C. J. Spanos
Statistical Process Control
and
Computer Integrated Manufacturing
Run to Run Control, Real-Time SPC, Computer
Integrated Manufacturing.
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C. J. Spanos
The Equipment Controller
Today, the operation of individual pieces of equipment can
be streamlined with the help of external software
applications. SPC is just one of them.
CIM
database
Maintenance
Workcell
Coordinator
Monitoring
Equipment
BCAM
Local
Database(s)
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Statistical
Process
Control
Fault
Diagnosis
Modeling
and
Simulation
Recipe
Generation
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C. J. Spanos
The Workcell Controller
Most process steps are so interrelated that must be
controlled together using feed forward and feedback loops.
Crucial pieces of equipment must by controlled by SPC
throughout this operation.
test
Adaptive
Control
Adaptive
Control
Equipment
Model
Equipment
Model
Step
test
Step
test
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C. J. Spanos
Model Based Control
All actions are based on the comparison of response
surface models to actual equipment behavior.
Malfunction alarms are detected using a multivariate
extension of the regression chart on the prediction residuals
of the model.
Control alarms are detected with a multivariate CUSUM
chart of the prediction residuals.
Control limits are based on experimental errors as well as
on the model prediction errors due to regression. Hard limits
on equipment inputs are also used.
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C. J. Spanos
The Idea of Statistically Based Feedback Control
1. Original Operation
2. Process Shifts
3. Shift is detected by MBSPC
4. RSM is adapted
5. New Recipe is generated
response
yn
2
4
3
yf
yo
5
new RSM
1
original RSM
xo
xf
controlling input
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C. J. Spanos
Feedback Control
Model-based, adaptive Feedback Control has been
employed on several processes.
Initial
Settings
Parameter
Estimator
Equipment
Model
Recipe
Update
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yes
Controller
t Test
Spin Coat
& Bake
M
Model
Update? No
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C. J. Spanos
Feedback Control in Resist Application
Adaptive
Controller
Input
Settings
Incoming
Spin-Coat
Wafer
& Bake
Equipment
Outgoing
Wafer
Thickness
& Reflectance
Measurement
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C. J. Spanos
Feedback Control in Resist Application (cont.)
12600
Target
Model Prediction
Experimental Data
12400
12200
12000
11800
44
40
36
32
28
24
20
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0
10
20
30
40
50
60
Model Prediction
Target
Experimental Data
0
10
20
30
Wafer Number
40
50
60
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C. J. Spanos
Alarms in Resist Application Control
20
Alarm (a)
16
Alarm (b)
12
8
Alarm (c)
UCL
4
0
0
10
20
30
40
15
50
60
Alarm
Alarm
10
Alarm
UCL
5
0
0
10
20
30
40
50
60
Wafer Number
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C. J. Spanos
Adapting the Regression Model
The regression model has many coefficients that may
need adaptation.
What can be adapted depends on what measurements
are available.
2
3
1
4
yn = aox2+box +c’n
yn = anx2+bnx +c’n
yn = aox2+b’nx +c’’n
yo = aox2+box +co
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C. J. Spanos
Adapting the Regression Model (cont)
In multivariate situations it is often not clear which of
the gain or higher order variables can be adapted in the
original model.
y
x2
C
A
B
x1
In these cases the model is “rotated” so that it has
orthogonal coefficients, along the principal components
of the available observations. These coefficients are
updated one at a time.
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C. J. Spanos
Model Adaptation in Resist Application Control
-13500
2.00
-14000
1.95
-14500
1.90
-15000
0
10
20
30
40
50
60
0
10
20
30
40
50
60
1.85
135
134
133
132
131
Wafer Number
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C. J. Spanos
Feed-Forward Control
Models can also be used to predict the outcome and
correct ahead of time if necessary.
Projected
CD Spread
Model
No
Recipe
Update
In
Spec?
Yes
Standard
Setting
M
Exposure
Develop
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C. J. Spanos
Modified Charts for Feed Forward Control
LCL
LSL
UCL
σ/√n (prediction spread)
USL
σ (equipment spread)
No FF
Yield Loss
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False Alarm Probability
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C. J. Spanos
Feed Forward/Feedback Control Results (cont)
92
90
Target = 88.75%
88
86
84
82
Open Loop
FeedForward
80
78
0
5
10
15
20
Wafer No
25
30
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C. J. Spanos
Concurrent Control of Multiple Steps
Equip.
Model
Equip.
Model
Equip.
