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Process Capability
What it is
• Process Capability looks at short term capability and long term
performance of a process with regard to customer specifications.
• Standard indexes are used: Cp, Cpk, Pp and Ppk. These can be
converted into ppm.
A simple view of Process Control and Process Capability
• process control - refers only to the “voice of the process” - looking at
the process using an agreed performance measure to see whether
the process forms a stable distribution over time.
• process capability - measures the “goodness of a process” comparing the voice of the process with the “voice of the customer”.
The voice of the customer here is the specification range (tolerance)
and/or the nearest customer specification limit.
The objective is to get as close to the theoretical best that your process
can achieve by eliminating special causes of variation, so that only
common (natural) causes are acting on the process, and then to reduce
these to a minimum, whenever possible.
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Process Capability
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Process Capability
What it is
Process Control
Note - no reference to
specs !
In Control
(Special Causes Eliminated)
Out of Control
(Special Causes Present)
Process Capability
In Control and Capable
(Variation from Common
Causes Reduced)
Lower Spec Limit
Upper Spec Limit
In Control but not Capable
(Variation from Common Causes
Excessive)
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Process Capability
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Process Capability
What it is
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2
CAPABILITY
PERFORMANCE
Short Term
In Control
Pooled std dev
Long Term
Not in Control
Total / overall std dev
Cp
Pp
Cpk
Ppk
compares
How
spec range
a
(tolerance)
much
variability to process
b
How
centred
width
how close
process
centre is to
nearest
spec limit
Cp or ENTITLEMENT is the theoretical best
hat a process can achieve.
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Process Capability
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Process Capability
What it is
The 4 capability Capability Indexes: explaining the terms . . .
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2
CAPABILITY
PERFORMANCE
Short Term
In Control
Pooled std dev
Long Term
Not in Control
Total / overall std dev
Cp
Pp
Cpk
Ppk
compares
a
b
How
spec range
(tolerance)
much
variability to process
How
centred
width
how close
process
centre is to
nearest
spec limit
Not (necessarily) in Control: common
causes and special causes acting
(possible drifts or shifts in the process)
long term
600
550
500
450
400
350
300
Time
short term
In Control: only common causes acting (no
sudden drifts or shifts in the process)
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Process Capability
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Process Capability
What it is
The 4 capability Capability Indexes: explaining the terms . . .
1
2
CAPABILITY
PERFORMANCE
Short Term
In Control
Pooled std dev
Long Term
Not in Control
Total / overall std dev
Cp
Pp
Cpk
Ppk
compares
a
b
How
spec range
(tolerance)
much
variability to process
How
centred
width
how close
process
centre is to
nearest
spec limit
600
550
500
450
400
350
300
Time
Pooled or total standard deviation - used in manual calculations:
Pooled (or combined):
Total (or overall):
sP =
sT =
sqrt [ sum (d.f. *s2) / sum (d.f.) ]
sqrt [ sum (x - x) 2 / (n-1) ]
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Process Capability
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Process Capability
What it is
The 4 capability Capability Indexes: explaining the terms . . .
1
2
CAPABILITY
PERFORMANCE
Short Term
In Control
Pooled std dev
Long Term
Not in Control
Total / overall std dev
Cp
Pp
Cpk
Ppk
compares
a
b
How
spec range
(tolerance)
much
variability to process
How
centred
width
how close
process
centre is to
nearest
spec limit
LSL
USL
Cp, Pp compares specification range (tolerance)to process width
regardless of where the process is centred.
It is the ratio of the specification width to 6 x process standard
deviation.
Cp = USL-LSL
6sP
Pp = USL-LSL
6sT
sP = pooled standard deviation
6
sT = total standard deviation
Process Capability
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Process Capability
What it is
The 4 capability Capability Indexes: explaining the terms . . .
1
2
CAPABILITY
PERFORMANCE
Short Term
In Control
Pooled std dev
Long Term
Not in Control
Total / overall std dev
Cp
Pp
Cpk
Ppk
compares
a
b
How
spec range
(tolerance)
much
variability to process
How
centred
width
how close
process
centre is to
nearest
spec limit
X
LSL
USL
Cpk, Ppk measure how close the process centre is to the nearest customer
spec.
