Quality Improvement:
from Autos and Chips to Nano and Bio
C. F. Jeff Wu
School of Industrial and Systems Engineering
Georgia Institute of Technology
• Legacies of Shewhart and Deming.
• Quality improvement via robust parameter design:
Taguchi’s origin in manufacturing.
• Extensions of RPD: operating windows and
feedback control.
• Incorporation of physical knowledge/data.
• Advanced manufacturing: new concept/paradigm?
1
Shewhart’s Paradigm
• Developed statistical process control (SPC) to quickly detect
if a process is out of control. Classify process variability into
two types.
• Common (chance) causes: natural variation, in control.
Toyota
GM
UC L
Sample Mean
25.0
22.5
UC L
_
_
_
X
X
20.0
LC L
17.5
15.0
LC L
1
2
3
4
5
6
7
8
Sample
9
10
11
12
13
14
15
2
Shewhart’s Paradigm
• Developed statistical process control (SPC) to quickly detect
if a process is out of control. Classify process variability into
two types.
• Common (chance) causes: natural variation, in control.
• Special (assignable) causes: suggests process out of control.
1
22
1
UC L
Sample Mean
21
20
_
_
X
19
LC L
18
1
3
5
7
9
11
13
15
17
19
21
23
Sample
3
Walter Shewhart
• American physicist, mathematician, statistician.
Developed SPC while working for Western Electric (Bell
Telephone). Original 1924 work in one page memo, 1/3
of which contains a control chart. Background: to tackle
manufacturing variation.
• SPC should be viewed more as a scientific methodology,
than a charting technique.
• Deming was introduced to Shewhart in 1927; was
tremendously influenced by the SPC methodology;
Deming’s key insight: Shewhart’s SPC can also be applied
to enterprises; this led to his later work and big impact in
quality management.
4
Deming’s Statistical Legacies
• As Shewhart, Deming was a physicist, mathematician,
statistician. He studied statistics with Fisher and Neyman
in 1936.
• He edited the book “Statistical Method from the
Viewpoint of Quality Control” in 1939.
• He devised sampling techniques used in the 1940 Census,
developed the Deming-Stephan algorithm, an early work
on iterative proportional fitting in categorical data.
• His bigger impact in quality management started with his
visits and lectures in Japan in 1950’s.
5
Design of Experiments (DOE)
• If a process is in control but with low process
capability, use DOE to further reduce process
variation. Pioneering work by Fisher, Yates, Finney,
etc. before WWII.
• DOE in industries was widely used after the war;
George Box’s work on Response Surface
Methodology.
• Genichi Taguchi’s (
) pioneering work on
robust parameter design. Paradigm shift: use DOE
for variation reduction, which is the major focus of
my talk.
6
Robust Parameter Design
• Statistical/engineering method for product/process
improvement (G. Taguchi), introduced to the US in
mid-80s. Has made considerable impacts in
manufacturing (autos and chips); later work in other
industries.
• Two types of factors in a system:
– control factors: once chosen, values remain fixed;
– noise factors: hard-to-control during normal
process or usage.
• Parameter design: choose control factor settings to
make response less sensitive (i.e. more robust) to
noise variation; exploiting control-by-noise
interactions.
7
Variation Reduction through
Robust Parameter Design
Robust Parameter
Design
Traditional
Variation Reduction
Control
X=X1→ X=X
X=X21
Noise Variation (Z)
Response Variation (Y)
Y=f(X,Z)
8
Shift from Traditional Strategy
• Emphasis shifts from location effect estimation to
dispersion effect estimation and variation reduction.
• Control and noise factors treated differently: C×N
interaction treated equally important as main effects C
and N, which violates the effect hierarchy principle. This
has led to a different/new design theory.
• Another emphasis: use of performance measure ,
including log variance or Taguchi’s idiosyncratic
signal-to-noise ratios, for system optimization. Has an
impact on data analysis strategy.
9
Robust optimization of the output voltage
of nanogenerators
(b)
(a)
2 µm
(c)
RL
0
z
-42 mV
0 mV
-7
-14
-21
-28
-35
-42
Nano Research 2010 (Stat-Material work at GT)
10
Experimental Design
Control factors
Noise factor
11
New setting is more robust
Mean Value of Electrical Pulses (mV)
40
120nN,30
137nN,40
µm/s
µm/s
30
20
10
0
0
10
20
30
Number of Scans
40
50
12
Further Work Inspired by
Robust Parameter Design
Two examples:
• The method of operating windows to widen
the designer’s capability.
