Process Capability Analysis - Links to dept and Project
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Transcript Process Capability Analysis - Links to dept and Project
Basic Training for Statistical
Process Control
Process Capability & Measurement
System Capability Analysis
Outline
Process
Capability
Natural
Tolerance Limits
Histogram and Normal Probability Plot
Process
Capability Indices
Cp
Cpk
Cpm
& Cpkm
Measurement
System Capability
Using
Control Charts
Using Factorial Experiment Design (ANOVA)
Hands
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On Measurement System Capability Study
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Process Capability
Process Capability Analysis (PCA)
Is
only done when the process is in a state of
Statistical Control
Meaning:
Process
NO SPECIAL CAUSES are present
does not have to be centered to do PCA
Yield
will improve if process is centered, but the value
is in knowing what / where to improve the process
PCA is
done periodically when the process has been
operating in a state of statistical control
Allows
for measuring improvement over time
Allows for marketing your competitive edge
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Process Capability Analysis
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Process Capability - Timing
Process Capability Analysis is performed
when there are NO special causes of
variability present – ie. when the process is
in a state of statistical control, as
illustrated at this point.
Improving Process Capability and
Performance
Continually Improve the
System
Characterize Stable Process
Capability
Head Off Shifts in Location,
Spread
Time
Identify Special Causes - Bad
(Remove)
Identify Special Causes - Good
(Incorporate)
Reduce Variability
Center the Process
LSL
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0
USL
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Process Capability
Process
Capability is INDEPENDENT of product
specifications
Most
specifications are set without regard for process capability
However, understanding process
capability helps the engineer to
set more reasonable specifications
PCA reflects
PCA is
only the Natural Tolerance Limits of the process
done by examining the process
Histogram
Normal
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Probability Plot
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Natural Tolerance Limits
The
natural tolerance limits assume:
The
process is well-modeled by the Normal Distribution
Three sigma is an acceptable proportion of the process to yield
The
Upper and Lower Natural Tolerance Limits are
derived from:
The
process mean () and
The process standard deviation ()
Equations:
UNTL 3
LNTL 3
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Natural Tolerance Limits
1 :68.26% of the total area
2 :95.46% of the total area
3 :99.73% of the total area
-3
or
LNTL
-2
-
+
+2
+3
or
UNTL
The Natural Tolerance Limits cover 99.73% of the process output
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PCA: Histogram Construction
Verify
rough shape and location of histogram
Symmetric
(roughly bell-shaped)
Mean = median = mode
Quickly
confirm applicability prior to statistical analysis
Can
be very hard to distinguish a Normal Distribution from a
t-Distribution
Sometimes even a Normal distribution doesn’t look normal
More
Verify
location of process with respect to Specifications
Quick
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data and columns (bins) can make a difference
inspection will show what to do to improve the process
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PCA: Normal Probability Plot
A Normal
Plot better clarifies whether the
distribution is Normal by a visual inspection for:
Non-random
patterns (non-Normal)
Fat Pencil Test (Normal if passes)
C
u
m
C
u
m
C
u
m
F
r
e
q
F
r
e
q
F
r
e
q
X
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X
Process Capability Analysis
X
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PCA: Parameter Estimation
The
Normal Plot mid-point estimates the process mean
The
slope of the “best fit” line for the Normal Plot estimates
the standard deviation
Choose
The
the 25th and 75th percentile points to calculate the slope
Histogram mode should be close to the mean
The
range/d2 (from Histogram) should be close to the
standard deviation
Can
also estimate standard deviation by subtracting 50th percentile
from the 84th percentile of the Histogram
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Process Capability Indices
Cp:
Measures
the potential capability of the current
process - if the process were centered within the
product specifications
Two-sided Limits:
USL LSL
Cp
6
One-sided Limit:
LSL
USL
Cpl
Cpu
3
3
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Cp Relation to Process Fallout
Cp
Ratio
0.50
0.60
0.80
1.00
1.20
1.40
1.50
1.60
1.80
2.00
Two-Sided Specification Fallout
(ppm)
133614
71861
16395
2700
318
27
7
2
0.06
0.0018
Recommended
Existing
Minimum Ratios:
Process
Existing, Safety / Critical Parameter
New Process
New, Safety / Critical Parameter
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One-sided Specification Fallout
(ppm)
66807
35931
8198
1350
159
14
4
1
0.03
0.0009
(D. C. Montgomery, 2001)
1.25 (1-sided)
1.45
1.45
1.60
Process Capability Analysis
1.33 (2-sided)
1.50
1.50
1.67
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Process Capability Indices
Cpk:
Measures
actual capability of current process - at its’
current location with respect to product specifications
Formula:
Cpk min(Cpu , Cpl )
Where:
Cpu
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USL
3
Process Capability Analysis
LSL
Cpl
3
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Process Capability Indices
Regarding
Cp and Cpk:
Both
assume that the process is Normally distributed
Both assume that the process is in Statistical Control
When they are equal to each other, the process is
perfectly centered
Both are pretty common reporting ratios among
vendors and purchasers
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Process Capability Indices
Two very
different processes can have
identical Cpk values, though:
because
spread and location interact!