It is (difference between the process average and the nearest specification)
(3 x the process standard deviation).
Cpkl =
X-LSL
3sP
Cpku = USL-X
3sP
Cpk = min {Cpkl, Cpku}
Ppkl =
X-LSL
3sT
Ppku = USL-X
3sT
Ppk = min {Ppkl, Ppku}
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Process Capability
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Process Capability
How to use it
• Use Minitab output whenever possible, since it combines the indexes
with a graphical representation of the process: actual sample, estimated
short term capability and estimated long term performance
• Also use as a rule of thumb the following chart
Red (Bad)
Yellow (OK)
Green (Good)
Cp
Cpk
Pp
Ppk
Sigma
< 1.00
< 1.00
< 1.33
< 1.33
< 4.5
1.00 - 1.33
1.00 - 1.33
1.33 - 1.67
1.33 - 1.67
4.5 - 5.5
> 1.33
> 1.33
> 1.67
> 1.67
> 5.5
(Cpk x 3) +1.5 = sigma
Caution:
Cpk is an index much misused: It is only applicable to normally
distributed variable data that is measured in the short term.
Conversions from Cpk to ppm and sigma assume that all defectives are
occurring at one tail of the distribution with an average sigma shift of
1.5 sigma. (industry standard).
Cpk MUST be seen as part of a package of information.
Capability studies for non-normal data (Weibull) do not give Cpk
values
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Process Capability
Example
Using Minitab:
Process Capability Analysis for Data
LSL
USL
Process Data
USL
ST
LT
520.000
Target
*
LSL
420.000
Mean
435.833
Sample N
30
StDev (ST)
10.7176
StDev (LT)
59.6888
Potential (ST) Capability
Cp
1.56
CPU
2.62
CPL
0.49
Cpk
0.49
Cpm
*
Overall (LT) Capability
250
350
450
Observed Performance
550
Expected ST Performance
650
Expected LT Performance
Pp
0.28
PPM < LSL
366666.67
PPM < LSL
69795.44
PPM < LSL
PPU
0.47
PPM > USL
100000.00
PPM > USL
0.00
PPM > USL
79256.43
PPL
0.09
PPM Total
466666.67
PPM Total
PPM Total
474659.24
Ppk
0.09
9
69795.44
395402.81
Process Capability
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Process Capability
Example
Using Minitab, with non-normal data
Process Data
USL
6.00000
Target
*
LSL
2.00000
Mean
5.65406
Sample N
50
Shape
1.58256
Scale
6.29977
Process Capability Analysis for Weibull
Calculations Based on Weibull Distribution Model
LSL
USL
Overall (LT) Capability
Pp
0.19
PPU
0.09
PPL
Ppk
0.35
0.09
Observed LT Performance
PPM < LSL 120000.00
PPM > USL 400000.00
PPM Total
520000.00
Expected LT Performance
PPM < LSL 150164.01
PPM > USL 396235.71
PPM Total
546399.72
0
5
10
15
20
25
Note: For Weibull Capability Analysis, data must have positive values, and
LONG TERM metrics only are given.
NO values for Cpk are given, because the data is non-normal
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Process Capability
How it helps
• A Process Capability study is the end result of the analysis done on
process output data.
• A Process Capability study reflects what our customer sees.
• It indicates what our short term and long term situation looks like.
• Recognise however that our processes need to be stable (in statistical
control) as well as capable.
• Before anything, we must have faith in our measurements, hence the
need for a measurement system analysis.
References
• ASG aTQ training modules:
• 3.3, 3.4, 3.5 : (MSA) Measurement System Analysis
• 4.1, 4.2, 4.3, 4.5 : Process Capability
• 8.4, 8.5, 8.6, 8.7 : SPC (and non-SPC control)
• ASG “seniors” aTQ training module 1.5 : Capability
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Process Capability
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