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Process Capability
Training and Explanation
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Purpose of EasyTools
There are lots of Quality tools around that can help
improving many situations of the daily quality life. The
problem with many tools is that you need training and
experience to use them effectively.
EasyTools is a collection of easy to use and mostly self
explaining tools that everybody can use.
No need for weeks of training or years of experience.
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Purpose and Contents
Purpose:
• To get a basic feeling on capability studies.
Contents:
• Normal Distribution
• Scattering
• Process Potential
• Machine Capability
• Process Capability
• Preliminary Process Capability
• Formulas for capability and potential
• Customer and internal requirements
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The Normal distribution
Assume you have a chicken farm and you measure the
weight of the eggs. Their weight is around 50g – means
some eggs have only 45g but some have 55g. If you
make a distribution curve where you show how many
eggs have what weight, you will get following curve.
0,0900
m = 50
0,0800
0,0700
0,0600
0,0500
0,0400
0,0300
0,0200
Sigma = 5
0,0100
0,0000
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
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Capability
The Capability is the ratio of Tolerance to Scattering
90
80
70
60
Tolerance
Scattering
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
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How to measure scattering?
Assume you have a normal distribution – then 99% of
all data lie within +- 3 sigma.
The capability is 1
if ~99% of the data lie
within the tolerance
(+- 3 sigma).
+-Sigma
+-2 Sigma
+-3 Sigma
The capability is better
than 1
if more than ~99% of
the data lie within the
tolerance.
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Potential versus capability
The better the data lie in the middle of the
tolerance the better the capability.
The potential is what we could achieve if the
scattering is the same but the data would lie in the
middle.
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Different capability types
Cmk - Machine capability
Short term study. Take a sample of e.g. 50 parts as they are
produced, measure the characteristic you are interested and
calculate the Cmk.
Cpk - Process capability
Long term study. Take samples over a long time (e.g. 3 month;
e.g. each week 5 parts), measure the characteristic you are
interested and calculate the Cpk.
Ppk – Preliminary Process capability
Mid term study. Take samples over a mid time (e.g. 3 weeks; e.g.
each day 3 parts), measure the characteristic you are interested
and calculate the Ppk.
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Capability formulas
The formulas for Cpk and Ppk are the same as for Cmk.
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Potential formulas
USL - LSL
Cm =
6s
The formulas for Cp and Pp are the same as for Cm.
See visualisation of capability
A comprehensive article about capabilities can be
found at
http://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm
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Capability requirements
Our Customers’ requirements are:
Cpk > 1.00
Cpk for safety items > 1.33
Our requirements should be:
Cpk > 1.33
Cpk for safety items > 1.67
Sigma
Cpk
ppm
3
1,00
2700
4
1,33
64
5
1,67
0,5
6
2,00
0,002
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