k variation thinking 2ws02 industrial statistics a. di bucchianico
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Variation thinking
2WS02 Industrial Statistics
A. Di Bucchianico
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SPC: Philosophy
Let the process do the talking:
Goal: realize constant quality by controlling the
process with quantitative information
Constant quality means: quality with controlled and
known variation around a fixed target
Operator should be able to do the routine
controlling
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Variation I
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Variation II
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Variation III
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109876543210
-1-2-3-4-5-6-7-8-9
-10
Example: Dartec
disqualificationwhen outside range
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Examples of variation patterns10
9876543210
-1-2-3-4-5-6-7-8-9
-10
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Metric for sample variation: range
easy to compute (pre-computer era!)
rather accurate for sample size < 10
minimum maximumrange
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Metric for sample variation: standard deviation
11
1
22
1
2
n
XnX
n
XXS
n
ii
n
ii
• 2nd formula easier to compute by hand • 2nd formula less rounding errors• correct dimension of units• n-1 to ensure that average value equals
population variance (“unbiased estimator”)
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Visualisation of sample variation
Box-and Whisker plot
Histogram for dartecok
-9 -6 -3 0 3 6 9
dartecok
0
5
10
15
20
25
30fr
equen
cy
histogram
Box-and-Whisker Plot
-8 -4 0 4 8
dartecok
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all observations first 60 observationsHistogram for dartecnotok
dartecnotok
frequency
-6 -3 0 3 6 90369
121518
dart
ecn
oto
k
0 20 40 60 80 100-6-30369
Histogram for dartecnotok
dartecnotok
frequency
-7 -4 -1 2 5 8 1105
1015202530
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Variation and stability
Can variation be stable?
yes, if we mean that observations
– follow fixed probability distribution
– do not influence each other (independence)
stability -> predictability
How to handle a stable production process?
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Why stable processes?
• behaviour is predictable
• processes can be left on itself: intervention may
be expensive
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Deming’s funnel experiment
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Lessons from funnel experiment
• tampering a stable process may lead to increase
of variation
• adjustments should be based on understanding of
process (engineering knowledge)
•we need a tool to check for stability
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Attributive versus variable
two main types of measurements:
– attributive (yes/no, categories)
– variable (continuous data)
hybrid type:
– classes or bins
use variable data whenever possible!
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Statistically in control
•Constant mean and spread
•Process-inherent variation only
•Do not intervene
Measurement
Tijd
XX
XX
X
X
X
X
XX
X
XX
X
X
XX
Intervene?
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Statistically versus technically in control
“Statistically in
control”
– stable over
time /predictable
“Technically in control”
– within
specifications
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Statistically in control vs technically in control
statistically controlled process:
– inhibits only natural random fluctuations (common causes)
– is stable
– is predictable
– may yield products out of specification
technically controlled process:
– presently yields products within specification
– need not be stable nor predictable
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Priorities
what is preferable:
– statistical control or
– technically in control ??
process must first be in statistical control
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Variation and production processes
Shewhart distinguishes two forms of variation in production
processes:
• common causes
– inherent to process
– cannot be removed, but are harmless
• special causes
– external causes
– must be detected and eliminated
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Chance or noise
How do we detect special causes ?
use statistics to distinguish between chance and
real cause
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Shewhart control chart
graphical display of product characteristic which is important for
product quality
X-bar Chart for yield
Subgroup
X-b
ar
0 4 8 12 16 2013,6
13,8
14
14,2
14,4
UpperControl Limit
Centre Line
Lower Control
Limit
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Control charts
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Why control charts?
•control charts are effective preventive device
•control charts avoid tampering of processes
•control charts yield diagnostic information
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Basic principles
• take samples and compute statistic
• if statistic falls above UCL or below LCL, then out-of-control signal: e.g.,
X-bar Chart for yield
Subgroup
X-b
ar
0 4 8 12 16 2013,6
13,8
14
14,2
14,4
how to choose control limits?
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Normal distribution
•often used in SPC
•“justification” by Central Limit Theorem:
– accumulation of many small errors
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Meaning of control limits
•limits at 3 x standard deviation of plotted statistic
•basic example:
9973.0)33(
)33(
)33(
)(
ZP
XP
XP
UCLXLCLP
XX
XX
UCL
LCL
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Example
• diameters of piston rings
• process mean: 74 mm
• process standard deviation: 0.01 mm
• measurements via repeated samples of 5 rings yields:
mmLCL
mmUCL
mmn
x
9865.73)0045.0(374
0135.74)0045.0(374
0045.05
01.0
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Specifications vs. natural tolerance limits
never put specification limits on a control chart
control chart displays inherent process variance
during trial run charts (also called tolerance chart of tier chart) often
yields useful graphical information