Cpk Vs. ppm
Table
The
performance of a process
may be characterized
in terms of how close it gets to hitting its target or meeting its
specifications
and how consistent it is in doing so. For a process whose output
data comprise a normal
distribution, its performance can be conveniently quantified in terms of
its process capability index,
Cpk.
The Cpk
of a process measures how centered
the output of the process is between
its lower and upper specification limits and how variable (and therefore how
stable
or nonstable) the output is. In
fact, the Cpk is expressed as the
ratio
of how far the
mean
of the output data is from the closer spec limit (the centering of the
process) to three times their
standard deviation (the
process variability).
If the mean of the process
data is closer to the
lower
spec limit LSL and the standard deviation of
the process data is Stdev, then
Cpk = (MeanLSL) / (3 Stdev). If the mean of the process
data is closer to the
upper
spec limit USL, then
Cpk = (USLMean) / (3 Stdev).
An
ideal process is one whose output is always dead center between the spec
limits, such that the mean of its output data equals this dead center
and the standard deviation is zero. The Cpk of this ideal process
is infinite.
As a process becomes less
centered between the spec limits or as it becomes more variable, its Cpk
decreases. As its Cpk decreases, the probability of it exhibiting
an output that is
outside its specification limits increases. Thus,
every Cpk value corresponds to a percent defective rate, which may be
expressed in parts per million, or
ppm.
Table 1 shows some Cpk
values and their equivalent ppm rates. In the semiconductor
industry, the Cpk goal for a process is normally set at
1.67, although a Cpk of 1.33 is still considered acceptable.
Table 1. Cpk Vs. ppm
Cpk 
Sigma 
ppm 
0.43 
 
193,600 
0.47 
 
161,510 
0.50 
1.50 
133,610 
0.53 
 
109,600 
0.57 
 
89,130 
0.60 
 
71,960 
0.63 
 
57,430 
0.67 
 
45,500 
0.70 
 
35,730 
0.73 
 
27,810 
0.77 
 
21,450 
0.80 
 
16,400 
0.83 
 
12,420 
0.87 
 
9,322 
0.90 
 
6,934 
0.93 
 
5,110 
0.97 
 
3,732 
1.00 
3.00 
2,700 
1.03 
 
1,935 
1.07 
 
1,374 
1.10 
 
967 
1.13 
 
674 
1.16 
~3.50 
465 
1.20 
 
318 
1.23 
 
216 
1.27 
 
145 
1.30 
 
98 
1.33 
4.00 
64 
1.37 
 
41 
1.40 
 
27 
1.43 
 
17 
1.47 
 
11 
1.50 
4.50 
7 
1.53 
 
4 
1.57 
 
3 
1.60 
~5.00 
0.5 
2.00 
6.00 
0.00198 
See also:
SPC;
Capability Indices;
Monitors and Controls;
Quality Systems
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