Transcript
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. Ppk. These can be converted into ppm. A simple view of Process Control and Process Capability • process control - refers only to the “voice “ voice of the process” process ” - look lookin ing g at at the process using an agreed performance measure to see whether the process forms a stable distribution over 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 specificatio specification n 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.
1
Process Capability v1.ppt
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)
2
Process Capability v1.ppt
Process Capability What it is
a
How much variability
b
How centred
compares spec range (tolerance) to process width how close process centre is to nearest spec limit
1
2
CAPABILITY
PERFORMANCE
Short Term In Control Pooled std dev
Long Term Not in Control Total / overall std dev
Cp
Pp
Cpk
Ppk
Cp or ENTITLEMENT is the theoretical best hat a process can achieve.
3
Process Capability v1.ppt
Process Capability What it is The 4 capability Capability Indexes: explaining the terms . . . 1
2
CAPABILITY
PERFORMANCE
Short Term In Control P ool ed st d dev
Long Term Not in Control Tot al / overal l s td dev
Cp
Pp
Cpk
Ppk
compares
How spec range (tolerance) a much variability to process
b
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) 4
Process Capability v1.ppt
Process Capability What it is The 4 capability Capability Indexes: explaining the terms . . . 1
2
CAPABILITY
PERFORMANCE
Short Term In Control P ool ed st d dev
Long Term Not in Control Tot al / overal l s td dev
Cp
Pp
Cpk
Ppk
compares
How spec range (tolerance) a much variability to process
b
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. *s 2) / sum (d.f.) ] sqrt [ sum (x - x) 2 / (n-1) ]
5
Process Capability v1.ppt
Process Capability What it is The 4 capability Capability Indexes: explaining the terms . . . 1
2
CAPABILITY
PERFORMANCE
Short Term In Control P ool ed st d dev
Long Term Not in Control Tot al / overal l s td dev
Cp
Pp
Cpk
Ppk
compares
How spec range (tolerance) a much variability to process
b
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 v1.ppt
Process Capability What it is The 4 capability Capability Indexes: explaining the terms . . . 1
2
CAPABILITY
PERFORMANCE
Short Term In Control P ool ed st d dev
Long Term Not in Control Tot al / overal l s td dev
Cp
Pp
Cpk
Ppk
compares
How spec range (tolerance) a much variability to process
b
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}
7
Process Capability v1.ppt
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 8
Process Capability v1.ppt
Process Capability Example Using Minitab:
Process Capability Analysis for Data LSL
Process Data USL
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
Pp
0.28
PPM < LSL
366666.67
PPM < LSL
PPU
0.47
PPM > USL
100000.00
PPM > USL
PPL
0.09
PPM Total
466666.67
PPM Total
Ppk
0.09
9
69795.44
0.00
69795.44
650 Expected LT Performance PPM < LSL
395402.81
PPM > USL
79256.43
PPM Total
474659.24
Process Capability v1.ppt
Process Capability Example Using Minitab, with non-normal data Process Data USL
6.00000
Target LSL
2.00000
Mean
5.65406
Sample N
Process Capability Analysis for Weibull
*
Calculations Based on Weibull Distribution Model
50
Shape
1.58256
Scale
6.29977
LSL
USL
Overall (LT) Capability Pp
0.19
PPU
0.09
PPL
0.35
Ppk
0.09
Observed LT Performance PPM < LSL
120000.00
PPM > USL 400000.00 PPM Total
520000.00
Expected LT Performance PPM < LSL
150164.01
0
5
10
15
20
25
PPM > USL 396235.71 PPM Total
546399.72
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
10
Process Capability v1.ppt
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
11
Process Capability v1.ppt