Model
Adaptive
Control
Adaptive
Control
Adaptive
Control
Original
Inputs
Spin
Coat
&
Bake
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T&R
Meas
Expose
R
Meas
Develop
CD
Meas
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C. J. Spanos
Resist Thickness Example
12000
Target = 11906Å
11500
11000
0
5
10
15
Wafer Number
20
Closed Loop
Open Loop
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C. J. Spanos
Resist Thickness Input
100
80
Closed Loop
Open Loop
60
40
0
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5
10
15
Wafer Number
20
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C. J. Spanos
Latent Image output
100
Closed Loop
Control Alarm
Open Loop
Malfunction Alarm
90
Target = 87.75%
80
70
0
5
10
15
Wafer Number
20
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C. J. Spanos
Latent Image Input
Closed Loop
1.00
Open Loop
0.90
0.80
0.70
0.60
0
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5
10
15
Wafer Number
20
20
C. J. Spanos
Developer Output
Closed Loop
Control Alarm
Open Loop
Malfunction Alarm
2.80
2.70
Target = 2.66 um
2.60
2.50
0
5
10
15
Wafer Number
20
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C. J. Spanos
Developer Input
Closed Loop
Open Loop
65
60
55
50 0
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5
10
15
Wafer Number
20
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C. J. Spanos
Process Improvement Due to Run to Run Control
5
4
3
2
1
Target
Dev. Malf.
2.65 2.75 2.85
CD in µm
Closed Loop Operation
2.55
Target
5
4
3
2
1
2.55
2.65 2.75
CD in µm
2.85
Open Loop Operation
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C. J. Spanos
Supervisory Control
The complete controller must be able to perform feedback
and feed-forward control, along with automated diagnosis.
Feed-forward control must be performed in an optimum
fashion over several pieces of the equipment that follow.
max Cpk
control
equip
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C. J. Spanos
The Concept of Dynamic Specifications
Specs are enforced by a cost function which is defined in
terms of the parameters passed between equipment.
A change is propagated upstream through the system
by redefining specifications for all steps preceding the change.
Model
Constraint
Mapping
Control
Model
Constraint
Mapping
Step
Control
Step
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C. J. Spanos
Specs to step A must change if step B "ages"
Out2A
Out2B
New spec
limits for A
Fixed spec
limits for B
Mapping
PC2
PC1
Model
of B
Out1A
Step
A
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Out1B
Step
B
Step
C
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C. J. Spanos
Specs are outlined automatically - Stepper example
Thickness
(Develop time varies between 55 and 65 seconds)
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C. J. Spanos
An Example of Supervisory Control
Baseline
20
FF/FB only
Target
10
10
Outliers
0
0.80.91.01.11.21.31.41.51.61.71.81.9
CDµm)
(
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Target
15
5
Target
20
15
5
Supervisory
20
15
10
Outliers
0
0.80.91.01.11.21.31.41.51.61.71.81.9
CDµm)
(
5
Outliers
0
0.80.91.01.11.21.31.41.51.61.71.81.9
CD(µm)
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C. J. Spanos
Results from Supervisory Control Application
Baseline
FF/FB Only
Supervisory
Th
PAC
LI
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C. J. Spanos
Control Results - CD
Baseline
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FF/FB Only
Supervisory
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C. J. Spanos
Summary, so far
Response surface models can be built based on designed
experiments and regression analysis.
Model-based Run-to-Run control is based on control alarms
and on malfunction alarms.
RSM models are being updated automatically as equipment
age.
Optimal, dynamic specifications can be used to guide a
complex process sequence.
Next stop: Real-time Statistical Process Control!
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C. J. Spanos
Autocorrelated Data
One important and widespread assumption in SPC is that the
samples take random values that are independently and
identically distributed according to a normal distribution
y t = µ + et
t = 1,2,... et ~ N (0, σ 2)
With automated readings and high sampling rates, each
reading statistically depends on its previous values. This
implies the presence of autocorrelation defined as:
ρk =
Σ (yi - y)(yi+k - y)
=0
Σ (yi - y)2
k = 1,2,...
The IIND property must be restored before we apply any
traditional SPC procedures.
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C. J. Spanos
Time Series Modeling
Various models have been used to describe and eliminate
the autocorrelation from continuous data.
A simple case exists when only one autocorrelation is
present:
yt = µ +ϕ yt-1 + et et ~ N (0,σ 2)
µ' = µ / (1-ϕ), σ' = σ / 1-ϕ2
et = yt - yt
The IIND property can be restored if we use this model to
"forecast" each new value and then use the forecasting
error (an IIND random number) in the SPC procedure.
