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Chapter 19: B. Statistical Process Control 299
( )
Percentage of nonconforming = 1P(
264 X 280)
100%
264
276 X 276 280
276
= 1
P
100
258 . 258 . 2.
58
%
( ( ))
= 1P 4. 65 Z 1. 55 100%
= 606 . %.
Continued
Thus, even though the value of C p did not change after the process mean experienced a
shift, the process is producing nonconforming units at a rate 30 times more than in the
previous example. This implies that C p did not measure the effect that the upward or
downward shift had on the ability of the process to produce products within the specification
limits.
This major drawback of C p makes it less reliable than many other process
capability indices available in the literature. We will study some of them here.
However, before we study other PCIs let us see another alternative but equivalent
interpretation of C p that is given by finding the percentage of specification band
used, that is
1
Percentage of specification band used = × 100.
Cp
A smaller percentage of specification band used indicates a better process.
Again, for reasons discussed above, this interpretation sometimes can also be
misleading.
The other two process capability indices, first used by the Japanese, are C pl
and C pu . These indices are related to the lower specification limit and upper specification
limit, respectively, and are defined as follows:
C
pl
=
m LSL
3 s
(19.64)
Part IV.B.5
C
pu =
The estimates of C pl and C pu are given by
USL m
. (19.65)
3s
Cˆ
Cˆ
pl
=
pu =
X LSL
3s ˆ
USL X
.
3s ˆ
(19.66)
(19.67)
To illustrate the computation of Ĉ pl and Ĉ pu we use the information in Examples
19.12 and 19.13.