advanced process capability
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Process Capability
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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 indexesare used: Cp, Cpk, Ppand 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 objectiveis to get as close to the theoretical best that your process
can achieve by eliminating special causesof variation, so that only
common (natural) causesare acting on the process, and then to reduce
these to a minimum, whenever possible.
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Process Capability
Process Control
Out of Control
(Special Causes Present)
In Control
(Special Causes Eliminated)
Note - no reference to
specs !
In Control but not Capable
(Variation from Common Causes
Excessive)
In Control and Capable
(Variation from Common
Causes Reduced)Lower Spec Limit
Upper Spec Limit
Process Capability
What it is
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Process Capability
What it is
Cpor ENTITLEMENT is the theoretical best
hat a process can achieve.
1 2
CAPABILITY PERFORMANCEShort Term Long Term
In Control Not in Control
Pooled std dev Total / overall std dev
aHowmuch
variability
compares
spec range(tolerance)
to process
width
Cp Pp
bHow
centred
how close
process
centre is to
nearest
spec limit
Cpk Ppk
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Process Capability
The 4 capability Capability Indexes: explaining the terms . . .
1 2
CAPABILITY PERFORMANCEShort Term Long Term
In Control Not in Control
Pooled std dev Total / overal l s td dev
a
How
much
variability
compares
spec range
(tolerance)
to process
width
Cp Pp
bHow
centred
how close
processcentre is to
nearest
spec limit
Cpk Ppk
300
350
400
450
500
550
600
Time
short term
long term
Not (necessarily) in Control:common
causes and special causes acting
(possible drifts or shifts in the process)
In Control:only common causes acting (no
sudden drifts or shifts in the process)
What it is
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Process Capability
The 4 capability Capability Indexes: explaining the terms . . .
1 2
CAPABILITY PERFORMANCEShort Term Long Term
In Control Not in Control
Pooled std dev Total / overal l s td dev
a
How
much
variability
compares
spec range
(tolerance)
to process
width
Cp Pp
bHow
centred
how close
processcentre is to
nearest
spec limit
Cpk Ppk
300
350
400
450
500
550
600
Time
Pooled ortotal standard deviation- used in manual calculations:
Pooled (or combined): sP= sqrt [ sum (d.f. *s2) / sum (d.f.) ]
Total (or overall): sT= sqrt [ sum (x - x)2/ (n-1) ]
What it is
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The 4 capability Capability Indexes: explaining the terms . . .
1 2
CAPABILITY PERFORMANCEShort Term Long Term
In Control Not in Control
Pooled std dev Total / overal l s td dev
a
How
much
variability
compares
spec range
(tolerance)
to process
width
Cp Pp
bHow
centred
how close
process
centre is to
nearestspec limit
Cpk Ppk
Process Capability
Cp= USL-LSL6sP
Pp= USL-LSL6sT
sP =pooled standard deviation sT =total standard deviation
USLLSL
Cp, Ppcompares 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.
What it is
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The 4 capability Capability Indexes: explaining the terms . . .
Process Capability
Cpk, Ppkmeasure 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).
Cpk= min {Cpkl, Cpku}Cpkl = X-LSL
3sP
Cpku= USL-X
3sP
Ppkl= X-LSL
3sT
Ppku= USL-X
3sT
Ppk= min {Ppkl, Ppku}
1 2
CAPABILITY PERFORMANCEShort Term Long Term
In Control Not in Control
Pooled std dev Total / overal l s td dev
a
How
much
variability
compares
spec range
(tolerance)
to process
width
Cp Pp
bHow
centred
how close
process
centre is to
nearest
spec limitCpk Ppk
X
USLLSL
What it is
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How to use it
Process Capability
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 ru le of thumbthe following chart
Cp Cpk Pp Ppk Sigma Red (Bad) < 1.00 < 1.00 < 1.33 < 1.33 < 4.5
Yellow (OK) 1.00 - 1.33 1.00 - 1.33 1.33 - 1.67 1.33 - 1.67 4.5 - 5.5
Green (Good) > 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:
250 350 450 550 650
LSL USL
Process Capability Analysis for Data
USL
Target
LSL
Mean
Sample N
StDev (ST)
StDev (LT)
Cp
CPU
CPL
Cpk
Cpm
Pp
PPU
PPL
Ppk
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
520.000
*
420.000
435.833
30
10.7176
59.6888
1.56
2.62
0.49
0.49
*
0.28
0.47
0.09
0.09
366666.67
100000.00
466666.67
69795.44
0.00
69795.44
395402.81
79256.43
474659.24
Process Data
Potential (ST) Capability
Overall (LT) Capability Observed Performance Expected ST Performance Expected LT Performance
ST
LT
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Process Capability
Example
Using Minitab, with non-normal data
0 5 10 15 20 25
LSL USL
Process Capability Analysis for Weibull
Calculations Based on Weibull Distribution Model
USL
Target
LSL
Mean
Sample N
Shape
Scale
Pp
PPU
PPL
Ppk
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
6.00000
*
2.00000
5.65406
50
1.58256
6.29977
0.19
0.09
0.35
0.09
120000.00
400000.00
520000.00
150164.01
396235.71
546399.72
Process Data
Overall (LT) Capability
Observed LT Performance
Expected LT Performance
Note:For Weibull Capability Analysis, data must have positive values, andLONG TERM metrics only are given.
NO values for Cpk are given, because the data is non-normal
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