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C. J. Spanos
Example: LPCVD Temperature Readings
Temp Readings from LPCVD Tube
LPCVD Temp Autocorrelation
608
608
607
607
606
606
605
605
604
604
603
603
602
602
Temp(t+1) = 758 - 0.253 Temp(t)
601
601
0
20
40
60
Time
80
100
601
603
605
607
Temp (t)
Temps are not IIND since future readings can be predicted!
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C. J. Spanos
The Residuals of the Prediction can be Used for SPC..
Temp. Readings from LPCVD Tube
Temperature Residuals
608
3
607
2
606
1
605
0
604
-1
603
-2
602
601
-3
0
20
40
60
Time
80
100
0
20
40
60
Time
80
100
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C. J. Spanos
Estimated Time Series
A "Time Series" is a collection of observations
generated sequentially through time.
Successive observations are (usually) dependent.
Our objectives are to:
Describe - features of a time series process
Explain - relate observations to rules of behavior
Forecast - see into the future
Control - alter parameters of the model
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C. J. Spanos
Two Basic Flavors of Time Series Models
Stationary data (i.e. time independent mean, variance and
autocorrelation structure) can be modelled as:
Autoregressive
zt = ϕ1 zt-1 + et et ~ N (0, σ 2)
zt = yt - µ
Moving Average
zt = θ 1 et-1 + et et ~ N (0, σ2)
zt = yt - µ
Mixture (i.e. Autoregressive + Moving Average) models.
yt = µ + ϕ1zt-1 + ϕ2zt-2 +...+ ϕpzt-p
+ et - θ1et-1 - θ2et-2 -...- θqet-q
ϕ: autoregressive
θ: moving average
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C. J. Spanos
First Order Autoregressive Model AR(1)
This model assumes that the next reading can be predicted
from the last reading according to a simple regression
equation.
zt = ϕ1 zt-1 + et et ~ N (0, σ 2)
zt = yt - µ
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
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40
AR
Forecast
Error
45
50
55
60
sample
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C. J. Spanos
Higher order AR(p) and ACF, PACF representation
Higher order autoregressive models are common in
engineering. Their structure can be inferredacf and pacf
plots.
Autocorrelation Function (acf):
ρk =
Σ (yi - y)(yi+k - y)
=0
Σ (yi - y)2
k = 1,2,...
k
Partial Autocorrelation Function (pacf):
zt = ϕ1zt-1
zt = ϕ1zt-1 + ϕ2zt-2
zt = ϕ1zt-1 + ϕ2zt-2 + ϕ3zt-3
zt = ϕ1zt-1 + ϕ2zt-2 + ϕ3zt-3+ ϕ4xt-4
...
k
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C. J. Spanos
First Order Moving Average Model MA(1)
This model assumes that the next reading can be predicted
from the last residual according to a simple regression
equation.
zt = θ 1 et-1 + et et ~ N (0, σ2)
zt = yt - µ
zt
0
time
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C. J. Spanos
Mixed AR & MA Models: ARMA(p,q)
In general, each new value depends not only on past readings
but on past residuals as well. The general form is:
yt = µ + ϕ1zt-1 + ϕ2zt-2 +...+ ϕpzt-p
+ et - θ1et-1 - θ2et-2 -...- θqet-q
ϕ: autoregressive
θ: moving average
This structure is called ARMA (autoregressive moving
average). The particular model is an ARMA(p,q).
If the data is differentiated to become stationary, we get an
ARIMA (Autoregressive, Integrated Moving Average) model.
Structures also exist that describe seasonal variations and
multivariate processes.
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C. J. Spanos
Summary on Time Series Models
Time Series Models are used to describe the
"autocorrelation structure" within each real-time signal.
After the autocorrelation structure has been described,
it can be removed by means of time series filtering.
The models we use are known as Box-Jenkins linear
models.
The generation of these models involves some
statistical judgmenttically.
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C. J. Spanos
Shewhart and CUSUM time series residuals
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C. J. Spanos
Fitted ARIMA(0,1,1) Example
Data
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ARIMA(0,1,1)
Residuals
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C. J. Spanos
So, what is RTSPC?
RTSPC reads real-time signals from processing tools.
It automatically does ACF and PACF analysis to build and
save time series models.
During production, RTSPC ”filters” the real-time signals.
The filtered residuals are combined using T2 statistics.
This analysis is done simultaneously in several levels:
• Real-Time Signals
• Wafer Averages
• Lot Averages
The multivariate T2 chart provides a robust real-time
summary of machine “goodness”.
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C. J. Spanos
Emerging Factory Control Structure
Central SPC
Alarm
Handler
Planning
and
Scheduling
"CIM-Bus"
Maintenance
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Workstream
Recipe
Management
SECSII
Server
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C. J. Spanos
The SPC Server
Accesses data base and draws simple X-R charts.
