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C. F. Jeff WuSchool of Industrial and Systems Engineering

Georgia Institute of Technology

Quality Improvement: from Autos and Chips to Nano and Bio

• 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?

Sample

Sam

ple

Mean

151413121110987654321

25.0

22.5

20.0

17.5

15.0

__X

UCL

LCL

Toyota

Sample

Sam

ple

Mean

151413121110987654321

25.0

22.5

20.0

17.5

15.0

__X

UCL

LCL

GM

• 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.

Shewhart’s Paradigm

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• 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.

Shewhart’s Paradigm

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Sample

Sam

ple

Mean

2321191715131197531

22

21

20

19

18

__X

UCL

LCL

1

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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.

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.

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.

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.

Y=f(X,Z)

Noise Variation (Z) Response Variation (Y)

Control X=X1

Y=f(X,Z)

Noise Variation (Z)

Control X=X1

Response Variation (Y)

Traditional Variation Reduction

Y=f(X,Z)

Noise Variation (Z) Response Variation (Y)

X=X1

Robust Parameter Design

Y=f(X,Z)

Noise Variation (Z) Response Variation (Y)

X=X1→ X=X2

Robust Parameter Design

Variation Reduction through Robust Parameter Design

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.

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(b)

0 mV

-42

-21

-14

-28

-35

-7

020

µmµm

-42 mV

x y

z2 µm

(a)

RL

(c)

Robust optimization of the output voltage of nanogenerators

Nano Research 2010 (Stat-Material work at GT)

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Experimental Design

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Control factors Noise factor

New setting is more robust

0 10 20 30 40 500

10

20

30

40

Number of Scans

Mea

n V

alue

of E

lect

rical

Pul

ses

(mV

)

120nN,30 m/s137nN,40 m/s

µµ

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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.

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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.

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Paper Feeder Example

Two failure modes• Misfeed : fails to feed a sheet• Multifeed: Feeds more than one sheet

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).

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OW Approach in Paper Feeder ExampleStack force is a critical parameter and is easy to measure. A small force leads to misfeed and a large force leads to multifeed.

misfeed operating window multifeed

0 l u stack force

(l, u): operating windowStack 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.

• 1. Find a control factor setting to maximize the signal-to-noise ratio

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.

N1:0

0

0

N2:

N3:

Operating window

𝑙1

𝑙2

𝑙3

𝑢1

𝑢2

𝑢3

Taguchi’s Two-Step Procedure

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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.

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Factors and LevelsControl factors Notation Levels

1 2 3 Feed belt material A Type A Type B -

Speed B 288 240 192 Drop height C 3 2 1 Center roll D Absent Present -

Width E 10 20 30 Guidance angle F 0 14 28

Tip angle G 0 3.5 7 Turf H 0 1 2

Noise factors Stack quantity N Full Low -

Joseph-Wu, 2004, TechnometricsData, courtesy of Dr. K. Tatebayashi of Fuji-Xerox.

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Optimization

old

newmisfeed multifeed

Analysis led to new design with wider operating window.

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Examples of Operating Window FactorsProcess/ Product

Failure or defect type1 2

Operating windowfactor

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

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Robust Parameter Design With Feedback Control

Dasgupta and Wu, 2006, Technometrics

• To develop a unified and integrated approach to obtain the best control strategy using parameter design. RPD with feedfoward control, Joseph (2003, Technometrics).

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Strategies for minimizing effect of noise on output

Robust parameter design Process Adjustment

Feedforward Control Feedback Control

(One-time activity;Limited applicability)

(Continuous activity;Wider applicability)

Offline and Online Reduction of Variation

Measure the noise Change adjustment factor

Measure the output Change adjustment factor

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Control factors:

Noise factors:

X1, X2, .., Xp

Adjustment Factor:

N1, N2, .., Nq

Ct

CONTROL EQUATION : Ct = f(et, et-1, …)

OUTPUT:

Yt = b(X,N,Ct-1 ,Ct-2 , …) + zt

Process dynamics

Process disturbance

Output error: et = Yt - target

Feedback Control with Control and Noise Factors

Functional form

FIND OPTIMAL SETTINGS OF :

X1, X2, .., Xp

PARAMATERS OF f

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An Example: the Packing Experiment

Target weight = 50 lbMain (course) feed = 38 lbDribble (fine) feed = 12 lb

C = 0

X (14 control factors)N (material composition)

Sampled bag weight (Y) = 49.5 lb

error = 49.5-50 = -0.5 lb

-C = kI (-0.5) = (0.1 ) (-0.5) = -0.05 lb

49.6

49.7

49.8

49.9

50

50.1

50.2

50.3

50.4

1 4 7 10

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49

C = 0.05

38.05 lb

11.95 lb

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Results and Benefits

• Optimum combination selected using plots and fitted model.

05

10

152025

30354045

50

49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.550.4250.3450.2650.1850.1050.0249.9449.8649.7849.70

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20

10

0

Fre

que

ncy

BEFORE ...

