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 - 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
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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

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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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