LSL
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USL
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Process Capability Indices
Cpm:
Measures
the current capability of the process using the process target center point within the
product specifications in the calculation
Formula:
USL LSL
Cpm
6 2 ( T )2
Where target T is:
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1
T (USL LSL)
2
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Process Capability Indices
Cpkm:
Similar
to Cpm - just more sensitive to departures
from the process target center point
Not really in very common use
Formula:
C pk
C pkm
2
T
1
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Measurement System Capability
Examines the relative variability in
the product
and measurement systems, together
Total
variation is the result of
Product
variation
Gage variation
Operator variation
Random variation
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2
total
gaging system variation
2
product
Process Capability Analysis
2
gage
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Measurement System Analysis
Measurement system can
X-bar
be assessed by
and R-Charts
Using
a single part as the rational subgroup
Is easy to visualize
Requires alternate interpretation of the control charts
Designed
Experiments
Using Analysis
of Variance
Allows assessment of part x operator interactions
Is statistically complex to compute & analyze
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X-Bar & R-Chart Method
Have
each operator measure the same part twice - so
the part becomes the rational sample unit
Parts
should be representative of those to be measured
Use
Use
a sample of 20 - 25 parts
a representative set of operators
Either
collect data from every operator, or
Randomly select from the set of operators
Collect
data under representative conditions
Carefully
specify and control the conditions for measurement
Randomly sequence the combination of parts and operators
Preserve the time-order of the collected data & note observations
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X-Bar & R-Chart Method
If each
operator measures the same part twice:
Variation
between samples is plotted on the X-Chart
Out
of control points indicate success in identifying
differences between parts
Variation
within samples is plotted on the R-Chart
Centerline
of R-Chart is the magnitude of the gage
variation
Out of control points indicate excessive operator to
operator variation (fix with training?)
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X-Bar & R-Chart Method
Out of control points indicate
ability to distinguish between
product samples (Good)
Out of control points indicate
inability of operators to use
gaging system (Bad)
UCL
UCL
x
LCL
R
LCL
Sample Number
Sample Number
R - Control Chart
X-Bar Control Chart
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X-Bar & R-Chart Method
Precision to Tolerance Ratio (P/T):
“Rule
of Ten”:
The
measurement device should be at least ten times
more accurate than the smallest measurement
Calculations:
Interpretation:
gage
R
d2
and P
T
6 gage
USL LSL
Resulting
ratio should be 0.10 or smaller if the gage is
truly capable
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X-Bar & R-Chart Method: R & R
Repeatability:
Inherent
precision of the gage
Reproducibility:
Variability
of the gage under differing conditions
Environment
Operator
Time
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…
2
gage
2
repeatability
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reproducability
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X-Bar & R-Chart Method: R & R
Process
is the same as before (20 - 25 parts, …):
But
we estimate the Repeatability from the Range Mean
computed across all the operators and all parts:
2
repeatabil ity
R
d2
And
we estimate the Reproducibility from the Range of
variability across all operators for each individual part:
2
reproducab
ility
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R
x
d2
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X-Bar & R-Chart Method: R & R
What to
More
do with the information?
variation is bad, so…
If
the reproducibility variation is larger, improve the
operators
If the repeatability variation is larger, improve the
gaging instrument
Hands-On Experiment
Micrometer
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Study
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Gage Capability Analysis: ANOVA
A form
of Designed Experiment:
Two-Treatment
Full Factorial with Replications
Analysis is done using ANOVA software
Comparisons
of variance components is through a
series of F-tests (either exceed critical region or look
for small p-value)
Can distinguish part X operator interaction
Want to find non-significant operator, interaction
terms, and a significant part term - capable system!
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