘Z’ Value: Zst 4.38 & Zlt 3.45
Business Benefit(s): $55K/mth ($333K for 6 mths)
Documentation Transferred to XXXXX
Process Owner?
Y
N
ANALYZE
IMPROVE
Planned:
9 Sep 05
Oct end
mid Nov
Actual:
9 Sep 05
31 Oct 05
9 Dec
CONTROL
mid Dec
31 Dec
Six Sigma in the Hospitality Industry
Since 2003 Six Sigma is also launched at the
Sheraton Hotel in Hong Kong

Most common used Six Sigma tools
at the Sheraton Hotel:
DMAIC
 Process map
 Fishbone diagram
 Pareto charts
 Hypothesis tests
Training were given to staff
Evaluation of how successful six sigma program is
through measurement of “return vs expense ratio”



Dr. Fugee Tsung, HKUST
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Six Sigma in Healthcare
Few references

“The Use of Control Charts in Health-Care and PublicHealth Surveillance” by Woodall, April 2006, JQT – a
discussion paper.

Tsung, F., Zhou, Z.H., and Jiang, W., " Applying
Manufacturing Batch Techniques to Fraud Detection with
Incomplete Customer Information ," IIE Transactions, in
press, 2006.
Dr. Fugee Tsung, HKUST
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Conclusion
Define
Control
Measure
Improve




Analyze
SPC research for business excellence
HKUST Quality Lab: http://qlab.ieem.ust.hk
Six Sigma Quality Research Center (SSQRC) in Nansha
(coming soon!)
Prof. Tsung’s email: season@ust.hk
Dr. Fugee Tsung, HKUST
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