• RPD combined with feedback control, both
offline and online adjustments.
13
Method of Operating Window (OW)
• Operating window is defined as the boundaries of a critical
parameter at which certain failure modes are excited.
Originally developed by D. Clausing (1994 and earlier) at
Xerox, Taguchi (1993).
• Approach:
̵ Identify a critical parameter: low values of which lead to
one failure mode and high values lead to the other failure
mode.
̵ Measure the operating window at different design settings.
̵ Choose a design to maximize the operating window.
14
Paper Feeder Example
Two failure modes
• Misfeed : fails to feed a sheet
• Multifeed: Feeds more than one sheet
15
Standard Approach
• Feed, say, 1000 sheets at a design setting;
observe # of misfeeds and # of multifeeds;
repeat for other settings; choose a design
setting to minimize both.
• Problems: require large number of tests to
achieve good statistical power; difficult to
distinguish between different design settings;
conflicting choice of levels (settings that
minimize misfeeds tend to increase
multifeeds).
16
OW Approach in Paper Feeder Example
Stack force is a critical parameter and is easy to measure. A small
force leads to misfeed and a large force leads to multifeed.
misfeed
0
operating window
l
multifeed
u
stack force
(l, u): operating window
Stack force: operating window factor
• No clear boundaries separating the failure modes
• Can be defined with respect to a threshold failure rate:
l = force at which 50% misfeed occurs,
u = force at which 50% multifeed occurs.
17
Taguchi’s Two-Step Procedure
N1:
𝑙1
0
N2:
0
𝑢1
𝑙2
𝑢2
N3:
0
𝑢3
𝑙3
Operating window
• 1. Find a control factor setting to maximize the
signal-to-noise ratio
𝑆𝑁 = −log
1
𝑛
𝑛
21
𝑙
𝑖=1 𝑖 𝑛
1
𝑛
𝑖=1 𝑢2
𝑖
,
where N1, N2,… represent noise factor conditions.
2. Adjust OW factor to the middle of the operating window.
• But the method lacks a sound justification.
18
A Rigorous Statistical Approach to OW
• Under some probability models for the failure
modes and a specific loss function, Joseph-Wu
(2002) showed that a rigorous two-step
optimization leads to a performance measure
similar to Taguchi’s SN ratio. The procedure
also allows modeling and estimation, in
addition to design optimization. See the
illustration with paper feeder experiment.
19
Factors and Levels
Control factors
Feed belt material
Speed
Drop height
Center roll
Width
Guidance angle
Tip angle
Turf
Noise factors
Stack quantity
Notation
A
B
C
D
E
F
G
H
1
Type A
288
3
Absent
10
0
0
0
Levels
2
Type B
240
2
Present
20
14
3.5
1
3
192
1
30
28
7
2
N
Full
Low
-
Joseph-Wu, 2004, Technometrics
Data, courtesy of Dr. K. Tatebayashi of Fuji-Xerox.
20
21
Optimization
Analysis led to new design with wider operating window.
misfeed
new
multifeed
old
22
Examples of Operating Window Factors
Process/
Product
Failure or defect type
1
2
Operating
window
factor
Wave
soldering
Voids
Bridges
Temperature
Resistance
welding
Under
weld
Expulsion
Time
Image transfer
Opens
Shorts
Exposure
energy
Threading
Loose
Tight
Depth of cut
Picture
printing
Black
Blur
Water
quantity
23
Robust Parameter Design With
Feedback Control
•
To develop a unified and integrated approach to
obtain the best control strategy using parameter
design. RPD with feedfoward control, Joseph (2003,
Technometrics).