50.550.450.350.250.150.049.949.849.749.6

30

20

10

0

Fre

que

ncy

AFTER ...

Prior to experimentation

s = 0.121

What was achieveds = 0.031

(Dasgupta et al. 2002)

What could have been achieved

s = 0.0159

In-Process Quality Improvement (IPQI)

ManufacturingDesign Measurement End Product Shipping

ConceptEvaluation

QualityManagement

(Designed Experiments) (SPC Techniques)

(Deming’s QC Philosophy)

IPQIApproach developed by Jan Shi (GT), IPQI slides courtesy of Shi

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Example of IPQI: Knowledge-based Diagnosis for Auto Body Assembly

Z

XY

On-line monitoring

Data BaseKnowledge Base

Process Navigator

Human- Computer Interface

Diagnosis Reasoning

Variation Animation

Root Causes

1. Engineering: Hierarchical Structure Model of Assembly Product/Process2. Statistical: Correlation, clustering, hypothesis testing

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Manifestation of a single fault

M1M2

Z

Y

C1 C2

C3

M3

P2P1

X

Fault Fault Pattern

P1

P2

C1

C2

C3

O

O

O

O

OO

P: PinC: ClampM: Measurement point

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Engineering analysis by rigid body motion

Fusion of Knowledge and Data

Principal Component Analysis (PCA)

•  

Relationship between PCA and Fixture Fault Pattern

•  

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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 analysis in wire slicing

Gaussian Process model 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

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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.

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Convex Up (+) Concave Up (-)

Effects of Warpage on Solder Bump Fatigue

Tan-Ume-Hung-Wu, 2010, IEEE Tran. Advanced Packaging

• PWB samples can have different initial warpage or can be flat.

─ PWBA warpage can be either convex or concave as shown below:

• Two packages (27x27-mm, 35x35-mm) ─ Each package placed at three different locations:

Location 1 Location 2 Location 3

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Factors studied in Finite Element Method (FEM)

• Factors:

maxw

shapew

pd

pl

sm

fN = fatigue life estimation of solder bumps (cycles)

maximum initial PWB warpage at 25C (mm)

2105.3, 3076.6, 3824.0

warpage shape +1: Convex up; -1 Concave up

package dimension (mm) 27 by 27, 35 by 35

location of package (mm) Center, 60-30, Outmost

solder bump material Sn-Pb, Lead-free

84 FEM runs were conducted.

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Objective: To verify and correlate 3-D finite element simulation results.

PWB with 3535 mm PBGA at Location 2

PWB with 3535 mm PBGA at Location 4 Standard Thermal Cycling Profile

Accelerated Thermal Cycling Test

Experimental Study of Solder Bump Fatigue Reliability Affected by Initial PWB Warpage

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FEM Simulation vs Experimental Study

-4000 -2000 0 2000 4000

14

00

16

00

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00

20

00

22

00

24

00

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00

28

00

angle

y

maximum PWB warpage

Fat

igue

life

(C

ycle

)

FEM Simulations

Experimental Data

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Integration of FEM and Physical Data• Use kriging to model the FEM data:

• Calibrate the fitted model with experimental data, leading to

1ˆ ( ) 1101.6 ( ) ( 1101.6 ),Tk outN x x N I

where = FEM output data.

where = fatigue life prediction, = maximum initial PWB warpage at 25C.

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Validation of Kriging Model

Case

Max. Initial Warpage

across PWB at Room

Temp. (mm)

PBGADimensio

n(mm)

Distance from

PBGA Center to

Board Center (mm)

Fatigue Life from Prediction Model (Cycles)

Experimental Fatigue

Life (Cycles)

Difference

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 %

• Compare experimental fatigue life with kriging model prediction under four untried settings. Outperforms FEM prediction.

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?

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Nanopowder Manufacturing Scale-up

Pump

Nanomiser®Flow Controller

Flame

Powder Collection & Dispersion System

Atomizing Gas

Solution

Filter

Atomizer

Control cost

Engineering knowledge

DataStatistical Model Calibration

Control & Evaluation

Quality Indices

Predictive Model Development

Jan Shi Lab

Challenges:• Nano-metrology analysis for

process control

• Variation propagation in multi-stage manufacturing process

• Process control capability

Goal: 1kg/day to 1000kg/day

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http://stemcelligert.gatech.edu

ApplicationsStem Cell Biology

Efficient, scalable &robust technologies

Reprogramming

Isolation

Manufacturing of diagnostic platforms & regenerative therapies

from stem cells

Pluripotent

Multipotent

Unipotent

Stem Cell Biomanufacturing

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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.

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Geometrical interpretation of the failing P2

P2F

d(P2, P1)

1

d(P1,M1)

2

d(P1, M2 )

3

d(P1, M3)

M1M2

Z

Y

C1 C2

C3

M3

P2P1

X

The relationships of variations among sensing data due to locator P2 failure:

Where - STD at Mi

- STD of faults d(a,b) - distance

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