Disables machine upon alarm
Benefits from automated data collection
Performs arbitrary correlations across the process
Can to build causal models across the process
Monitors process capabilities of essential steps
Maintains 2000+ charts across a typical fab
Keeps track of alarm explanations given by operators
and engineers.
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C. J. Spanos
Training for SPC
Operators: understand and "own" basic charts.
Process Engineers: be able to decide what to monitor
and what chart to use (grouping, etc.)
Equipment Engineers: be able to collect tool data.
Understand how to control real-time tool data.
Manufacturing
Manager:
understand
process
capabilities. Monitor several charts collectively.
Fab Statistician: understand the technology and its
limitations. Appreciate cost of measurements.
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C. J. Spanos
Summary of SPC topics
Random variables and distributions.
Sampling and hypothesis testing.
The assignable cause.
Control chart and operating characteristic.
p, c and u charts.
XR, XS charts and pattern analysis.
Process capability.
Acceptance charts.
Maximum likelihood estimation, CUSUM.
Multivariate control.
Evolutionary operation.
Regression chart.
Time series modeling.
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C. J. Spanos
The 1997 Roadmap
Year
Feature nm
1997
250
1999
180
2001
150
2003
130
2006
100
2009
70
2012
50
300
Area mm2
Density cm-2 3.7M
Cost µc/tr
3000
340
6.2M
1735
385
10M
1000
430
18M
580
520
39M
255
620
84M
110
750
180M
50
248
300
193?
300
157?
300
14
300
14
450
14
450
248
200
technology
wafer size
Function/milicent
20
15
10
5
0
1997
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1999
Function/milicent
2001
2003
2006
2009
2012
50
C. J. Spanos
Where will the Extra Productivity Come from?
(Jim Owens, Sematech)
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C. J. Spanos
The Opportunities
Year
Feature nm
Yield
Equipment
utilization
Test
wafers
1997
250
85%
35%
5-15%
1999 2001 2003 2006 2009 2012
180 150 130 100 70
50
95% 100? 100? 100? 100?
50%
Speed
15%
OEE
30%
Setup
10%
Test Wafers
8%
Quality
2% No Oper
10%
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No Prod Down Pl
3%
7%
Down Un
15%
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C. J. Spanos
Basic CD Economics
(D. Gerold et al, Sematech AEC/APC, Sept 97, Lake Tahoe, NV)
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C. J. Spanos
Application of Run-to-Run Control at Motorola
Dosen = Dosen-1 - β (CDn-1 - CDtarget)
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(D. Gerold et al, Sematech AEC/APC, Sept 97, Lake Tahoe, NV)
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C. J. Spanos
CD Improvement at Motorola
σLeff reduced by 60%
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(D. Gerold et al, Sematech AEC/APC, Sept 97, Lake Tahoe, NV)
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C. J. Spanos
Why was this Improvement Important?
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600k APC investment, recovered in two days...
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C. J. Spanos
Less Tangible Opportunities
Reduce cost of second sourcing (facilitate technology
transfer)
Dramatically increase flexibility (beat competition with more
customized options)
Extend life span of older technologies
Cut time to market (by linking manufacturing to design)
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C. J. Spanos
What is the current extend of “control” in our industry?
Widespread inspection and SPC
Systematic setup and calibration (DOE)
Widespread use of RSM / Taguchi techniques
Factory statistics is an established discipline
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C. J. Spanos
Advances for the Semiconductor Industry
An old idea - ensure equipment integrity - automatically
A new idea - perform feedback control on the workpiece
Isolate performance from technology
Isolate technology from equipment
Create a process with truly interchangeable parts
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C. J. Spanos
How do you steer your Process?
1980: short distance, wide road, but no steering wheel, bad
front end alignment
1998: longer distance, narrow road, no steering wheel,
tricky front end alignment
2005?
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C. J. Spanos
Changing the “do not touch my process” attitude
A stable process is one that is locally characterized and
locked. SPC is used to make sure it stays there.
An “agile” process is one that is characterized over a
region of operation. Process data and control algorithms
are used to obtain goals.
Can we reach the 2010 process goals with a “stable”
process?
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C. J. Spanos
In Conclusion
SPC provides “open loop” control.
In-situ data can be used for tighter run-to-run and
supervisory control.
Several technical (and some cultural) problems must be
addressed before that happens:
• Need sensors that are simple, non-intrusive and robust.
• User interfaces suitable for the production floor.
Next step in the evolution of manufacturing:
From hand crafted products, to hand crafted lines to lines
with interchangeable parts.
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