Dasgupta and Wu, 2006, Technometrics
24
Offline and Online Reduction of
Variation
Strategies for minimizing effect of noise on output
Robust parameter design
(One-time activity;
Limited applicability)
Process Adjustment
(Continuous activity;
Wider applicability)
Feedforward Control
Measure the noise
Change adjustment factor
Feedback Control
Measure the output
Change adjustment factor
25
Feedback Control with Control and
Noise Factors
Process
dynamics
Control factors:
X1, X2, .., Xp
Noise factors:
N1, N2, .., Nq
FIND OPTIMAL
SETTINGS OF :
Process
disturbance
OUTPUT:
Yt = b(X,N,Ct-1 ,Ct-2 , …) + zt
X1, X2, .., Xp
PARAMATERS OF f
Output error:
et = Yt - target
Adjustment
Factor:
Ct
CONTROL EQUATION : Ct = f(et, et-1, …)
Functional form
26
An Example: the Packing Experiment
50.4
50.3
50.2
50.1
X (14 control factors)
N (material composition)
50
49.9
49.8
49.7
49
46
43
40
37
34
31
28
25
22
19
16
13
7
10
4
1
49.6
Sampled bag weight (Y) = 49.5 lb
Target weight = 50 lb
38.05 lb
Main (course) feed = 38 lb
Dribble (fine) feed = 12 lb
11.95 lb
error = 49.5-50 = -0.5 lb
C=0
C = 0.05
-C = kI (-0.5) = (0.1 ) (-0.5) = -0.05 lb
27
Results and Benefits
• Optimum combination selected using plots
and fitted model.
AFTER ...
BEFORE ...
50
45
40
35
30
25
20
15
10
5
0
20
10
0
49.70 49.78 49.86 49.94 50.02 50.10 50.18 50.26 50.34 50.42
Prior to
experimentation
s = 0.121
30
Frequency
Frequency
30
20
10
0
49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5
What was achieved
s = 0.031
(Dasgupta et al. 2002)
49.6
49.7
49.8
49.9
50.0
50.1
50.2
50.3
50.4
50.5
What could have
been achieved
s = 0.0159
28
In-Process Quality Improvement (IPQI)
(Deming’s QC Philosophy)
Quality
Management
Concept
Evaluation
Design
Manufacturing
Measurement
End Product
Shipping
(SPC Techniques)
(Designed Experiments)
IPQI
Approach developed by Jan Shi (GT),
IPQI slides courtesy of Shi
29
Example of IPQI: Knowledge-based Diagnosis
for Auto Body Assembly
1. Engineering: Hierarchical Structure Model of Assembly
Product/Process
2. Statistical: Correlation, clustering, hypothesis testing
30
Manifestation of a single fault
M3
Z
Y
C3
Fault
Pattern
Fault
P1
X
C1
C2
P2
M1
P1
P2
P: Pin
C: Clamp
M: Measurement point
M2
O
C1
O
O
C2
O
C3
O
O
Engineering analysis by rigid body motion
31
Fusion of Knowledge and Data
Principal Component
Analysis (PCA)
Relationship between PCA
and Fixture Fault Pattern
32
Other Engineering Examples of IPQI
Manufacturing Process
Statistical methods
Engineering knowledge
Tonnage signature analysis
in forming
Wavelet analysis
Time and frequency
information due to press
and die design
Wafer profile modeling and Gaussian Process model
analysis in wire slicing
Dynamics model of wire
slicing operations
On-line bleeds detection in
continuous casting
Imaging feature extraction
and design of experiments
Mechanism of bleeds
formation in casting
Variation modeling and
analysis for multistage
wafer manufacturing
Data mining and
probability network
modeling
System layout and system
design information
33
From Knowledge to Data:
Physical-Statistical Modeling
• Simulation experiments have been widely used in lieu of
physical experiments. The latter are more expensive,
time-consuming or only observed when events like
flooding suddenly happen. SE can be an indispensible
tool in quality improvement, especially for paucity of
physical data or low failure rates.
• Example: validation of finite element experiment with
limited physical data in fatigue life prediction of solder
bumps in electronic packaging of chips.
34
Effects of Warpage on Solder Bump Fatigue
• PWB samples can have different initial warpage or
can be flat.
─ PWBA warpage can be either convex or concave as
shown below:
Convex Up (+)
Concave Up (-)
• Two packages (27x27-mm, 35x35-mm)
─ Each package placed at three different locations:
Location 1
Location 2
Location 3
Tan-Ume-Hung-Wu, 2010, IEEE Tran. Advanced Packaging
35
Factors studied
in Finite Element Method (FEM)
• Factors:
wmax maximum initial PWB
2105.3, 3076.6, 3824.0
warpage at 25C (mm)
wshape warpage shape
+1: Convex up; -1 Concave up
dp
package dimension (mm)
27 by 27, 35 by 35
lp
ms
location of package (mm)
solder bump material
Center, 60-30, Outmost
Sn-Pb, Lead-free
N f = fatigue life estimation of solder bumps (cycles)
84 FEM runs were conducted.
36
Experimental Study of Solder Bump Fatigue
Reliability Affected by Initial PWB Warpage
Objective: To verify and correlate 3-D
finite element simulation results.
