Recent Advances in Statistical Quality Control Prof. Fugee Tsung Hong Kong University of Science and...

Recent Advances in Statistical Quality Control

Prof. Fugee TsungHong Kong University

of Science and TechnologyEmail: [email protected]

Quality Lab: http://qlab.ieem.ust.hk

Dr. Fugee Tsung, HKUST 2

INFORMS International, Hong Kong 2006


Outline

I. SPC for profilesII. SPC for engineering

controlled processesIII. SPC for multistage processesIV. Quality techniques in service

industry


Ignore

DesensitizeRobust Design

CompensateEPC

Reduce/Eliminate

SPC

How to Handle Variation


Statistical Process Control (SPC): Role in Six Sigma

SPC is emphasized as the major tool used to control and sustain a Six Sigma process

Define

Improve Analyze

MeasureControl

I. SPC for Profiles


SPC: Basic Idea

3020100

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

Sample Number

Sam

ple

Mea

n

Mean=0

UCL=1.342

LCL=-1.342

?y

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).

),(~

),(~222

211

Ny

Ny

i

i

.,...,1

;,...,2,1

nifor

ifor


SPC: A Different Idea

3020100

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

Sample Number

Sam

ple

Mea

n

Mean=0

UCL=1.342

LCL=-1.342

?yx

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).

)( ii xfy


A Profile Example


Another Profile Example

II. SPC for engineering controlled processes


A Engineering Controlled Process

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1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

Sample Number

Sam

ple

Mea

n

Mean=0

UCL=1.342

LCL=-1.342

?yx

Process

EPC Controller

iDiI

iPi

iD

i

jiIiPi

yBkyB

kykx

ykykykx

)1(1

1


Window of Opportunity

(a) (b)

Tsung, Shi, and Wu (1999, JQT)


Dynamics and autocorrelation To monitor the engineering controlled

process, one may consider monitoring a Dynamic T2 statistic of the form

where 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

tTt

Lt XXDT 1

Tsung and Apley (2002, IIE Trans.)


Incoming signal confounding

yx

?Process

EPC Controller

Input assignable causes Output assignable causes

Model-void assignable causes


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, 135-144, 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 Feedback-Controlled 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.

III. SPC for Multistage processes


A Multistage Process

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1.0

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-0.5

-1.0

-1.5

Sample Number

Sam

ple

Mea

n

Mean=0

UCL=1.342

LCL=-1.342

?ykyk-1

kkkk

kkkkkk

vyCY

wByAy

11

Stage 1 Stage NStage kStage k-1

),0(~),,0(~ 22wkvk NwNv


Example: Printed Circuit Board Manufacturing

Exposure

Black Oxide

Lay-up

Hot Press

Cutting

Drilling

Inspection

…….

From Ding, Shi, and Ceglarek (2002)


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.


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 out-of-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.


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, 261-272, 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 Cause-Selecting 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.


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.


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.

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

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 XXXXFax. (852) XXXX XXXX

Six Sigma in Telecommunication Service

Dr. Fugee Tsung, HKUST

SIX SIGMA PROJECT COVER SHEET

CompletionDates Planned:

Actual:

DEFINE/ MEASURE ANALYZE IMPROVE CONTROL

Project Name:Black Belt/Green Belt LeaderBusiness Function:Project Initiation Date:

DEFINE/MEASURE ANALYZE

IMPROVE & CONTROL SUSTAIN

Initial Process Performance (Zigma): 2.64

Process Graph:

Target Process (Zigma: 3

Prioritization Tool for x’s:

Ending Process ‘Z’ Value:

Business Benefit(s):

Documentation Transferred to Process Owner? Y N

XXXXXX Dr Fugee Tsung

NWTbb Hotline Service Support

13 Aug 05

Fishbone to determine key process input

Matrix Flow & SIPOC to review the whole service process

T-Test and DOE

Vital X What ToolPrevioussetting New Setting

ControlProcedure

1Workflow review

(11 actions) Details of actions & control mechanism in page 2-3)

2Saff skill set(3 actions) Details of actions & control mechanism in page 3)

3 Testing tools Details of actions & control mechanism in page 3)

Zst 4.38 & Zlt 3.45

$55K/mth ($333K for 6 mths)

XXXXX

9 Sep 05

9 Sep 05 31 Oct 05

Oct end

9 Dec

mid Nov mid Dec

31 Dec

XXXXXX

Six Sigma in the Hospitality Industry


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”

Since 2003 Six Sigma is also launched at the Sheraton Hotel in Hong Kong

Six Sigma in Healthcare


Few references “The Use of Control Charts in Health-Care and

Public-Health 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.


Conclusion

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: [email protected]

Define

Improve Analyze

MeasureControl

Recent Advances in Statistical Quality Control Prof. Fugee Tsung Hong Kong University of Science and...

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