Spanos
EE290H F05
Introduction to Statistical Process Control
The assignable cause
The Control Chart
Statistical basis of the control chart
Control limits, false and true alarms and the
operating characteristic function
1
Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Managing Variation over Time
• Statistical Process Control often takes the form
of a continuous Hypothesis testing.
• The idea is to detect, as quickly as possible, a
significant departure from the norm.
• A significant change is often attributed to what is
known as an assignable cause.
• An assignable cause is something that can be
discovered and corrected at the machine level.
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
What is the Assignable Cause?
• An \"Assignable Cause\" relates to relatively strong
changes, outside the random pattern of the process.
• It is \"Assignable\", i.e. it can be discovered and corrected
at the machine level.
• Although the detection of an assignable cause can be
automated, its identification and correction often requires
intimate understanding of the manufacturing process.
• For example...
– Symptom: significant yield drop.
– Assignable Cause: leaky etcher load lock door seal.
– Symptom: increased e-test rejections
– Assignable Cause: probe card worn out.
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Example:
Investigate furnace temp and set up a real-time alarm.
3
2
1
0
-1
-2
-3
0 5000 10000 15000 20000
time
The pattern is obvious. How can we automate the alarm?
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
The purpose of SPC
A. Detect the presence of an assignable cause fast.
2. Minimize needles adjustment.
• Like Hypothesis testing
– (A) means having low probability of type II error and
– (B) means having low probability of type I error.
• SPC needs a probabilistic model in order to describe the
process in question.
5
Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Example: Furnace temp differential (cont.)
Group points and use the average in order to plot a known
(normal) statistic.
Assume that the first 10 groups of 4 are in Statistical
Control. Limits are set for type I error at 0.05.
2
UCL 1.2
1
0
-1
LCL -1.2
-2
0 10 20 30
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Example (cont.)
• The idea is that the average is normally distributed.
• Its standard deviation is estimated at .6333 from the first
10 groups.
• The true mean (μ) is assumed to be 0.00 (furnace
temperature in control).
• There is only 5% chance that the average will plot
outside the μ+/- 1.96 σ limits if the process is in control.
In general:
UCL = μ + k σ
LCL = μ - k σ
where μ and σ relate to the statistic we plot.
7
Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Another Example
Original data Averaged Data (n=5)
Variable Control Charts
Plot
1.150 1.070
UCL=1.0626
1.050
1.100
1.030
Mean of small shift
1.050
small shift
1.010
µ0=1.0006
1.000
0.990
0.950
0.970
0.900 0.950
LCL=0.9387
0.930
0.850
25
50
75
100
0 100 200 300 400 500
small shift
Mean of small shift
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
How the Grouping Helps
Small Group Size, Large Group Size,
large β. smaller β for same α.
Bad
Good
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Average Run Length
• If the type I error (α) depends on the original (proper)
parameter distribution and the control limits, ...
• ... the type II error (β) depends on the position of the
shifted (faulty) distribution with respect to the control
limits.
• The average run length (ARL) of the chart is defined as
the average number of samples between alarms.
• ARL, in general, is 1/α when the process is good and
1/(1-β) when the process is bad.
10
Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
The Operating Characteristic Curve
The Operating Characteristic of the chart shows the
probability of missing an alarm vs. the actual process shift.
Its shape depends on the statistic, the subgroup size and
the control limits.
β
These curves are drawn
Fig. 4-5 from Montgomery, = 0.05
for α pp. 110
deviation in #σ
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Pattern Analysis
3
2
1
0
-1
-2
-3
0 20 40 60 80 100
Other rules exist: Western Electric, curve fitting,
Fourier analysis, pattern recognition...
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Example: Photoresist Coating
• During each shift, five wafers are coated with photoresist
and soft-baked. Resist thickness is measured at the
center of each wafer. Is the process in control?
• Questions that can be asked:
a) Is group variance \"in control\"?
b) Is group average \"in control\"?
c) Is there any difference between shifts A and B?
• In general, we can group data in many different ways.
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Range and x chart for all wafer groups.
600
UCL 507.09
500
400
300
200
100
0 LCL 0.0
8000
UCL 7971.32
7900
7800
7700 LCL 7694.52
7600
0 10 20 30 40 Wafer Groups
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Comparing runs A and B
Range, Shift A
Range, Shift B
600
600
550
500
500
465
400
400
300
300
260
220
200
200
100 100
0 0
0 10 20 0 10 20
Mean, Shift A Mean, Shift B
8000 8000
7985
7958
7900 7900
7835
7831
7800 7800
7704
7700 7700
7685
7600 7600
0 10 20 0 10 20
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
Why Use a Control Chart?
• Reduce scrap and re-work by the systematic
elimination of assignable causes.
• Prevent unnecessary adjustments.
• Provide diagnostic information from the shape of
the non random patterns.
• Find out what the process can do.
• Provide immediate visual feedback.
• Decide whether a process is production worthy.
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
The Control Chart for Controlling Dice Production
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
The Reference Distribution
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3
2
1
2 3 4 5 6 7 8 9 10 11 12
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
The Actual Histogram
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4
3
2
1
2 3 4 5 6 7 8 9 10 11 12
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Lecture 10: Introduction to Statistical Process Control

Spanos
EE290H F05
In Summary
• To apply SPC we need:
• Something to measure, that relates to
product/process quality.
• Samples from a baseline operation.
• A statistical “model” of the variation of the
process/product.
• Some physical understanding of what the
process/product is doing.
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Lecture 10: Introduction to Statistical Process Control