PWB with 3535 mm PBGA at Location 2
Accelerated Thermal Cycling Test
PWB with 3535 mm PBGA at Location 4
Standard Thermal Cycling Profile
37
2600
2400
1600
1800
2000
2200
FEM
Simulations
1400
(Cycle)
Fatigue life
y
Experimental
Data
2800
FEM Simulation vs Experimental Study
-4000
-2000
0
2000
maximum angle
PWB warpage
4000
38
Integration of FEM and Physical Data
• Use kriging to model the FEM data:
Nˆ k ( x)  1101.6   ( x)T 1 ( Nout  1101.6I ),
where 𝑁𝑜𝑢𝑡 = FEM output data.
• Calibrate the fitted model with experimental data,
leading to
𝑁𝑓 𝑥 = 1830.3 − 540𝑤max + 𝑁𝑘 𝑥
= 2931.9 − 540𝑤max + 𝜙 𝑥 𝑇 Ψ −1 𝑁𝑜𝑢𝑡 − 1101.6𝐼
where 𝑁𝑓 𝑥 = fatigue life prediction,
𝑤max = maximum initial PWB warpage at 25C.
39
Validation of Kriging Model
• Compare experimental fatigue life with kriging model prediction
under four untried settings. Outperforms FEM prediction.
Max. Initial
Warpage
Case across PWB
at Room
Temp. (mm)
PBGA
Dimensio
n
(mm)
Distance
from
PBGA
Center to
Board
Center
(mm)
Fatigue
Experimenta
Life from
l Fatigue
Predictio
Difference
Life
n Model
(Cycles)
(Cycles)
1
-1.833
27  27
67
2633
2750
-4.3 %
2
-2.013
27  27
30
2465
2625
-6.1 %
3
-2.171
35  35
67
2507
2400
4.4 %
4
-2.425
35  35
30
2277
2250
1.2 %
40
Challenges in Advanced Manufacturing
• Typical features: small volume, many varieties, high
values. Recent example: additive manufacturing (3D
printing). Parts made-on-demand as in battle fields.
Situation more extreme than run-to-run control in
semi-conductor industries.
• Scalable manufacturing process: from lab, to pilot, to
mass scale production; bio-inspired materials (next
slides).
• What new concepts and techniques are needed to
tackle these problems? More use of comp/stat
modeling and simulations. What else?
41
Nanopowder Manufacturing Scale-up
Flow
Controller
Nanomiser
Atomizer ®
Flame
Filter
Pump
Goal: 1kg/day to 1000kg/day
Challenges:
• Nano-metrology analysis for
process control
• Variation propagation in multistage manufacturing process
• Process control capability
Solution
Powder Collection &
Dispersion System
Atomizing
Engineering
Gas
knowledge
Data
Control cost
Predictive Model
Development
Statistical Model
Calibration
Quality
Indices
Control &
Evaluation
Jan Shi Lab 42
Stem Cell Biomanufacturing
Stem Cell Biology
Applications
Manufacturing of
diagnostic platforms &
regenerative therapies
from stem cells
Isolation
Pluripotent
Multipotent
Unipotent
Reprogramming
Efficient, scalable &
robust technologies
43
http://stemcelligert.gatech.edu
Summary Remarks
• Quality management has made major economical
and societal impacts. Quality engineering is the
lesser known cousin. It has helped improve quality
and reduce cost; witness the revival of US auto
industries.
• Statistical design of experiments has a glorious
history: agriculture, chemical, manufacturing, etc.
• Wider use of product/system simulations is expected
in hi-tech applications. Further development requires
new concepts and paradigm not found in traditional
work.
44
Geometrical interpretation of the failing P2
M3
Z
C3
Y
X
C1
C2
M1
P1
M2
P2
The relationships of variations among sensing data due to locator P2 failure:
 FP2
d(P2 , P1 )
Where

1
d(P1 ,M1 )

2
d(P1 , M2 )

3
d(P1 , M3 )
𝜎𝑖 - STD at Mi
𝐹
𝜎𝑃2
- STD of faults
d(a,b) - distance
45